Proceedings of the Foundations for Interstellar Studies Workshop

New York City, 13 – 15 June 2017

Edited by Kelvin F. Long

Organised by the Institute for Interstellar Studies (USA) and City Tech City University New York

Copyright Statement © 2017 The papers shown in this document remain the copyright property of the individual authors and nobody may use them in other published material without those authors permission.

2 Preface This document contains the written proceedings for the Foundations of Interstellar Studies workshop that took place in New York 13-15 June 2015. This was a scientific technical meeting organised between the Institute for Interstellar Studies (a US based not-for-profit) and City University New York. The event was also sponsored by Stellar Engines Ltd and the Breakthrough Initiatives.

Post-workshop, a total of eighteen papers were written up and submitted to the Journal of the British Interplanetary Society. This includes in volume 71 of the journal, published during 2018 as special interstellar studies red covers which included:  First Step on the Interstellar Journey: The Solar Gravity Lens Focus, L. Friedman et al.  Experimental Simulation of Dust Impacts at Starflight Velocities, A. J. Higgins.  Plasma Dynamics in Firefly’s Z-Pinch Fusion Engine, R. M. Freeland.  Gram-Scale Nano-Spacecraft Entry into Star Systems, A. A. Jackson.  The Interstellar Fusion Fuel Resource Base of Our Solar System, R. G. Kennedy.  Tests of Fundamental Physics in Interstellar Flight, R. Kezerashvili.  Effects of Enhanced Graphene Reflection on the Performance of Sun-Launched Interstellar Arks, G. L. Matloff.  Heat Transfer in Fusion Starship, Radiation Shielding Systems, Michel Lamontagne.  Solar System Escape Mission with Solar Sail Spacecraft within a Framework of Post-Newtonian Gravitational Theory, Olga L Starinova and Irina V Gorbunova1. The organisers of the Foundations of Interstellar Studies workshop waited for some time so that the papers could be published in the journal first, but due to the long duration of submission to publish time, we decided to move ahead and show the papers in their original form as submitted to the journal in these official proceedings. This document therefore represents a scientific record of this meeting.

In these proceedings, we have attempted to style all of the papers for similar consistency where possible, whilst not taking away from the format intentions of the authors. In addition, not all of the presenting authors at the workshop decided to submit a paper post-meeting, so we have included just their abstract. Finally, some of the presenters were last minute inclusions in the workshop, and for those we did not even have an abstract, although they do have a presence in these proceedings.

The proceedings represent the papers presented over the three days of the meeting in three sessions. This included on the themes of (1) Energetic Reactions Engines (2) Sails and Beams (3) Breakthrough Propulsion. These are quite broad areas. During later workshop meetings, we would hope to narrow some of these subjects to more specific questions so as to facilitate more progress.

We hope that the papers in these proceedings serve to education, inspire and move the field of interstellar studies forward so that as the progress in science matures, so too will the possibility of achieving the ultimate vision; sending spacecraft to other star systems. 1st March 2019

1 This paper was selected and scheduled for the June 2017 meeting, however the authors were not able to attend and the paper was never presented. However, the authors later submitted the paper to JBIS anyway and it was later published (volume 71, issue 12, December 2018). Although it does not appear in these proceedings of the meeting, it is mentioned here. 3 Contents

Page

Participating Institutions 6

Welcome from the Chairman at Event 7

Introduction 8

Session 1: Energetic Reaction Engines 9

1. The Fusion Fuel Resource Based of our Solar System, Robert G Kennedy III 10

2. Heat Transfer in Fusion Starship Radiation Shielding Systems, Michel Lamontagne 22

3. Plasma Dynamics in Firefly’s Z-Pinch Fusion Engine, Robert Freeland 35

4. Continuous Electrode Inertial Electrostatic Confinement Fusion, Raymond J Sedwick, 46 Andrew M Chap and Nathan M Schilling

5. Direct Fusion Drive for Interstellar Exploration, Samuel Cohen, C Swanson, N 56 McGreivy et al,

6. High Beta Cusp Confinement: A Path to Compact Fusion, Regina Sullivan 76

7. Positron Propulsion for Interplanetary and Interstellar Travel, Ryan Weed 77

8. Combined Thermal Desorption and Electrical Propulsion of Sailcraft using Space 87 Environmental Effect, Elena Ancona and Roman Ya Kezerashvili

Session 2: Sails and Beams 89

1. Solar Sail Propulsion: A Roadmap from Today’s Technology to Interstellar Sailships, 90 Edward E Montgomery and Les Johnson

2. Enabling the First Generation of Interstellar Missions, Philip M Lubin 91

3. The Andromeda Study: A Femto-Spacecraft Mission to Alpha Centauri, Andreas M 93 Hein et, Kelvin F Long, Dan Fries et al.,

4. Reflective Control Devices for Attitude Control of Solar Sails, Jeremy Munday 139

5. Effects of Enhanced Graphene Reflection on Performance of Sun-Launched 141 Interstellar Arks, Gregory L Matloff

6. Gram-Scale Nano-Spacecraft Entry into Star Systems, A. A Jackson 145

4 7. Rigid Light Sail Dynamics and Control for Launch and Acceleration Using Controlled 153 Optical Metamaterials, Eric T Malroy

8. The Prediction of Particle Bombardment Interaction Physics due to Ions, Electrons 154 and Dust in the Interstellar Medium on a Gram-Scale Interstellar Probe, Kelvin F Long

9. Experimental Simulation of Dust Impacts at Starflight Velocities, Andrew J Higgins 170

Session 3: Breakthrough Propulsion 184

1. Pilot Wave Model for Impulsive Thrust from RF Test Device Measured in Vacuum, 185 Harold G White, James Lawrence, Andre Sylvester et al.,

2. Mach Effect Gravitational Assist Drive, Heidi Fearn, J. J. A. Rodal and J. F. Woodward 197

3. Entanglement and Chameleon Acceleration, Glen A Robertson 217

4. Tests of Fundamental Physics in Interstellar Flight, Roman Ya Kezerashvili 240

5. Breakthrough Propulsion Capability Development Strategy, Ron Litchford 248

6. Self-Sustained Traversable Wormholes and Casimir Energy, Remo Garattini 249

7. Human Exploration of the Solar System as a Precursor to Interstellar Travel: Outlook 260 and Realities, Ralph L McNutt Jr

8. The Equivalence of Internal and External Energy Source Interpretations of the 262 Casimir Effect and their Implications for Interstellar Travel, Robert L DeBiase

9. First Stop on the Interstellar Journey: The Solar Gravity Lens Focus, Louis Friedman 278 and Slava G. Turyshev

Poster Presentations

1. Mach Effects for In-Space Propulsion: An Interstellar Mission, Heidi Fearn et al 286

2. Continuous Electrode Inertial Electrostatic Confinement Fusion, Raymond Sedwick 287 et al

3. A Bussard Ramjet with Twist and Flare, Pete N Ness 288

4. Fostering Breakthroughs in Interstellar Propulsion, John G Hartley 289

5. Reflective Control Devices for Attitude Control of Solar Sails, Jeremy N Munday et al 290

6. The Equivalence of Internal and External Energy Source Interpretations of the 291 Casimir Effect, Robert L DeBiase

5 Participating Institutions

The following organisations and institutions were represented at the meeting or were involved in the meeting such as through sponsorship. Their participation is acknowledged here.

 Breakthrough Initiatives, USA  British Interplanetary Society, UK  California Institute of Technology, USA  California State University Fullerton, USA  City York City College of Technology, USA  Harvard Club of New York City, USA  Harvard University, USA  Icarus Interstellar, USA  Initiative for Interstellar Studies, UK  Institute for Interstellar Studies, USA  GA Research LLC, USA  Johns Hopkins University, USA  Lockheed Martin Skunk Works, USA  Lunar and Planetary Institute, USA  McGill University, Canada  MontTech LLC, USA  NASA Headquarters, USA  NASA Johnson Space Center, USA  Positron Dynamics Inc, USA  Princeton Plasma Physics Laboratory, USA  Samara National Research University, USA  Stellar Engines Ltd, UK  Tennessee Valley Interstellar Workshop, USA  Texas A&M University, USA  The Planetary Society, USA  University of Bergamo, Italy  University California Santa Barbara, USA  University of Maryland, USA

6 Welcome from the Chairman at Event

Dear Participants,

Welcome to the Foundations of Interstellar Studies workshop on Interstellar flight at City University New York. This event has been a joint collaboration between City Tech and the Institute for Interstellar Studies. Over the next few days you will hear many interesting physics and engineering talks which are relevant to the challenges of interstellar travel. Our goal, is to facilitate interactions through informal conversations and bring people together to discuss current problems in the hope that some solutions can be realized, or future research directions planned. The nearest star system is the Centauri A/B and Proxima Centauri system. Alpha Centauri A, also known as Rigil Kentaurus, is the primary member of the binary system that is around ten percent larger and more luminous than the Sun. Alpha Centauri B is its companion star, smaller and less luminous than the Sun with a mass ten percent less than the Sun. Proxima Centauri, is a small main sequence star, with a mass of around an eighth the mass of the Sun. These make up our closes star system that in the future we may be able to visit using technologies not yet invented. Since 1988 we have discovered over 3,000 exoplanets in over 2,700 planetary systems. This has been mainly due to the success of programs like the Kepler Space Telescope using techniques such as the radial velocity and transit methods. Now that we know there are many star systems we could visit, this opens up the possibility of life existing there too. The only way to find out, is to build robotic spacecraft and send them there to conduct in-situ reconnaissance. Then, sometime later, human exploration and colony ships will likely follow. In the pursuit of this we will surely make many discoveries, but also ensure the survival of our species as we diffuse through the galaxy. The technologies we create, are also likely to have a transformative effect on human society here on Earth. This is an inspiring goal for the future of human kind. The discussions that we have over the next few days at City Tech will help towards planning for this future, where the reach of human kind extends outside of our Solar System, and around the worlds of other stars. The papers from this workshop will be submitted as a set of proceedings to the venerable Journal of the British Interplanetary Society. This is an exciting adventure, and we are on this journey towards the stars together. We extend to you a warm welcome and good luck in the research that follows this innovative meeting.

Co-Chairman,

Kelvin F. Long BEng Msc FBIS CPhys

Professor Roman Kezerashvili Ph.D D.Sc Executive Director, Initiative for Interstellar Studies (UK)

Professor of Physics Chairman, Institute for Interstellar Studies (USA)

Chairman Physics Department

The City University of New York

7 Introduction For century’s human kind has looked towards the stars in wonder at how many there is, how they were created, and what powers them. Today, we have a better understanding for the answer to these questions, although the question of whether there is life or intelligent life around such systems still remains unknown to our scientific methods of enquiry. Yet, as we set out on the early part of the 21st Century, we are in a unique position with the understanding of the Universe that we have arrived at today. With this has also arisen the speculative possibility that one day we may build ships and just like Columbus setting out across the Atlantic in search of the New World, our ships may set out across the vastness of space in search of new planets for which we can call our homes.

Some of the early philosophical considerations about the possibility of interstellar travel can be found in the works of science fiction, and in the 20th century authors like Arthur C Clarke, Isaac Asimov and Robert Heinlein inspired our imaginations with a plethora of possibilities. Some of these authors were also scientists and so their speculative ideas were often based on what may be one day possible. This also includes authors like Robert Forward, Gregory Matloff, Stephen Baxter and Larry Niven. Eventually, their efforts caught the attention of the wider scientifically minded population, and from this began to emerge actual ideas about how we may one day cross the great sea of suns.

Some of these ideas utilise energetic fusion energy, the same energy that powers stars. Others suggest we can annihilate a matter and antimatter particle together to produce much more efficient reactions, and also go further. Some imagined that maybe we don’t need to carry any fuel, but instead we can mind the hydrogen of the interstellar medium instead, in a kind of interstellar ramjet. The idea of not carrying any fuel was also an attractive way to get around the famous Tsiolkovsky rocket equation and its mass penalties. This led to innovative ideas like microwave and optical laser beaming, and others like particle beaming. Some went even further and considered that the revolutions in physics that occurred at the start of the 20th century in the discoveries of special and general theory of relativity and quantum mechanics, may give rise to faster than like warp drives or vacuum energy drives. All of these may one day be possible, but for now they are just clever ideas which like the fundamental technological maturity required when applying them to an actual mission.

For this reason, scientific conferences and workshop are an essential part of bringing people together to discuss ideas, solutions, inventions and conjectures, no matter how speculative they may be. For it is only under the scrutiny and debate of other like-minded people that such theoretical ideas can be matured, or shot-down. Indeed, the ultimate test is experimentation itself, but most of the field is far from this point.

The Foundation of Interstellar Studies workshop was set up to garner scientific technical progress on problems relating to interstellar studies but with a focus on specifically proposed solutions, rather than just a reinstatement of the problem, and authors making proposals for solutions or how to attack existing problems is a requirement for presentation.

Much of the format for these meetings was taking from the famous Shetland Island and Solvay on physics meetings of the last century. Some key elements of this included close association by key workers, concentrations on given topics, absence of distracting interests and providing an opportunity for free intimate discussions within a small group. It is early days, and whilst we may not achieve this model in the first meeting, in time we hope to do so in subsequent meetings, and thereby demonstrate real progress towards the goal of achieving interstellar flight. These proceedings, represents the first steps in this direction.

8 Session 1: Energetic Reactions Engines

The following is a report from the Energetic Reaction Engines session. The Chairman for this session was Kelvin F. Long. The purpose of this session was to bring together papers which discussed any engines which involved the ejection of matter or energy rearwards from a vehicle for thrust generation, e.g. electric, plasma, nuclear thermal, fission, fission-fragment, fusion, antimatter catalysed fusion, antimatter. Specific problems identified for possible focus were to include:

(1) Credible fusion ignition physics models for high gain (2) Practical methods for achieving antimatter catalysed fusion (3) Mitigation and shielding methods for large radiation fluxes from energetic engines (4) The design of large magnetic fields for use in space transportation (5) Efficient acquisition and mining methods for large quantities of fuels.

9 THE FUSION FUEL RESOURCE BASE OF OUR SOLAR SYSTEM

R.G. Kennedy1, 2. 1,2 Institute for Interstellar Studies-US, 112 Mason Lane, Oak Ridge, Tennessee 37830, USA. Email: [email protected] [email protected]

If a self-propelled ship is going to get to another star in less than many millennia, humanity will need vast quantities of highly energetic fusion fuels. Even fission will not do the job. However, the ten lightest fusion chain reactions that the human race knows about (some of which have sub-chains, and five of which involve hydrogen) have major, engineering, energetics or logistics liabilities. In 1985’s Interstellar Migration and the Human Experience ed. by Finney & Jones, William K. Hartman presented "Resource Base of the Solar System". In this work we repeat his approach 32 years later in order to estimate the human race's patrimony of lazy fusion fuels, and the total number of missions that could fly. Keywords: Elemental Abundance, Aneutronic Fusion, Fusion Fuels, Resource Base, Solar System

1. Background Review & Analysis Nothing really big will happen in space without an industrial base (material and energy) behind it. The energy required for anything interstellar is literally astronomical. A kg dropped from LEO has 10X its weight in TNT; at 3% of c, it has energy equal to the Hiroshima bomb, at 90% of c, it has the energy of Ivy MIKE. The material demands are equally great. Humanity will not step beyond Sol system, even via machines, without an extremely wealthy and extremely powerful industrial space-faring culture behind it.

1.1 Three Classes of Interstellar Missions. Three basic classes of one-way interstellar missions based on known physics, each separated from the next by roughly six orders of magnitude in mass, have been described in the literature.

Class One: "Starchip" (~3 g), "Starwisp" (103 g), and "Dragonfly" (106-107 g), all robotic probes boosted once by beamed microwave or laser power from Earth or the inner solar system for a one-way >0.05-0.10c flyby of a single target system.

Class Two: Firefly and Daedalus, fully functional vessels crewed either by robots (kiloton-range, 109-1011 g) or living beings (megaton-range), self-propelled by fusion or antimatter, for <0.10c flight for possibly multiple flybys or sub-package drop-off at multiple target stars along the way.

Class Three: Worldships (gigaton-range, 1015-1017 g), generation ships self-propelled by fusion or antimatter, traveling at ~0.01c for rendezvous with a single target system.

While the first class of mission is within reach of a civilization limited to terrestrial resources in the next century or so, the latter two would be such enormous enterprises requiring literally astronomical amounts of energy and matter, that they could only be accomplished with off-world resources. Since the Industrial Revolution began 2 centuries ago, the economic growth rate has been about 3% per year, more or less. Applying the Rule of 72, that means a doubling period of 24 years, about 1 human generation. Assuming continued uninterrupted economic growth over the long term, and that we manage to get off-world in a big way with cheap access to space, I expect we would have the energetic and material resources to throw something significant at another star in about another two or three centuries. By “significant” I do not mean, “fast flyby at some fraction of c with a ‘Forward Swarm’ of chip sats”

10 1.2 Notional 160-Year Timeline for a Forward Swarm of Chipsats to Nearest Star? The most unexpected hence valuable outcome of the Space Solar Power working track at TVIW-2016 was the realization by the participants that, given the establishment of space-based solar power infrastructure in the next half-century, a 160-horizon for a robotic interstellar flyby mission of a star within 10 LY, for a mission- specific cost of 1011 dollars, is credible with known physics and reasonable extrapolation of power-beaming technologies. Right now, it is not clear how we would get a meaningful science return, but assuming that signaling capability is developed somehow, and working backwards from a certain political requirement, here’s a notional timeline: July 4, 2176 picture arrives @home (from nearest neighbors up to 10 LY) for America’s Quadricentennial 2166 Swarm of wafersat(s) arrives at distant star(s); acquires imagery, begins transmission 2066 “Be ready to send” (launch Forward Swarm up to 10%c up to 10 LY) 2030 commence national SPS program building on-orbit power grid with spare capacity 2021 commence Decadal Survey-like process for Interstellar missions 2020? dinner with the President-Elect?

1.3 “Significant” Defined As cool as that would be, no, by “significant” we mean something much bigger and more capable, with enough delta-vee to slow down and rendezvous with the target system, perform open-ended activity and send back significant science data for a long time. Such a technical capability would have to mass at least a kilotonne, with an initial mass one to two orders of magnitude greater in order to deliver that package to the destination. Something on the order of the fusion-propelled Daedalus or Firefly concepts. It is reasonable to assume that at some point the human race will figure out how to contain and control stable self-sustaining fusion reactions using some combination of electric and magnetic fields. So we can take that as a given. Taking the published figures at face value, with today’s technology, a “one-off” unmanned Firefly probe (24,000-tonne initial 2-stage mass in LEO, 90% deuterium fuel) would cost on the order of ten trillion dollars, about the GDP of the United States. The figure is dominated by the cost of the building the probe. The cost of the bigger, older, simpler Daedalus (150,000-tonne initial mass in LEO, 2 stages, 99% deuterium/helium-3 fuel) would be on the rough order of several hundred trillion dollars, equivalent to total global product for five years. The figure is dominated by the cost of the He-3 fuel (millions of dollars per kg). Since only 30 kg of He-3 exist in human hands at the moment, we won’t discuss Daedalus further.

1.4 What Compelling Reason? What would justify such a costly mission using irreplaceable consumables (the boron fuel discussed later in this paper)? It is claimed that responding to a First Contact would certainly justify that expense. Here’s why: The most significant and unexpected hence valuable outcome of the “C-for-Commo” working track at Tennessee Valley Interstellar Workshop (TVIW) 2014 was the realization by the participants that detection and interpretation of CETI signals are major problems that cannot wait until First Contact to be dealt with. Of these, interpretation is much harder. By pure coincidence, this finding was almost identical to the consensus of the “Communicating across the Cosmos” conference conducted by the Search for Extraterrestrial Intelligence (SETI) Institute on the other side of the USA at the same time, unbeknownst to Track C’s participants. As pointed out by this author and other co-authors (Sam Lightfoot, Eric Hughes, Paul Shuch) in a JBIS paper a couple of years ago (see “Communications, SETI, and Strategies”, JBIS 68, 2015): Thus, what must happen after a detection is to mount a physical mission to Go Out There and put sensors on target in order to observe the embodiment or somatic nature of the intelligence being detected. Without context, seeing it, interacting with it, and getting more knowledge in near-real time, we will have less-than-zero hope of anything approaching meaning, much less engaging in dialogue. If the goal is dialogue, we must interact, and it must be over less-than-interstellar distances (no latency). First Contact (info) leads to First Contact (physical). Note that we are not explicitly saying this ship must have a crew, or at least, not a living breathing crew that would require a massive life-support system or a perfectly efficient closed-cycle ecology. It’s one thing to set off

11 on a multi-generation worldship from which your remote descendants would found a new world around another sun. It is difficult to imagine a multi-generational trip to answer an intellectual question, or just to answer the mail (Though a religious order might do just that.) Absent suspended animation which does not exist yet, a trip with the original living breathing investigators would have to be limited to a human’s working lifetime, 50-70 years, and still allow time for productive work on the far end. The trouble is, there are not that many stars in such a small travel radius of less than 10 LY. Because of “regression to the mean”, even if one began with the most brilliant scientists and linguists, one could not count on the children from such a small number of parents, to be as smart. Thanks to the Law of Large Numbers, the best brains would always be back on Earth, but out of real-time touch with their subject that is necessary for this particular kind of mission.

Table 1. list of 10 target star systems within 10 LY Spectral.type Distance Age Joint probability Target name habitable planet M5.5 4.25 LY 4.9 GY “earth-like” in Proxima Centauri G2 4.37 LY Goldilocks α Centauri A K1 4.4 GY detected! α Centauri B 0 super-earths 10.7% [Dole62] Barnard’s Star aka V2500 Ophiuchi M4 5.98 LY 7-12 GY 0 > neptunian Luhman 16 A (binary brown dwarf system) L7.5 ?? 6.5 LY subjovian?? Luhman 16 B T0.5 Wolf 359 M6.5 7.86 LY 0.1-0.4 GY 0 > neptunian Lalande 21185 M2 8.31 LY 5 – 10 GY 0 > jovian Sirius A (binary blue system) A1 0.2-0.3 GY 8.60 LY 0 > superjovian Sirius B dwarf A2 Luyten 726-8 A (binary red dwarf system) M5.5 ?? 8.73 LY ?? Luyten 726-8 B aka UV Ceti M6 Ross 154 aka V1216 Sagittarii M3.5 9.60 LY ~1 GY ?? Ross 248 aka HH Andromedae M6 10.32 LY ?? 0? K2 10.52 LY 0.4-0.8 GY 1 jovian, 3.3% ε Eridani [Dole62]

Whether the living investigators and funders are on-board or back at home, time is likewise as precious as throw-weight. Unlike interplanetary freight in the near future or worldship travel in the far future, an interstellar probe, especially an urgent mission that involves a possible First Contact, would be under boost the entire way, either accelerating or decelerating. The velocity profile would be all up or all down—no cruising. Anyway, the question of living crew in the second class of mission is as moot as Daedalus—a kilotonne vessel is far too small to support life for that many decades. Therefore the “crew” would have to be a very advanced machine, or some sort of organic-metallic hybrid, i.e. a cyborg. According to the roboticist Hans Moravec, robots are our “mind children” anyway. Cite Mind Children. See also Proceedings of “Practical Robotic Interstellar Flight: Are We Ready?” 29 Aug – 01 Sep 1994, New York University, New York. Certainly, driverless vehicles seem to be arriving much faster than a skeptical roboticist, as this author predicted 30 years ago.

2. Fusion

2.1 Candidate Fusion Cycles Getting a self-propelled object to another star in under a millennium calls for Isp on the order of a million seconds. This is far beyond even fission; only fusion (and even more energetic antimatter) will do. Fusion is all about binding energy – small but weakly-bound nuclei such as deuterons combine into more tightly-bound nuclei, like alpha particles (He-4), which is very tightly bound indeed. The difference shows up as energy, usually

12 in the form of very fast-moving reaction products. The most troublesome one of these is the charge-less fast neutron.

Figure 1. Average Binding Energy for Nucleons

In addition to the proton-proton reaction going on inside our own star, there are ten other light fusion reactions that we know about. Some of these have subsequent chains; others are useless for interstellar flight and can be quickly eliminated. We will look at each candidate in turn, but first a word about the neutron.

2.2 Useless Neutrons and the Rocket Equation At Douglas Aircraft, we had a rule of thumb that every excess pound of weight was worth $150 (in early 1980s dollars, say $400-500 today) in terms the net present value of the excess fuel consumed over the 25-year service life of the aircraft. That opportunity cost of $150 per pound is worth more than virtually every other thing except precious metals. In the conventional world of chemical rockets into LEO and the inner solar system, in which the specific impulse (Isp) of typical launchers ranges from 200-500 seconds, that opportunity cost climbs sharply to 100-1000X as much as in aviation (i.e., $10,000 - $100,000 per kg). Choices about the payload of a chemically-fueled scientific mission to the outer solar system can easily have an opportunity cost measured in millions of dollars per kg, which would already make that more valuable than any precious metal on Earth, exceeded in specific value only by certain famous gemstones.

Now remember that Isp is in the exponent of the Rocket Equation, and then imagine the opportunity cost of wasted mass in a craft going 10 percent of c, which is 100,000 times faster than a passenger jet, for a hundred year journey at least. So we come to the neutron problem. In every mission that slows down at the target instead of just flying fast by it, fuel for deceleration becomes the predominant component of the “payload”, which is a second stage sufficient for rendezvous. The trouble with most of the fusion reactions examined in some detail below, is that neutrons are produced in similar numbers and proportion to other desirable reaction products like protons and alpha particles. Since neutrons are both fast and lacking in charge, they cannot be manipulated or controlled,

13 and radiate outward isotropically. A majority of the precious energy of the deceleration fuel dearly-bought across light-years, is thrown away, carried off by a useless neutron. This is especially bad when there is a large disparity in mass between the products. Since momentum is conserved, having a light product (e.g., a neutron) and a heavy product (e.g., an alpha particle) with equal momenta means that the neutron goes away with X times as much velocity, hence that particle escapes with X /(X+1) of all the energy. While a neutron reflector (say a sheet of lightweight metal like beryllium backed by a lightweight hydrogenous polymer polyethylene) at the forward end of the reactor could convert some of this flux to net forward momentum, much of the neutron’s impact energy would convert to useless heat. In any case, it is obvious that a reflector has geometric limits—subtend at most one-tenth of a unit sphere centered on the reactor. This means at most, five percent of the wasted energy could be transformed into momentum by the mirror. Most of the wasted energy stays wasted. Though they would help, and should be used in interplanetary travel, mirrors are not the answer to the neutron problem in interstellar flight. In 20 minutes, half of the free neutrons decay into proton by emitting electrons. It’s too bad that fast neutrons can’t be persuaded to stick around long enough for that to happen inside containment—they’d be much more useful and easier to handle. So on this basis we can see two basic sub-types of fusion-fueled craft, and missions.

2.3 Fusion Reactions Considered. The most common fusion reaction is the complicated multistep one going on inside our Sun now. In proton+proton fusion, stable helium-4 is generated one of four possible ways, but the overall result is:

This is the hottest reaction, hence hardest. So, ubiquitous as it is, we do not know how to replicate it artificially. p-p burning’s reaction density (10 watts per cubic meter, versus a billion times as much in a high-power fission reactor) as suggested by this quote: “The half-life of a proton in the core of the Sun before it is involved in a successful proton-proton fusion is estimated to be about one billion years, even at the extreme pressures and temperatures found there.” is horribly anemic and utterly unsuitable for flight, or even stationary power generation. tritium+tritium fusion, being the coolest temperature of all fusion reactions, is the one we first mastered at small scale, in the form of “boosting” the explosive yield of fission bombs with scads of fast neutrons:

Followed by deuterium+tritium fusion. Having the next lowest temperature of all fusion reactions, it should be the next easiest, and indeed it is, for it is the one we first mastered at large scale, in the form of a thermonuclear bomb

But T-T and D-T burning have three major drawbacks— (1) engineering, right now we can only make bombs with this one; a breakeven, steady-state reaction has not been achieved— 2 (2) efficiency, about /3 to ¾ of the total yield, ~10 to 14 MeV, is carried off by a useless fast neutron. Since they are charge-less, it is very difficult to manipulate or harness neutrons. (3) logistics, the tritium has a half-life of only 12 years. Even for bombs, it has to be bred and replaced continually. For a decades-long voyage, not to mention centuries-long, tritium is a totally unsuitable fuel.

For reason (3), we also eliminate helium-3+tritium fusion, with two outcomes of similar probability:

14 Due to a somewhat higher coulomb barrier than either D-D or D-T, this reaction requires higher temperatures, but while not completely aneutronic, it has an admirably low proportion of useless neutrons in its two possible branches. However, in addition to tritium’s short half-life, unfortunately, nature has not been generous with us in re: He-3. The total supply of He-3 on Earth is extremely limited. deuterium+helium-3 fusion is the one that “back to the moon” advocates always talk about:

Both reaction products can be ionized, therefore are harness-able in a reaction drive. But no one actually knows how to burn D-He3, and there are side reactions in which the deuterons react with each other instead of the helium-3, thereby producing useless neutrons. However, that’s just an engineering problem. The main drawback is logistics: where are the necessary kilotonnes of helium-3 per mission going to come from? Although He-3 is a stable nuclide, which is both primordial and also continually produced in the sun therefore present in the solar 1 wind, its abundance is /10,000 that of He-4. Being “noble”, it is immune to natural chemical processes that concentrate other elements for our use and convenience. Being a very light gas, it almost immediately escape the Earth when released. Therefore, its terrestrial abundance and its practical availability is still extremely low. At present only ~30 kg of He-3 is in human hands.

Figure 2. Abundance as a Function of Atomic Number helium-3+lithium-6 fusion yields two alphas and a very energetic proton, which would be a very useful for a reaction drive:

In addition to hydrogen and helium, lithium is the only other primordial element made in the Big Bang (primordial nucleosynthesis). 13.7 GYa, the BB stopped after 20 minutes, at lithium, A=7. In the cosmos, the latter three elements are about as rare as noble metals. Like boron, lithium is not made in stellar nucleosynthesis, nor in supernovae (neither S-process nor R-process). Stars tend to consume whatever lithium, beryllium, and boron they are born with. [4] Some lithium is produced by spallation of carbon and oxygen atoms struck by galactic cosmic rays (GCR, which are bare energetic nuclei stripped of all their electrons) in deep space, but the macroscopic flux of lithium into the solar system is miniscule. Lithium is an important, valuable metal used in electric vehicles and the renewable energy sector. Like boron below, its abundance in the Earth’s crust due to its light weight belies its extreme rarity in the cosmos. Like boron, lithium is primarily found in lakebeds as evaporite deposits from hydrothermal activity; mining these extracts about 100,000 tonnes in the form of lithium carbonate per year. Global reserves at current prices of $10-20 per kg are >10,000,000 tonnes, enough for about a century at current rates of consumption. Li-7 is the most common isotope at 92.5%; the fusible isotope Li-6 constitutes less than 8% of all lithium, which practically

15 puts this fuel into the same category of cosmic abundance as boron-11. Mass-separation with just one amu of difference is difficult and relies on toxic processes (such as mercury) which would increase the delivered cost of the fuel considerably. Laser separation would ameliorate the toxicity issues and other complications at the expense of electricity.

However, the same fundamental disadvantage of He-3 scarcity applies to any reaction that uses it, including this one. helium-3+helium-3 fusion, aneutronic, produces an alpha particle and two energetic protons:

An energetic proton is the perfect propellant—its ionization and resulting high charge-to-mass ratio means it can be readily manipulated with electrostatic fields, and it have the lowest possible mass (1 amu) which approximates the theoretical maximum performance for any physical exhaust. However, due to a much higher coulomb barrier (helium isotopes have twice the charge compared to hydrogen isotopes), this reaction requires much higher temperatures than people know how to stably create right now. Also, this reaction just doubles down on the scarcity of the reactant. So all-He-3 burning is likewise eliminated as a candidate reaction for interstellar propulsion.

Next is deuterium+deuterium fusion, with two flavors of equal probability:

One problem with D-D burning is that neutron coming off the second branch, wasting about 1/3 of the total energy right off the bat. In addition, the tritium and helium-3 are produced in equal numbers since the branches have equal probability, and will react with each other since the reactants and the products are all in the same soup of energetic particles. See the helium-3+tritium fusion reaction above. The more popular secondary branch produces a fast neutron right away, losing a good fraction of the energy, while the less popular secondary branch produces an alpha and a high-energy deuteron, taking us back to the beginning, albeit at a lesser concentration. The limit of this recursive process is that perhaps half the total energy is lost as fast neutrons. However, for interplanetary traffic in the future, with pit stops and ample resources of deuterium virtually everywhere in the solar system, the neutron penalty might be acceptable. deuterium+lithium-6 fusion (LiD is a solid at STP) was also first used in thermonuclear development, in the first “dry” weaponized design. This reaction has the most diverse array of branches, yielding the most complicated soup of products:

Of principal interest is the first branch, yielding two very high energy alphas, making it ideal for a reaction drive. The second and fourth branches are burdened with free neutrons. This is especially bad in the fourth branch due to the disparity in mass between the products (7:1). Since momentum is conserved, having a light product and a heavy product with equal momenta means that in this case, the neutron goes away with 7 times as much 7 velocity, hence that particle escapes with /8 of the energy. The third side branch yields products that appear similar to the reactants in the next reaction below. Li-7’s presence with a proton on the right side of the equation (lower energy, higher entropy) suggests that it is

16 important for the rare Li-6 isotope to be separated from the common Li-7 with a high degree of purity. This bears further investigation. Historical note of interest: like its lighter sibling lithium-6, lithium-7 can also react with a neutron under the right circumstances. This unforeseen property of the Li-7 isotope was at the root of the runaway Castle BRAVO incident of 1954, which ran away to 15 megatons instead of the planned 6 (largest blast ever conducted by the United States, albeit unintentionally). While it may be physically possible to continually “breed” nuclear fuel enroute from stable precursors with slow “thermal” neutrons, as a practical engineering matter, producing thermal neutrons is fairly difficult. With current technology, the task requires massive hugely inefficient apparatus that is inconsistent with the harsh mass constraints on space travel, let alone an interstellar voyage. proton+lithium-6 fusion is a neutron-free reaction which yields helium-3 and a relatively low-energy alpha. This would appear to be more useful for synthesizing He-3. Again, the low relative abundance of the fusible isotope Li-6 (<8% of all lithium) which puts this fuel into the same practical abundance category as boron-11, while its difficult, toxic mass-separation makes the delivered cost of the fuel considerably higher than boron-11’s.

proton+boron-11 fusion is another neutron-free reaction yields three alpha particles and nothing else. While boron-11 would have a much higher Coulomb barrier than hydrogen (requiring about 10X higher temperature than a D-T reaction) a 500-keV proton can be readily manipulated in a beam for optimizing collisions.

All alphas mean high efficiency, and high potential for direct electricity generation (avoiding thermodynamic conversion losses) as well as a reaction drive. Being a solid, the fuel is orders of magnitude more compact than liquid deuterium, which would make the ship a lot smaller, and fuel storage much simpler. Boron-11 is the most common isotope, 80%. Trouble is, its abundance in the solar system appears to be down with rare earths, another logistics problem. The Big Bang stopped making elements at lithium, A=7. Like lithium, boron is not made in stellar nucleosynthesis, nor in supernovae (neither S-process nor R-process). Furthermore, stars tend to consume whatever lithium, beryllium, and boron they are born with. [4] Therefore there is no boron in the solar wind, neither ours nor anybody else’s. Since boron was made neither in the Big Bang nor stellar processes, the reader can see why the cosmic abundance of boron is lower than lithium. Like lithium, boron’s abundance in the Earth’s crust due to its light weight belies its extreme rarity in the cosmos, about as rare as some noble metals. Some boron is produced by GCR spallation of C and O atoms in deep space, an astrophysics puzzle only solved late in the 1990s at CERN which explains about a third of the boron we see. GCRs themselves are rich in Li/Be/B, say 25% or one-in-four versus the cosmic abundance of one-in-a-million. Boron may also be produced when carbon and oxygen nuclei in flight from supernovae crash into hydrogen and helium in the interstellar medium. Neutrino spallation of carbon-12 could be another source of boron-11. But macroscopically speaking, the boron flux into the solar system is still negligible. Despite its extreme rarity, boron is an inexpensive material with hundreds of industrial uses today, as well as other surprisingly prosaic uses, like laundry detergent. Like lithium, boron is primarily found in lakebeds as evaporite deposits from hydrothermal activity. Far more boron is mined than lithium, about 6,000,000 tonnes 3 per year, as hundreds of compounds but mostly borates, B2O , which is mostly oxygen by weight. The pure boron-11 component of this flow is 1-2 megatons per year. Global reserves at the current price of $1 per kg exceed a gigatonne, enough for two centuries at current rates of consumption. About 80% of all boron is the fusible isotope boron-11, so at the current price, that reserve is about 300 megatonnes. Boron is known to have “refractory” contamination issues with carbon, inverse of the boron contamination problem in nuclear-grade graphite that plagued Manhattan Project-era engineers. Boron-10 is separated from boron-11 in the nuclear industry because it is such a good absorber of neutrons. , Confusingly for our purpose, the remaining boron-11 is referred to as “depleted”.

17 3. Boron

3.1 Boron Inventory of the Solar System Having identified a promising candidate, using boron as a proxy for “interstellar-grade fusion fuel”, we will now estimate the boron inventory of the solar system.

Sun: There is no boron in the solar wind. Mercury: I have not reviewed results from MESSENGER, but it seems to this author that the innermost planet, at R=0.4 AU, is unlikely to possess boron in useful concentrations where only the heaviest elements could condense from the protoplanetary disk. Venus: Some cosmic catastrophe resurfaced Venus and made the entire planet spin backward. Whatever did this likely stripped off light elements, depleting it of volatiles like water than can process boron to useful concentrations. Furthermore, the resurfacing churned the crust and mantle hundreds of km down, and it appears that tectonic activity, which might be a point source of new material that might contain light elements like boron, has stopped. Earth: The best candidate in the solar system to get boron at mine-able concentrations would seem to be right here on terra firma. Our world also has the steepest, albeit not the deepest, gravity well in the system. It has fully differentiated, so the lightest elements and refractories float, and hydrothermal processes have had four and a half gigayears to further render the stuff into soluble compounds and concentrate them. Mars: Boron has been found on Mars by the Curiosity rover. However, any tectonic and hydrothermal processes stopped there billions of years ago. So whatever’s on the surface is all there is.

If boron exists beyond the solar system’s “snow line” at all, it is likely to be either thoroughly mixed with the gas giants’ bulk, or the compounds that it likes to make with hydrogen have snowed out on the metallic hydrogen layers of the gas giants.

Belt and Jupiter. Any assemblage of ordinary material will pull itself into a sphere if R>100 km. It may be that water-ice worlds big enough (R>1000 km) to have melted and differentiated (Ceres, Ganymede, Callisto) may have concentrated boron compounds among their other metallic salts. Europa, which would otherwise be a good candidate, must be left alone until it is determined if life is there. (Note: this criterion may be applied to any prospecting mission to any water-ice-world). Io churns itself inside out so much that no compound could separate out.

Outer Moons & Plutoids. It would seem that a knowledge of cryogenic chemistry but it should be noted that the reaction rate chemistry is generally an exponential function of temperature. If so, after accreting, the outer moons and plutoids may not have stayed liquid long enough for chemistry to work. Even if liquid continues to exist at very deep layers in those bodies, there may not have been enough time since their formation for the sluggish reaction rates to concentrate the trace elements to industrially useful levels.

3.2 Estimating Number of Interstellar Missions Having identified a promising candidate, using boron as a proxy for “interstellar-grade fusion fuel”, we will now estimate the boron inventory of the solar system. We can see two broad classes of fusion-fueled craft, and missions, separated into two different fuel ecologies, Interplanetary and Interstellar. Interplanetary - the neutron penalty will be tolerable for D-D fusion will be sufficient for commerce around the solar system, with plenty of sources for raw material and place to re-fuel. Possible crossover exception: Because the neutron flux would convert to low-grade heat in a reactor that was big enough, the D-D cycle might also be useful for a worldship that does not get above 1% of c. Besides propulsion, a worldship has also substantial demands for space heat. Since for all practical purposes deuterium is unlimited in the Solar System, it will be sufficient to fuel interplanetary commerce and industry for the foreseeable future, as well as the first stages of

18 Class Two interstellar probes, and worldship drives in the far future. The possible number of trips would be very large. Interstellar – the neutron penalty is unaffordable for a high-speed interstellar probe, which despite the high mass fraction, will still be limited to just one start and one stop. The best candidate aneutronic reaction now known to us is fusing 500 keV protons with boron-11 plasma. Perhaps the first stage of an unmanned interstellar probe out of the solar system could be D-D and then dropped. But the deceleration stage to rendezvous with the target system will need every microsecond of Isp it can get. We cannot waste that precious mass of the second stage, so expensively launched, on producing useless neutrons that we mostly can’t manipulate. The second stage must be p-B. If all the boron-11 available to us at current low prices ~300,000,000 tonnes, were dedicated to this task, the human race would have enough fuel to launch a Firefly- class probe every other week for a millennium—30,000 flights. That seems more than sufficient to get a good look at the neighborhood. There is plenty of headroom in the price elasticity to make a much greater reserve available while still providing for local industrial consumption.

3.3 What If We Needed More Boron Than We Have? Perhaps we could make some boron the way Nature does, spallation of carbon and oxygen with galactic cosmic rays. The reader may recall that the USA once had to manufacture synthetic elements. Tritium is an essential component of thermonuclear weapons. Half of it decays into helium-3 in just 12.3 years, which is why it does not naturally occur on the surface of the Earth, and why it is utterly unsuitable for an interstellar fuel. Because the tritium at the heart of those tens of thousands of H-bombs had to be continually replaced, we synthesized it (via spallation also) at a time in a giant complex of production reactors at Savannah River (whose main purpose was to produce plutonium). [PICTURE] The program cost $2B a year a gram to run. Over the entire 33-year history of that program, 1955-1988, the USA made 225 kg of tritium, at a fully burdened delivered cost of $200- 300 million per kg. While we don’t have any tritium in our pockets (that I know of), here is something comparable: a transplutonium production rod that this author designed a generation ago, to go inside the heart of the (never built) 300-megawatt Advanced Neutron Source reactor. This little rod, and a few dozen others like it, get stuffed with plutonium and other actinides like curium and americium, to be cooked for three weeks in the most intense neutron flux on Earth. After than, 99.9% of the plute has split into useless (and dangerous) daughter products, but one part in a thousand manages to survive the long climb up the transmutation ladder to become californium-252, einsteinium-254, and fermium-257. This author is unaware of the current value today, but 25 years ago, DoE sold Cf-252 for 50 million dollars per gram. The price tag for an amount of fermium-257 that you could actually see would have to be expressed in scientific notation. Boron’s price inelasticity is not known to this author, but at the present level of $1/kg for unpurified un- separated boron, there appears to be plenty of headroom to increase supply if necessary using economic incentives rather than a crash transmutation program. However, the energy of spallative nucleosynthesis, up to 100 GeV/n, is near the top end of the most powerful accelerators on Earth (~1-10 TeV). For a proper interstellar probe, we’d need ten of kilotons of boron-11 (worth a few quadrillion dollars if it were all synthetic). It is difficult to imagine the wealth of a civilization that could do that, but several centuries to a millennium of uninterrupted compound growth could get us there. Applying the Rule of 72, three centuries of 3% real growth means a dozen doublings, which is a factor of 4096 which is a 300- quadrillion dollar economy. Perhaps they could afford making arbitrary quantities of synthetic elements on demand. We cannot.

Conclusions So where’s the resource base of the preferred interstellar fuel of the future? It’s here! [20 Mule Team] And unless we find a big lode somewhere else in Sol System, what we have on the surface of the Earth is about all

19 that we’ll ever have. It is our patrimony, a gift from the depths of interstellar space, and best used to return there.

Figures 3a & 3b.

• In the near term, boron’s price inelasticity is not known to this author, but at the present level of $1/kg for unpurified un-separated boron, there appears to be plenty of headroom to increase supply if necessary using economic incentives rather than a crash transmutation program. • If we go interstellar 2 or 3 centuries hence, you can be sure we won’t be washing dirty underwear in 20 Mule Team Borax anymore. Dishwater may become valuable • In the far future, we might imagine some sort of fuel rationing regime, either by pricing or government fiat, in which fuels like boron-11 are rationed or simply reserved for the most important missions, the interstellar ones. • Do other exotic light fusion reactions exist? Surely in this giant table, 2600 things taken 2 at a time, there must be undiscovered but possibly reactions. • Investigate further the burning of Li-6 with protons and other reaction with Li-7’s as well as sensitivity of these reactions to the purity of reactants. • Develop the field of ultra-cold chemistry, with liquid gas solvents such as H2, N2, CH4, NH3, etc. What sorts of differentiation and concentration processes could take place and on what industrially useful timescales? • Investigate boron-sulfur chemistry to inform the existence of boron on Io. Conjecture: If we ever meet someone’s worldship fueled with boron-11, we’ll know that they’re either very rich or desperate.

Acknowledgements The author would like to acknowledge David Bowman, Ph.D., who guided me with the nuclear physics. Among other claims to fame, he’s the discoverer of boron-17 (by virtue of making some), and my neighbor.

References [1] C. Sagan, ed., “Communications with Extraterrestrial Intelligence”, MIT Press, 1973. [2] W.K. Hartman, "The Resource Base in Our Solar System", in B.R. Finney and E.M. Jones (eds.), Interstellar Migration and the Human Experience (Proceedings of the Conference on Interstellar Migration held at Los Alamos in May 1983), Univ. of Calif. Press, Berkeley, p.26-41, 1985. [3] R. M. Freeland et al., "Firefly Icarus: An Unmanned Interstellar Probe using Z-Pinch Fusion Propulsion", JBIS, S68-S80, 2015. [4] B. Gordon, S. B. Haxel, and S. Mayfield, "Relative abundance of elements in the Earth's upper crust," U.S. Geological Survey; http://pubs.usgs.gov/fs/2002/fs087-02/ , 2002, retrieved 15 Mar 2017.

20 [5] E. Vangioni-Flam, M. Cassé, and J. Audouze, “Lithium-Beryllium-Boron: Origin and Evolution”, Institut d'Astrophysique de Paris, 98 bis Bd Arago 75014 Paris, astro-ph/9907171, June 1999. [6] Communicating Across the Cosmos: Summary of a Workshop on Interstellar Message Design, http://www.seti.org/weeky-lecture/communicating-across-cosmos-summary-workshop-interstellar-message- design, (accessed 14 May 2015). [7] S. Dole, Habitable Planets for Man, Blaisdell Publishing Company, 1964.

21 HEAT TRANSFER IN FUSION STARSHIP RADIATION SHIELDING SYSTEMS

Lamontagne, Michel Icarus Interstellar mlamontagne @icarusinterstellar.org

Fusion starship designs require radiation shielding from neutrons and X-rays created by the drive. Even nominally aneutronic fusion reactions, such as Deuterium+He3, produce neutron fluxes through side reactions that may create large cooling requirements in drive structural elements. This paper aims to quantify these emissions and describe the heat transfer systems required to handle these heat loads. Neutrons and X-ray emissions are established for three fusion drive designs, Daedalus [1], a Daedalus variant named l’Espérance and Icarus Firefly [2]. From nearly zero for Daedalus, they rise to 220 GW for l’Espérance and to 8400 GW for Firefly. The geometric structure of the vehicles is analyzed in order to determine the impingement rate for the neutron and X-Ray radiation. The open nozzle proposed by Miernik [3] is used as an example of design, allowing up to 97% of the radiation to escape. Firefly, the most severely heat loaded design, requires 260 GW of cooling. Two methods are compared to remove the heat to the radiators. Temperature change using Q=mf×cp×Δt for gas and liquid flows, and Q=mf×Ve for phase change. The fluid paths are determined and pump and compressor power requirements are calculated. Then radiator areas and masses are determined. The physical arrangements of radiators are examined in regards to view factors, radiator placement and the influence of these on radiative power. Phase change in liquid metals provides the most powerful heat extraction method for the powers levels involved in starship propulsion, and radiators need to be placed as close to the drive as possible to avoid important mass penalties.

Keywords: Fusion, heat transfer, heat transport, radiation

1. Introduction Fusion starship designs require radiation shielding from neutrons and X-rays created by the drive. Even nominally aneutronic fusion reactions, such as Deuterium+He3, can produce neutron fluxes through side reactions that will create large cooling requirements in drive structural elements. Bremsstrahlung radiation from the electrons in the plasma also contributes to the radiation load.

For this paper, three ship design were used, that cover the spectrum of possible heat loads. The original Daedalus from the JBIS study [1], a Daedalus variant called l’Espérance, and Robert Freeland’s Icarus Firefly(2).

The three ships have similar characteristics, although Daedalus is a 2 stage ship, summarized in the following table 1:

Value Unit Daedalus Stage 1 Stage 2 L’Espérance Icarus Firefly Ship overall mass M tonnes 52 700 5450 30 000 24 000 Propellant m tonnes 46 000 4000 27 660 21 725 Ship dry mass tonnes 2500 1450 2 340 2 275 Propellant mass flow ṁ kg/s 0,72 0,072 0,044 0,05 Main fusion reaction D+He3 D+He3 D+D D+D Fusion energy release WEf GJ/kg 353 000 353 000 320 000 320 000 Burnup fraction bf 0.15 0.09 .22 0.8 Power P=ṁ×bf×WEf GW 44 000 3 100 3 700 12 900 Neutron, x-ray loss fraction 0 0 6% 65% Radiation loss GW 0 0 220 8 400 Power to nozzle GW 44 000 3 100 3 480 3 600 Thermal load GW 9 1 17 260 Radius of nozzle m 50 20 20 25 Temperature K 1600 2000 2600 Mass (nozzle + accessories) tonnes 22 Nozzle wall Area m2 15 700 2 500 500 240 Coolant - - Helium Beryllium Radiator area m2 (1) (1) 40 000 174 000 Radiator temperature K - - 1 750 2 500 Radiator system mass tonnes - - 800 1 591 Table 1, Ship characteristics and basic performance equations (1) For Daedalus, the nozzle wall is also the radiator.

Figure 1, general vehicle arrangements

23 | P a g e

2. The Fusion Heat Load The neutrons and X-ray emission levels for the three vehicles vary widely; from nearly zero for Daedalus to 220 GW for l’Espérance and to 8400 GW for Firefly. The large variations are almost entirely due to differences in neutron and x-ray absorption levels in the fusion reactions.

Products Total Energy Energy Energy Energy release → Reaction N MeV/ MeV/ MeV/ MeV GJ/kg fusion fusion fusion 1 D + T → He4 3.49 + n0 14.1 17.59 340 000 5 2 D + D → He3 0.82 + n0 2.45 3.27 79 ,000 4 3 D + D → T 1.01 + p+ 3.02 4.03 97 000 4 4 D + He3 → He4 3.6 + p+ 14.7 18.3 353 000 5

4 0 2p 5 6D → 2He 8.92 + 2n 16.55 + + 17.72 43.22 348 000 12

Table 2 : Fusion reactions

Daedalus uses Inertial Confinement Fusion of frozen fuel pellets and reaction 4 from table 2, D+He3, as it’s main power source. However, some side reactions of reactions 1, 2 and 3 are inevitable, so some neutrons are liberated. Neutrons absorption was calculated in the original study using a very wide neutrons cross section for neutron capture; 80 Barns [1]. With the large diameter of the ICF pellets used by Daedalus and the compression level chosen (2000 times the initial density of the pellet for the second stage), this effectively rendered the fusion reaction aneutronic. The value of 80 barns has been called into question in latter studies, notably the hypothesis that most of the neutrons would be thermalised in the pellet core and that Bremsstrahlung radiation would also be absorbed in the propellant pellet [5, 6]. These studies propose that up to 2.5% of the reaction energy may be lost as neutrons.

To study the effect of neutron loads, L’Espérance was developed as an alternative design to Daedalus, with neutron emission levels based on deuterium deuterium fusion using ICF pellets. Reaction 5 from table 2 summarizes the cascade reaction of deuterium+deuterium. About 40% of the reactions products are high energy neutrons. Using high energy neutron cross sections of about 1.5 Barns, the radiation load that escapes the pellet core is about 6% of the fusion energy [5] or 220 GW. It is also assumed, as for Daedalus, that most of the Bremsstrahlung radiation is absorbed in the pellet outer layers.

Icarus Firefly uses a Z-pinch continuous fusion drive that has no neutron capture capabilities and the same D+D fusion reaction as L’Espérance. So it presents the upper limit of neutron emissions. It also emits a significant amount of Bremsstrahlung radiation. Up to 65% of the fusion energy is lost as high energy neutrons or as X-rays, or 8 400 GW. As Firefly has a very high burnup fraction, the resultant thrust is similar to the other vehicles despite the high losses.

24 | P a g e

3. Geometry

Figure 2 Examples of Closed and open nozzles; Daedalus and l’Espérance. The Daedalus image also shows the heat shield, protecting the fuel tanks from the thermal radiation from the nozzle walls.

3.1 Overall vehicle geometry Daedalus is a very compact vehicle, with close proximity between the fuel tanks and the drive. This configuration is possible because there is only a thermal radiation load, and no high energy radiation load, on the vehicle.

Firefly and l’Espérance adopt stretched out configurations, using the inverse square law to reduce the size and loading of the radiation shields and their associated mass, and to allow space for radiators. 3.2 Nozzle and shield geometries For Daedalus, the nozzle has closed walls. The nozzle also serves as the reaction chamber and as the drive radiator. The metallic structure of the nozzle heats up to 1600 K in order to dissipate some X- ray radiation and induced eddy currents in the nozzle wall. In fact, the size of the Daedalus nozzle was chosen in order to allow for the radiative cooling of the nozzle walls. The first stage can radiate 9 GW while the second stage is sized for 1 GW.

The open nozzle concept of l’Espérance and Firefly has been used for a number of design studies [3, 6, 7]. It allows most of the high energy radiation to leave the reaction area unhindered. Radiation that does hit structural elements is transformed into heat that must be removed. Detailed calculations should show some neutron reflection and re-radiation, depending on the materials, reducing the heat load. This has not been taken into account in the present evaluation. The impingement is a function of geometry; for a point source, the hemispherical nozzle of Daedalus covers 50% of radiative area. If such a nozzle was used for Icarus Firefly, the thermal loading would be 4 times 200 GW and totally unmanageable. The Firefly nozzle and reaction areas were designed to be as open as possible and have only 6% of impingement area. This is at the extreme limit of stability for such a structure. With an open nozzle, the thermal load is reduced to 260 GW, still a large number, but less excessive. Due to the form of the pinch, a long thin line, the radiation is not a

25 | P a g e

point source but a line source. This increases the thermal load on the structure and complicates the geometry. The thin structure required to reduce the heat load is susceptible to buckling. The reaction takes place outside the nozzle, while for ICF the reaction happens inside the nozzle. This increases the number of irradiated surfaces for Firefly. The l’Espérance nozzle has a structurally more conservative impingement area of 15%. The sum of the cooling loads is 17 GW for a nozzle about the same size of the one of the Daedalus second stage.

The area subjected to radiation includes the nozzle, the reaction area, the payload and propellant radiation shield, structural elements, superconducting magnets and conductors as well as the energy recovery system. The superconducting elements require protection from all radiation, as the low temperature requires refrigeration, adding to the heat load and energy requirements, and superconductors are sensitive to high energy radiation damage, eventually losing their superconducting properties. Room conducting superconductors would not change the situation significantly.

The structure of l’Espérance and Firefly needs to be actively cooled, as the neutron radiation gain is much higher than the radiation loss at temperatures below the melting point of even the most refractory materials. For the Daedalus nozzle/reaction chamber the Molybdenum walls at 1600 K are in thermal equilibrium.

Figure 3 Magnetic coil shielding

A superconducting magnetic coil and its shielding. In the shield, the liquid metal coolant absorbs neutrons, the high density metal (probably tungsten) absorbs x-rays, heating up considerably. The coolant evaporates and the gas carries away the heat to be radiated into space at the radiators. The multilayer insulation protects the superconductors from the thermal radiation from the hot shield, and the liquid nitrogen coolant removes any leftover heat, to be radiated away at low temperature radiators. In the image, the fusion reaction is to the right.

26 | P a g e

The payload and fuel tanks radiation shield is another source of heat load. Beyond the obvious need to protect the payload, it is important to shield the fuel tanks from neutron radiation. All the fusion starship designs use cryogenic fuels that must be protected from the drive radiation. At the low temperature of the tanks, and the much higher temperature required to keep the radiators at a reasonable size, the cycle efficiency is low and the power used to create the cryogenic conditions is considerably larger than the heat gain that is removed from the fuel tanks. This power must be radiated away as well. Existing refrigeration systems have a number of inefficiencies that further increase the radiation load. For example, with a tank at 4 K and radiators at 300 K the power required to remove 1 MW is about 123 MW. The total radiation is then 124 MW. See the Carnot Cycle equation in appendix A. The geometry of these tank radiators must be such that they are not themselves heated by the thermal radiation from the drive radiators of from the neutron shields.

4. Thermal Shields 4.1 Multilayer insulation can provide protection from thermal radiation loads, as in figure 2 where it protects the tanks, and figure 3 where it protects the superconductors from the thermal loads coming from hot shielding elements. Daedalus used a thermal shield composed of 120 layers of reflective film between the nozzle and the tanks, as well as some more layers on the tanks themselves, to bring thermal radiation gain down to practically zero. The other ships use very similar designs, and such thermal barriers are in common use on satellites today.

4.2 View factors for radiators and shields The view factor indicates how much of a radiation source will impinge on another one, and how the overall performance will be affected. View factors are tabulated for a number of standard cases [8]. The three Firefly radiators lose about 15% of their efficiency due to their view factor. The four l’Espérance radiators lose about 10% of their efficiency due to their view factor.

5. Cooling System Design The design of the cooling system begins with the lowest temperature in the system, the radiator exit temperature, and with the highest temperature, the shield elements that absorb the neutron and x- ray radiations. These temperatures are limited by material considerations: melting points, material deformation under stress and high temperature corrosion. The Daedalus team chose Molybdenum, l’Espérance uses carbon-carbon composites and Firefly a mix of Zirconium Carbide and carbon- carbon. The design is an iterative process, where each choice influences a number of parameters. One a rough radiator temperature has been set, the radiator area can be determined using the Stefan Boltzmann law and the view factors. The choice of the heat transfer method is the next step.

5.1 Phase change vs temperature change There are two possible methods that can be used to remove the heat from the radiation shields in L’Espérance and Firefly. Temperature change for gas and liquid flows, described by: Pr=ṁ×cp×Δt (1) and liquid to gas phase change using: Pr=ṁ×Ve (2)

Table 3 lists some fluids that could be used for spaceship cooling using the vaporization phase change or a 500C temperature change, for 100 GW of power. Phase change in liquid metals provides the most powerful heat extraction method using the lowest coolant mass flow. They are good choices for the powers levels involved in starship propulsion.

27 | P a g e

However, to avoid the risk of corrosion, Helium can be an interesting alternative, in particular for lower heat loads.

Temperature Latent Heat difference of Specific required to Mass flow Boiling vaporisation heat equal for 500 C temp. Mass flow for Substance point (Ve) (cp) vaporisation difference in fluid phase change K kJ/kg kJ/kg°C °C Tonnes/s Tonnes/s Helium 4 21 5.19 4 39 4762 Hydrogen 20 449 14 32 14 223 Water 373 2270 4.18 543 48 44 FLiBe 1703 11433 2.4 4630 84 9 Lithium 1615 21159 3.58 5910 56 5 Beryllium(1) 2742 32444 1.82 17827 110 3 Aluminium 2792 10500 0.897 11706 223 10 Table 3 Mass flow required to carry 100 GW of power 1)Firefly’s cooling circuit operates at half an atmosphere at the radiators, so the Beryllium phase change happens at a lower temperature, 2500 K.

Watson’s Equation for heat of vaporization combined with Clapeyron equation for vaporization temperature can be used to modify the phase change temperature by varying the pressure used in the radiator system, (see equations in appendix A). However, the heat liberated by phase change goes down as pressure goes up. Eventually, we will reach the triple point of the fluid, and there will no longer be a gas phase change but a circulating supercritical fluid. Phase change is also advantageous for radiator performance as it happens at a fixed temperature. The entire surface of the radiator is at the phase change temperature, while for temperature change heat transfer the radiator temperature varies over the whole surface, with an average temperature of about two thirds of the entry temperature. This increase the required area of the radiator system by about 50% and the system mass in the same proportion.

Once a heat transfer method is chosen, the mass flow required for heat transfer is calculated from either equation (1) or (2). The density of the fluid at the chosen temperature must then be determined. With the mass flow and density, the next step is to choose the velocity of the heat transfer fluid in the system. The velocity sets the pressure drop across the system, and therefore the size of the pumping system required to move the fluid. The velocity is itself a function of pipe diameter, so this step is basically choosing a pipe size. This paper uses 10 m/s for fluid flows and 100 m/s for gas flows.

5.2 Coolant and shield temperatures The coolant temperature will be higher than the radiator surface temperature. The heat transfer coefficient of the coolant also forces an additional temperature difference between the average fluid temperature and the wall of the radiator. For gases in particular, this difference in temperature can be significant. See the Gnielinski correlation to calculate the heat transfer coefficient. A similar temperature difference will exist between the radiation shield and the coolant, so care must be taken to ensure the shield is not hotter than its material limits. Liquids have much higher heat transfer coefficient than gases, so this favors liquid coolants and phase change coolants. Many of these equations are approximations, and need to be confirmed by experiment.

Using the Stefan Boltzmann law, and since the heat transfer to the wall is equal to the heat transfer to space, we can solve the following equations to find the fluid temperature.

28 | P a g e

4 4 Pr= eBA(Twall -Ts ) (3) Pt= hA(Tfluid-Twall) (4) when Pr=Pt

The thermal environment of the operating vehicle is subject to many heat sources, using the average temperature used at Earth orbit, 200K, is a safe design choice for Ts, and has little impact on the results.

Pipe sizing Pipe sizing allows us to determine the velocity of the coolant as well as its overall mass, since the volume of the pipe can be determined from the circuit length and pipe diameter. It also determines the coolant circuit time, which is simply the circuit length divided by velocity. Radiator placement also influences the mass of the cooling system. Taking Icarus Firefly as an example, it requires 8 tonnes per second of beryllium phase change. Placing the radiators at 500 m from the reaction area, with a piping velocity of 5 m/s, would require a circuit time of 200 seconds, and an extra coolant mass of 1600 tonnes. Plus the weight of the pipes.

The structural resistance of the piping limits the possible operating pressures for the coolants. Small bore piping can be quite thin, but large diameter pipes can be problematic. The hoop stress equation can be used to determine a first order requirements for the pipe sizes. σ=Pr/t (5) If the piping is chosen too small, the pumping power will increase dramatically, the required pressure will also increase and the pipe walls will need to be thicker, adding mass to the vehicle. For this paper the hoop stresses chosen were kept under 200 MPa. 5.3 Pumps, pipes and compressors To find the pump or compressor power to circulate the coolant the following equations can be used:

Pp=Q×Δp/ƞ (6)

Which is valid for both the compressors used for gases and the pumps used for liquids. Pump or compressor efficiency ƞ is usually between 0.6 and 0.8.

The most important consideration is fluid velocity. Pumping pressure goes up to the square of the velocity and pumping power to the cube of the velocity. So we need to keep the velocity as low as possible, without oversizing the pipework. Since we know the required coolant flow Q, the only unknown is the pressure drop Δp. To find the pressure drop we need to solve a series of classical fluid dynamic and heat transfer equations and to do multiple iterations until we find optimum values. The required steps are: First determine the viscosity of the fluid at the operating temperature, then calculate Reynold’s number and the friction factor, and from these determine the pressure drop using the Darcy Weisbach equation.

Pumping system mass is a factor of technological development; in particular new superconducting pumps are lighter than their equivalent classical counterparts. A value of 2 kW/kg was used for this paper.

6. Results The following table list the most important results in the design of the cooling systems:

29 | P a g e

Value Unit L’Espérance Icarus Firefly

Cooling heat load Pr GW 17 260

Cooling method Temperature change Phase change

Main structural material Carbon Zirconium carbide

Melting point K about 4 000 3 800

Coolant Helium Beryllium

Mass flow m tonnes/s 6,5 8

Pressure max p kPa 2 000 1 000

Pressure min p kPa 50

Density p kg/m3 0,49 1 560

Volume flow m3/s 13 000 5,1

Specific heat Cp W/kgK 5,2 3,3

Viscosity μ kg/m*s 0,00006 0.0011

Heat of vaporization kJ/kg n/a 32 400

Radiator temperature (average) Tw K 1750 2 450

Heat shield temperature K 2 450 2 600

Coolant temperature, to radiator K 2 200 2 550

Coolant temperature, from K 1 700 2 500 radiator

Convective temperature K 180 16 difference

Mains, dia pipe size liquid Dm m n/a 0,47

Mains dia. pipe size gas Dm m 4 0,25

Radiators, pipe size Dr m 0,015 0,015

Pumping power Pp MW 46 7

Pump mass tonnes 16 80

Radiator area m2 40 000 174 000

Radiator system mass tonnes 800 1 600

30 | P a g e

7. Discussion Despite having an order of magnitude less heat load, the helium cooled l’Espérance has a similar system weight to Firefly. The very large volume of helium increases component masses, the high pressures require stronger pipe walls and the lower radiator temperature reduces their efficiency. Helium has been used as a coolant in very high temperature reactors (VHTR) at about 1250 K, and is therefore a much better knew coolant than the exotic molten beryllium of Firefly. If liquid Beryllium was used for heat transfer for l’Espérance rather than helium, the cooling system would weigh about 100 tonnes.

The maximum radiator temperature (Twall) is a function of available materials. Structural strain and thermal fluence reduce the maximum temperatures that materials can withstand. Theoretical maximum strain values are reduced by up to 75% at high temperatures. Corrosion is another significant problem at high temperatures. Heat pipe research has provided some insightful information, but the number of applications for them is limited, so their development is not very advanced.

The possibility of recovering thermal energy is often raised in the context of the large radiative powers required for these vehicles. However, thermoelectric systems and turbine based systems require large temperature differences. This means the cold side radiators will be very large, increasing the overall mass of the ship. Therefore there is no point to try to recover the thermal energy, since the overall mass gain will cancel any benefit from the energy gain by increasing the fuel requirements. Direct energy conversion offers a far better path to recovering energy from the drive.

Corrosion for high temperature gases such as hydrogen, gaseous lithium or gaseous beryllium is a serious concern, and requires refinements of existing materials. Some mixes are incompatible, such as hydrogen and carbon. Use of high temperature coatings has been successful in the aircraft industry for the protection of turbine blades, and might be transferable to starships.

Conclusions It is possible for fusion starships with neutron and x-ray loads to have adequate performances despite mass penalties due to the cooling systems. Neutron and x-ray heating has important effects on vehicle mass and the reduction of neutron and x-ray emissions in the drive is a key part of fusion starship design. Research is needed in the behaviour of materials at high temperatures if the designs sketched out in this paper are ever to be realized.

31 | P a g e

References [1] A. Bond & A. R. Martin. "Project Daedalus." JBIS 31, S5-S7, 1978. [2] R. M. Freeland et al.,"Firefly Icarus: An Unmanned Interstellar Probe using Z-Pinch Fusion Propulsion", JBIS (2015), 68, pp.68-80 [3] J. Miernik, et al. "Z-Pinch fusion-based nuclear propulsion." Acta Astronautica 82.2 (2013): 173- 182. [4] J. H. Lienhard IV, A Heat Transfer Textbook, 4th edition, University of Houston, Massachusetts Institute of Technology [5] T. H. Rider, "Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium." Physics of plasmas 4.4 (1997): 1039-1046. [6] R. B. Adams, et al. "Conceptual design of in-space vehicles for human exploration of the outer planets." (2003). [7] C. D. Orth, "Interplanetary Space Transport Using Inertial Fusion Propulsion, ICENES-98." The Ninth International Conference on Emerging Nuclear Energy Systems, Proceedings, Tel-Aviv, Israel. 1998. The Vista spaceship. [8] J. R. Howell, “A catalog of radiation configuration factors”, McGraw-Hill, 1982. (web.) Siegel, R., Howell, J.R., Thermal Radiation Heat Transfer, Taylor & Francis, 2002. [9] W. Hoffelner, "Materials for the very high temperature reactor (VHTR): A versatile nuclear power station for combined cycle electricity and heat production." CHIMIA International Journal for Chemistry 59.12 (2005): 977-982.

Appendix A: Heat transfer equations

Conduction: Pressure drop Darcy–Weisbach Watson’s Equation for heat of 1) P=U×A×(Ti-To) equation: vaporization: P= Power (kW) 7) dp=f×(L/D)×((p×v2)/2) 0.38 13) Ve2= Ve ×((Tc - T2)/(Tc - Tn)) U= Heat transfer coefficient dp =pressure drop (Pa) Ve2=vaporisation energy at new = k/x f=friction factor pressure (kJ/kg) x=material thickness (m) L=Length of pipe (m) Ve= standard vaporisation energy k=thermal conductivity D=Diameter of pipe (m) (W/m°K) p=density (kg/m3) (J/kg) A= Area (m2) v =average velocity (m/s) Tn=standard pressure boiling point Ti= Interior temperature (°K) (°K) To=Outside temperature (°K) Haaland friction equation: T2= New temperature (°K) 8) f= (-1.8×log(((e/D)/3.7)1.11 + Tc= temperature at critical point (°K) -2 Convection: (6.9/Re))) 2) P=h×A×(T -T ) e= pipe roughness factor (m) s f Gnielinski correlation(3): h= convective heat transfer Re=Reynolds number Convective heat transfer in pipes coefficient (dimensionless) 14) h= ((f/8) x (Re - 1000) x Pr) / T =Surface temperature (°K) D=pipe diameter (m) s (1+(12.7 x (f/8)1/2 x (Pr 2/3 -1))) x k/D Tf= Environment temperature (°K) Reynolds number (Re): h = convective heat transfer rate for 9) Re = ⍴vD/μ a gas in a Radiation: ⍴=density (kg/m3) pipe (W/m2K) 3) P= A×e×B(Tr4-Tf4) v=average fluid velocity (m/s) f = friction factor e= emissivity (no units) D=Diameter of pipe (m) Re=Reynolds number B= Stephen Boltzman constant μ=dynamic viscosity Pr= Prandtl number = approx. 1 for -8 2 4 = 5.67e W/m K (kg/m×s)or(Pa×s) turbulent flows Tr= Temperature of radiator See table 5 for μ and p D= Pipe diameter (m) (°K) k = Thermal conductivity of the Tf= Environment temperature Sutherland gas viscosity:

32 | P a g e

3/2 (°K) 10) μ=μ0 x ((T0+C)/(T+C)) x (T/To) coolant (W/mK) T = actual gas temperature (K) See table 4 for k (gases) Phase change: T0= reference gas temperature (K) 4) P=m×Ve μ = actual gas viscosity (Ns/m2) 2 Carnot cycle: m= mass flow (kg/s) μ0 =reference gas viscosity (Ns/m ) (15) COP= T /(T -T ) Ve= Vaporisation energy See table 3 for C and T L H L o and (kJ/kg) See table 5 for Ve Perfect Gas Law: (16) Q=Qc/COP COP=Coefficient of performance 11) d=Mw×p / R×T 3 Mass/energy flow: d=density (kg/m ) TL= Temperature of the cold system 5) P=m×Cp× (T1-T2) R=perfect gas constant = 8.314 (K) m= mass flow (kg/s) (J/°K×mol) TH=Temperature of the hot system (K) Cp=specific heat (kJ/kg°K) Mw=molecular weight (g/mol) Q= External power required (W) (J/s) T1=Initial temperature (°K) p=pressure (kPa) Qc= Power from the cold system (J/s) T2=Final temperature (°K) T=temperature (°K) See table 2 for Mw Multilayer insulation: Compressor or pump power: 17) U=4BT3/N(2e-1)+1 6) P=(Q×dp)/n Clapeyron’s Equation, vaporization dp=pressure change (kPa) temperature: T is the average temperature between the two surfaces, Ts+Ti/2 Q=Volume flow (m3/s) 12) p2=pn×e^Ve/R(1/Tn-1/T2) n=pump/compressor p2=new pressure at boiling point e=Emissivity of the layers efficiency (kPa) N=number of layers (usually between 0.6 and 0.8) pn=atmospheric pressure = 101 (kPa) Ve= vaporisation energy at standard pressure (kJ/mol) Tn=boiling temp. standard pressure (°K) T2= New temperature (°K)

33 | P a g e

Appendix B: Gas properties for heat transfer (For Sutherland’s viscosity equation) Reference Specific Sutherland temperatur Reference heat Molecular Gas constant e viscosity capacity weight Thermal conductivity C T0 μ0 Cp w [K] kg/m×s kJ/kgK g/mole mW/cmK Air 120 291.15 0,00001827 1,2 28,97 0.051+0.7438x103T- Nitrogen (N2) 111 300.55 0,00001781 1,3 28 0.1573x106T2 0.07979+0.6671x103T- Oxygen (O2) 127 292.25 0,00002018 32 0.05479x106T2 Carbon dioxide (CO2) 240 293.15 0,0000148 44 0.7897+0.03623x103T+0.0180 Hydrogen (H2) 72 293.85 0,00000876 14 2 9x106T2 0.7073+0.02368x103T+0.1048x Deuterium(D2) 1) 5,1 4 106T2 Ammonia (NH3) 370 293.15 0,00000982 4,5 17 Helium 79.4 273 0,000019 5,4 4 2.684x10-3*T0.71 Argon 0,5 40 Table 4 Gas properties, C and T0 fox equation yy 1)The viscosity of deuterium is approximately 1,4 times that of hydrogen.

Latent Heat of vaporisation Specific heat Dynamic Triple point Substance Boiling point (Ve) (cp) viscosity temperature K kJ/kg kJ/kg°C kg/m×s K Water 373 2270 4.18 0,00013 FLiBe(1) 1703 11433 2.4 0,003 Lithium 1615 21159 3.58 0,00035 Beryllium(2) 2742 32444 1.82 0,0011 Aluminium 2792 10500 0.897 0,0027 Table 5 Liquids properties for heat transfer

1)FliBe is a Fluorine Lithium+ Beryllium salt. 2)Firefly’s cooling circuit operates at half an atmosphere, so the Beryllium phase change happens at a lower temperature, 2500 K. 3)See table 4

34 | P a g e

PLASMA DYNAMICS IN FIREFLY’S Z-PINCH FUSION ENGINE

Robert M. Freeland II [email protected] 8817 Riverlachen Way Riverview, FL 33578

Abstract Project Icarus is a theoretical design study for an unmanned, fusion-based probe to Alpha Centauri using “current or near-future technology [1]” The project was started in 2009 and is now drafting its Final Report. The leading design to come out of the project is a vessel dubbed “Firefly”, built around a continuous, open-core Z-pinch fusion engine. This engine is based on experimental work by Uri Shumlak at the University of Washington [2] showing that a Z-pinch plasma can be stabilized via sufficient “shear” flow of plasma through the pinch. There are nevertheless some major differences between the Firefly drive and Shumlak’s test device, the implications of which are discussed herein. Keywords: Project Icarus, Fusion Propulsion, Z-Pinch Fusion, Firefly, Alpha Centauri.

1. Introduction Firefly is one of several designs for an unmanned, fusion-based interstellar probe put forth by the Project Icarus Study Group. This vessel is described in the paper “Firefly Icarus: An Unmanned Interstellar Probe Using Z-Pinch Fusion Propulsion” published in the March 2015 issue of JBIS. [3]

Figure 1: Firefly Schematic [4]

Figure 2: Firefly Upon Main Engine Shutdown [5]

35 | P a g e

Z-Pinch Background An electromagnetic “pinch” is formed whenever a high current passes through a medium. The current (shown in Figure 3 as yellow arrows) generates a magnetic field (shown in Figure 3 as blue arrows) directed in concentric lines around the current flow, and that field reacts with the current itself to create a force directed inward. This “pinches” the medium. Figure 3: Z-Pinch Current & Field

2.1 Pinch History Pinches occur in nature – most notably as lighting, where the electrical discharge ionizes the air and then pinches the resulting plasma, resulting in a sonic boom commonly known as thunder. The earliest known example of a man-made pinch was by Martinus van Marum in 1790 in Holland [7] He discharged 100 Leyman jars through a wire and the apparatus exploded. It was over 100 years before the physics of this phenomenon was understood, when Pollock and Barraclough studied a

36 | P a g e copper tube in 1905 that had been pinched by a bolt of lightning. [8] That copper tube is still on display at the School of Physics, University of Sydney, Australia (See Figure 4.) Figure 4: Copper Pipe Crushed by the Z-Pinch from a Lightning Strike [6]

The study of pinches for fusion began with the publication in 1934 of Willard Harrison Bennett’s analysis of the radial pressure balance in a static Z-pinch [9]. The Bennett Pinch Relation is named in his honor. The concept was researched heavily for potential use in a terrestrial fusion reactor until the mid-1950’s, when Kruskal and Schwarzschild published work describing various magneto- hydrodynamic (MHD) instabilities in Z-pinch plasmas [10]. Research into Z-pinch fusion languished thereafter, until Uri Shumlak published his paper in 1998 showing that a sheared axial flow could mitigate hydrodynamic instabilities [2]. Shumlak’s subsequent work – including a plethora of lab tests at the University of Washington – has been indispensable for this project [12]. In addition to Shumlak’s work, Sandia National Labs is studying Z-pinches with their high-powered “Z Machine”, and NASA is researching Z-pinch propulsion at their Charger One facility at the Marshall Space Flight Center in Huntsville [13]. That puts Z-pinch technology at TRL 4, though the use of Z- pinches for fusion falls somewhat lower.

2.2 Bennett Pinch Relation The Bennett Pinch Relation is the fundamental equation governing the mathematics of Z-pinches. It describes the plasma in a Z-pinch at equilibrium, where the magnetic pressure (as described by Maxwell’s Equation) is balanced against the plasma pressure (as described by the Ideal Gas Law).

Shumlak [14] gives this formula:

(1) …but Haines [15] gives this formula:

(2) Haines’ temperatures are in eV instead of Kelvin, so Haines is using “e”, rather than the Boltzmann Constant, to convert temperature to Joules. Substituting this transformation yields the formula from Shumlak for Ti = Te, while also explaining how to handle different particle temperatures. Z is the atomic number, which together with N defines the number of electrons in the plasma. Note that N is the linear number density (ions per meter) rather than the usual ions per volume.

The constant terms are typically rolled into a single constant Cp = 8πkB/u0, such that: 2 N (Ti + ZTe) = I / Cp (3)

37 | P a g e

Z-Pinch Fusion It was recognized as early as the 1930s that a pinch of sufficient strength, with the appropriate fuel, could conceivably be used to initiate fusion. The mathematics of a fusing plasma are more complex though, because a fusing plasma provides a secondary (and ideally dominant) source of energy to the plasma, over and above the energy provided by the pinch current.

3.1 Core Temperature The expanded form of the Bennett Relation given in Equation #13 provides a way to determine how the plasma reacts as it fuses, and where the output energy is deposited.

At the moment of ignition, the plasma is assumed to be at equilibrium with Ti = Te, but once fusion begins, new ion species are produced with significantly more energy than the initial plasma. The plasma temperature becomes the mean of all these particle temperatures:

T = Σi(ni(Ti+ZiTe)) (4)

 Te = T0 is the initial electron / plasma temperature  Ti is the initial temperature of each ion

 Zi is the number of electrons for each ion species

 ni = Ni / N is the mole fraction of each ion species

The plasma temperature rises, pushing against the containment generated by the pinch current. The pinch seeks a new equilibrium, and assuming containment is maintained, there exists a second Bennett Relation describing the equilibrium temperature of the fusing plasma: 2 Tp = I / (Cp N (1+Zp)) (5) …where Zp = Σi(NiZi)/N is the weighted average atomic number for the ions in the plasma. But if the electrical current remains constant, how can the Bennett Relation hold as temperature rises? The right side of Equation #3 is then entirely constant, so the only thing that can change to offset the rise in temperature is the linear number density N of the ion species. There are two factors causing N to shrink. Firstly, the fusion core is converting pairs of lighter ions into single heavier ones, thereby reducing the total number of ions in the pinch. Secondly, the Bennett Relation is NOT a traditional number density (particles per volume), but rather a linear number density (particles per meter). N = Nt/L = ṅ/vz (6) where Nt is the total number of ions in the pinch, L is the length of the pinch, ṅ is the particle flow rate, and vz is the axial velocity. N decreases as the axial velocity of the particles increases down the line, thereby distributing a fixed number of particles Nt over a greater length L. Unfortunately, allowing N to vary violates a basic assumption behind much of the theoretical work on Z-pinches – including Shumlak’s. To get around this, Firefly’s full-length pinch is modeled as a series of shorter pinches with different initial conditions, assuming that N remains constant over those shorter segments. The key is to calculate the new number density Ns for each segment based on the new ion species, and then to use that to calculate the new pinch temperature and radius.

Differences vs. SHUMLAK’S Experimental Device Shumlak's experimental device is essentially an MPD thruster with the outer wall (electrode) extended aft and then capped at the end. The MPD portion -- which Shumlak calls the "acceleration region" -- ionizes a puff of gas and accelerates that plasma into the tail end of the device, which Shumlak calls the "assembly region". If the outer wall (electrode) were not capped off, it would serve as a nozzle, focusing its jet of plasma more directly aft. Figure 5: Shumlak’s ZaP Experimental Device [16]

38 | P a g e

Besides the obvious difference of scale and purpose, there are some major design differences between the Firefly drive and Shumlak’s ZaP test device: 1. Firefly uses an entirely different plasma injection strategy, at much higher velocities. 2. Firefly works in continuous, rather than single-shot mode. 3. Firefly has an open core with three conducting rails, rather than a solid reaction chamber. 4. Firefly’s pinch is strong enough to produce actual fusion. What follows is an examination of the implications of these differences on the mathematics describing the Z-pinch drive, versus the math presented by Shumlak for his apparatus.

4.1 High-Speed Plasma Injectors In Shumlak’s test apparatus, gas is injected into an “acceleration region”, which is essentially an MPD thruster. There the gas is ionized and accelerated into the pinch. The same current which ionizes and accelerates the plasma also pushes aft to the tail end of the device to form the pinch. Unfortunately, this single-potential, single-current arrangement doesn’t work for a continuous drive, because the incoming plasma will always provide a path of least resistance that foregoes the pinch. The end result is just an MPD thruster, with no pinch. It was thus necessary to separate the plasma injectors from the Z-pinch itself, isolating the two circuits and allowing them to operate at different potentials and power levels. Firefly accomplishes this via a ring of separate plasma injectors forward of the inner electrode (cathode) that drive plasma into the pinch region at several hundred kilometers per second. Several technologies were evaluated to provide this input plasma at sufficient velocity. Both MPD thrusters and 4-grid ion thrusters currently under study at the ESA [18] appear promising. Essentially, the Firefly drive then becomes a two-stage drive, with the input thrusters providing the high-velocity plasma to the Z-pinch drive. In fact, the input thrusters could provide low-thrust maneuvering propulsion for the vessel itself, when the full Z-pinch drive would be overkill.

4.1.1 Minimum Axial Flow Speed According to Shumlak’s research, the key to maintaining a stable Z-pinch plasma is to keep the outer sheath of plasma moving with sufficient speed. Shumlak [19] states in his 2012 paper: "Stability requires an axial flow speed greater than a fraction of the Alfvén speed such that vz ≥ 0.1 vA for a uniform shear…” The Alfvén speed, in turn, is calculated as follows: 1/2 vA = B / (μ0 ρ) (7) … where the field strength B is given by:

B = μ0 I / 2πa (8)

39 | P a g e

The plasma density ρ is a function of the pinch volume, which in turn is a function of the pinch diameter discussed in Section 4.4.1.

4.2 Continuous Operation All lab work on Z-pinches thus far has been conducted on single-shot discharges that happen in fractions of a second. This is primarily due to the power requirements for these devices, as discussed below. Nevertheless, Shumlak postulates that a stable pinch could be sustained indefinitely if sufficient sheared flow of plasma could be maintained through the pinch, and sufficient power were available to drive it. This raises the tantalizing possibility of a continuous fusion drive that could avoid the stresses and inefficiencies of high-frequency cycling. (All other designs considered by the Project Icarus team – including the original Daedalus design from the 1970’s – were cycled).

4.2.1 Pinch Current The Z-pinch fusion drive requires a very high, continuous electrical current to compress the plasma to fusion conditions and to contain the resulting fusion core. For Firefly’s drive, the necessary current is ~5 MA, with a voltage of a couple hundred kV, and total input power of hundreds of GW. This is an extraordinary amount of power – a significant fraction of the total power consumption for the entire United States in 2005 (3340 GW) [21]. The current is similarly remarkable, being an order of magnitude greater than the 300 kA current carried in a positive lightning strike [22]. As of this writing, the highest continuous current ever produced in a lab is 100 kA in July 2014 by the National Institute for Fusion Science (NIFS) in Japan, using yttrium-based superconductors [23], though the Qatalum plant in Qatar has rectifiers nominally capable of providing 350 kA of DC current [24]. Nevertheless, the voltages themselves are well within mankind’s current experience. The Van de Graaff generators at the Holifield Heavy Ion Research Facility (HHIRF) at Oak Ridge National Laboratory (ORNL) produced 25.5 MV in the 1980s [25]. The Firefly voltage is right at the top end of the voltage currently used in North American high-voltage power substations [26].

4.2.2 Energy Recapture Clearly, electrical power levels of this magnitude cannot be supplied by any conventional power plant. The Cattenom Nuclear Power Plant in France represents the state-of-the-art in terrestrial fission reactors, with four reactors producing 1.3 GW of electrical power each [27]. It would nevertheless take ~2500 such fission reactors to provide enough power for Firefly! The only practical source of input power for this is the fusion reactor itself, via direct energy conversion of charged particles in the exhaust plume. Research is still underway to evaluate various technologies for accomplishing this, including Venetian Blind collectors and other, more exotic approaches. Energy recaptured from the exhaust must then be carried back forward to complete the circuit. This is accomplished via three conducting “rails” that run parallel to the Z-pinch core. These rails also serve as structural members to translate the force on the aft electrode / magnetic nozzle forward to the rest of the vessel.

4.3 Open Core Firefly’s drive produces an extraordinary amount of waste heat in the form of high-energy neutrons and X-rays. It was obvious from the outset that shielding all of this would require unworkable mass, so Firefly was conceived to employ an unshielded fusion core. Nevertheless, it was determined early in the design process that even a thin, solid tubular reaction chamber akin to Shumlak’s test device would present unsustainable heat loads, so the Firefly team decided to eliminate the reactor walls

40 | P a g e altogether, leaving just three conducting rails to carry the return current. This left a naked fusion core, and thus the Firefly moniker. This open-core, three-rail design introduces some differences in the plasma dynamics during startup, as discussed below. Moreover, Firefly’s continuous operation introduces a new mode of operation distinct from the “startup” mode that has heretofore been studied in the lab.

4.3.1 Initiating Shumlak’s Pinch In Shumlak’s experimental apparatus, propellant gas is injected into a conducting tube 1m long with a central electrode at one end and an end-cap with a small hole at the other end. A large voltage is applied between the electrodes, ionizing the gas and allowing a high current to flow between them. That current causes the plasma to constrict – first at the central electrode, and then outward to the end of the tube.

Figure 6: Shumlak’s Pinch Initiation [16] (The images in Figure 6 are taken from the doctoral thesis of Sean Knecht [16], a student in Shumlak’s ZaP lab at the University of Washington.)

4.3.2 Initiating Firefly’s Pinch The initiation of Firefly’s drive is similar to that of Shumlak’s test device, but with some important differences arising from the continuous inflow of fresh plasma, and the separation of the injectors from the pinch. (Images in this sequence courtesy of Icarus Designer Michel Lamontagne). (1) An electrical potential of a couple hundred kV is applied to the electrodes before any gas is injected into the drive. Since there's no path for current to flow, this is an open circuit. (The whole drive is essentially a giant gas discharge switch.)

41 | P a g e

Figure 7: Initial Drive Condition

(2) When plasma is injected into the drive, it still doesn't close the circuit initially, because it doesn't contact any part of the anode. Instead, the plasma flows down to the point of the cathode while diverging somewhat, and then it bounces against the plasma coming in from opposite angles to further diverge toward the tail end of the drive. This plume forms an hourglass shape with its neck near the tip of the cathode.

Figure 8: Plasma Injection Prior to Initiation

(3) When that plasma reaches the side rails (anode) near the tail end of the drive, the circuit is completed, sparking three bolts of lightning from the three rails to the cathode. (In practice, the plasma will inevitably reach the rails at slightly different times owing to minor asymmetries in the device, as well as random fluctuations in the plasma divergence. But in the initial microsecond that the current starts flowing from that rail, it will push the plasma toward the other two rails and thereby spark them as well. Thus, it's essentially three simultaneous bolts.) Those three bolts are still attached at the rails, curving in to meet up at the tip of the cathode.

(4) The bolts "zip" down to the aft electrode ring, pushing the plasma into a tighter funnel shape, with its open end at the aft electrode ring, and its point at the tip of the

42 | P a g e

cathode. The walls of the funnel curve, with a significant flare at the tail end to meet that aft electrode.

Figure 9: Active Z-Pinch

(5) Meanwhile, there's more plasma flowing in at the forward end of the drive. As before the pinch initiation, this plasma diverges somewhat on its path to the point of the cathode, but the current coming from the aft electrode ring is hungry for an easier path to the cathode, so it spreads out a little to use this incoming plasma as a circuit path. This current pulls that plasma toward the pinch. The end result is that the pinch region flares at the forward end as well, where it meets the cathode. The resulting geometry is a narrow hourglass shape, with open ends at the two electrodes, and a very thin section in the middle. (6) Now that the pinch is fully formed, fusion occurs in the central region of the pinch where the hourglass is squeezed tight. That's the brightest part of the drive, though the excess energy is mostly thrown off in the X-ray spectrum. The fusion super-heats the plasma, which has nowhere to go but aft. This produces a jet of hot plasma exiting the center of the aft electrode ring, which doubles as a magnetic nozzle. The plume diverges somewhat and cools on exit.

4.4 Actual Fusion The biggest difference between Firefly’s drive and Shumlak’s test apparatus, of course, is that Firefly’s Z-pinch is strong enough to fuse deuterium. This introduces a tremendous source of additional energy to the plasma in the middle of the pinch, and assuming that containment is maintained, the Bennett Pinch Relation dictates that the rise in plasma temperature must be offset by lower linear number density, which equates to higher axial velocity. That is to say, the fusion core heats the plasma and ejects it out the back. This is, of course, the entire purpose of the drive. Firefly models this via a series of pinch segments, where the output from one segment is fed into the next. The fusion in each segment yields a hotter, faster plasma entering the next segment. The open question is what unforeseen impacts the fusion heating might have on the structure / stability of the pinch. In a non-fusing pinch as studied in the lab, the initiation of the pinch tends to choke off the plasma flow, ultimately allowing instabilities to develop. It seems possible that the fusion core’s energy input may help prevent this stagnation, but proper MHD simulations and/or lab work would be needed to explore this.

43 | P a g e

4.4.1 Pinch Dimensions Shumlak’s formula for calculating the pinch diameter / density is based on the premise that gas in an "accelerator region" is forced into the "assembly region", where it gets compressed by the strong current of the pinch. Thus, the mass, temperature, and volume in the pinch are functions of the mass, temperature, and volume in the initial accelerator region. Moreover, Shumlak assumes that this compression is adiabatic, such that P/ργ remains constant from the initial conditions to the pinched plasma, where P is the total plasma pressure, ρ is the mass density of the plasma, and γ = 5/3 is the ratio of specific heats. Combining this with the Ideal Gas 2 Law (PV = NgkBT) and the Bennett Pinch Relation (T = I / Cp N (1+Zp)) – and remembering that the traditional number density “Ng” in the Ideal Gas Law is different from the linear number density “N” in the Bennett Pinch Relation – eventually yields: 3/2 3 Vp = Va [CpNTa(1+Z)] / I (9) …where Cp = 8πkB/μ0, N = linear number density, I = pinch current, and Ta and Va are the initial plasma temperature and volume. Assuming the pinch region is a cylinder, this gives the radius of the pinch: 1/2 a = (Vp/πL) (10) This is acceptable as a first approximation, but in a pinch that’s producing actual fusion, the assumption of isentropic compression is completely wrong; rather, there’s a significant external source of heat to the system. The implications of this have not yet been properly incorporated into Firefly’s drive model.

Conclusions Z-pinches have already reached TRL 4, with lab experiments at the University of Washington, Sandia National Labs, and NASA’s Charger One facility in Huntsville. Nevertheless, additional research is needed to address open questions about the design of a Z-pinch fusion drive:

(1) A continuous drive needs a well-engineered solution for energy recapture from a continuous, high-speed ion stream. Without this, continuous drive operation is impossible, and a Z-pinch fusion drive would have to be pulsed to allow for inductive charging of a capacitor bank to power the next shot. Such an arrangement is in many ways simpler, but it’s less than ideal.

(2) Lab tests need to be done to confirm that a stable plasma can be maintained indefinitely with sufficient input flow. This is one of Shumlak’s key assertions, but it can only be tested with a continuous pinch, and the power requirements of such a device all but preclude such a test without some form of energy recapture as discussed above.

(3) The mathematics of a Z-pinch plasma need to be rederived for a fusing plasma, as the Bennett Pinch Relation underlying most of the published work assumes adiabatic compression. On the short timescales of single-shot, non-fusing tests, this is sufficient, but for a continuous, fusing plasma, this assumption is completely false and leads to erroneous results. The Z-pinch drive offers a viable, near-term option for fusion propulsion, with performance sufficient to get an interstellar probe to Alpha Centauri in less than 100 years using pure deuterium fuel, but more research is needed to complete the design. Acknowledgements Much of the first half of this paper was lifted from our 2015 Firefly paper published in JBIS. This design would not be possible without the work of Uri Shumlak and his team (particularly Sean Knecht) at the University of Washington.

44 | P a g e

Input was also received from other members of the Project Icarus team, including my co-author on our 2015 Firefly paper, Michel Lamontagne.

References [1] K.F. Long, R.K. Obousy, A.C. Tziolas, A. Mann, R. Osborne, A. Presby, M. Fogg, “Project Icarus: Son of Daedalus - Flying Closer to Another Star”, JBIS, 62 No. 11/12, pp.403-416, Nov/Dec 2009. [2] U. Shumlak & N.F. Roderick, “Mitigation of the Rayleigh–Taylor Instability by Sheared Axial Flows”, Physics of Plasmas 5, 1998. [3] R.M. Freeland & M. Lamontagne, "Firefly Icarus: An Unmanned Interstellar Probe using Z-Pinch Fusion Propulsion", JBIS (2015), 68, pp.68-80 [4] Firefly schematic produced by Michel Lamontagne based on the 2015 design. [5] Firefly image produced by Michel Lamontagne based on the 2015 design. [6] J. Brian, “Historical Collection of the School of Physics”, University of Sydney, Australia. Used under GFDL. [7] M. Marum, “Proc. 4th Int. Conf. on Dense Z-Pinches (Vancouver 1997)”, Am. Inst. Phys. Woodbury, New York, 1997. [8] J.A. Pollock & S. Barraclough, Proc. R. Soc. New South Wales, 1905. [9] W.H.Bennett, "Magnetically Self-Focussing Streams", Phys. Rev. 45, 1934. [10] M. Kruskal & M. Schwarzchild, "Some Instabilities of a Completely Ionized Plasma", Proc. Royal Society, London, 1954. [12] UAW ZAP Flow Z-Pinch Experiment: Publications, http://www.aa.washington.edu/research/zap/publications.html Retrieved 11/1/2013 [13] Advanced Concepts Office (ED04), Marshall Space Flight Center, “Z-Pinch Pulsed Plasma Propulsion Technology Development”, “Final Report”, October 8, 2010. [14] U. Shumlak et al, “The Sheared-Flow Stabilized Z-Pinch”, Transactions of Fusion Science & Technology, Vol. 61, 2012. [15] M.G. Haines, “A Review of the Dense Z-pinch”, Plasma Phys. & Controlled Fusion 53, 2011. [16] S.D. Knecht, “Inner Electrode Modifications on the ZaP Flow Z-Pinch”, Doctoral Dissertation, University of Washington, 2008. [18] D. Fearn, The Application of Gridded Ion Thrusters to High Thrust, High Specific Impulse Nuclear- Electric Missions, Journal of the British Interplanetary Society, Vol. 58, No. 7/8, pp. 257-267, 2005. [19] U. Shumlak et al, “Advanced Space Propulsion Based on the Flow-Stabilized Z-Pinch Fusion Concept”, 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 9 - 12 July 2006, Sacramento, California. [20] U. Shumlak et al, “The Sheared-Flow Stabilized Z-Pinch”, Transactions of Fusion Science & Technology, Vol. 61, 2012. [21] Energy Information Administration, US Department of Energy, “U.S Energy Consumption by Source, 1949–2005”, http://www.eia.doe.gov/aer/txt/ptb0103.html, Retrieved 5/25/2007. [22] National Weather Service, NOAA, “The Positive and Negative Side of Lightning”, JetStream Jan 2010, http://www.srh.noaa.gov/jetstream/lightning/positive.htm, Retrieved 6/11/2011. [23] National Institute for Fusion Science (NIFS), Japan. July 27, 2014 Press Release. http://rt.com/news/175968-japan-highest-electrical-current/, Retrieved 2/10/2015. [24] Qatalum Website, “Primary Aluminum Plant”, https://www.qatalum.com/AboutUs/Technology/Pages/Primary-Aluminum-plant.aspx Ret. 2/15/2015. [25] Oak Ridge National Laboratory, http://web.ornl.gov/info/ornlreview/v36_1_03/article_34.shtml Ret. 2/6/2015. [26] Occupational Safety and Health Administration. US Dept. of Labor, Electric Power eTool: Illustrated Glossary: Substations". Retrieved 11/1/2011. [27] Gallery. “Power Plants Around The World”, "Nuclear Power Plants in France". Feb 1, 2012. Retrieved 2/28/2014.

45 | P a g e

CONTINUOUS ELECTRODE INERTIAL ELECTROSTATIC CONFINEMENT FUSION

Raymond J. Sedwick*, Andrew M. Chap, and Nathan M. Schilling

Department of Aerospace Engineering, University of Maryland, College Park, MD, USA *Corresponding author, [email protected]

One of the greatest impediments to space exploration is a lack of abundant power, in particular as missions extend farther from the sun. Nuclear fusion, while not technically a renewable like solar photovoltaics, offers such a high energy density that the distinction becomes meaningless over foreseeable mission lifetimes. An ideal implementation of fusion power for space would be aneutronic, removing mass requirements for reactor shielding and eliminating material activation and damage. It would ideally also leverage direct energy conversion, eliminating the need for massive radiators required to support thermodynamic power conversion. Continuous Electrode Inertial Electrostatic Confinement Fusion is a concept currently under development that may lend itself to utilizing the proton-boron reaction with power conversion provided by a standing wave direct energy conversion concept. This paper presents an overview of the technology and provides a high-level, top-down system design for a 1 MW reactor. Keywords: Fusion Energy, Space Power Generation, Inertial Electrostatic Confinement

Nomenclature

2 퐴퐹 = Area of the face of a polyhedron (m ) 2 퐴푆 = Surface Area of a circumscribed sphere (m ) E = Number of polyhedral edges (-)

EF = Energy release during a fusion event (eV) e = fundamental unit of charge (C) F = Number of polyhedral faces (-) 푙퐸 = Length of a polyhedral edge (m) N = Number of polyhedral nodes (-) -3 푛푃 = Density of protons during fusion (m ) -3 푛퐵 = Density of boron atoms during fusion (m ) -3 푛푒 = Density of electrons in the core (m ) 푃 = Fusion power generated (W) 풫 = Period between fusion events (s) 푟1 = Inner (core) radius of electrode (m) 푟2 = Outer radius of electrode (m) 푟푖푐 = Radius of the inner core (m) 푇푒푉 = Electron temperature (eV) 푡푤 = Wall thickness of electrode (m) 휙 = Raised core trap potential (V) 2 휎퐹 = Fusion cross section (m )

46 | P a g e

1. Introduction Inertial Electrostatic Confinement (IEC) as a concept for fusion power generation has been around since the mid-1960’s. Since that time, the concept has been researched and refined as a fringe approach to fusion power, with the general consensus being that fundamental issues such as ion thermalization will remain insurmountable to ever achieving – let alone exceeding – breakeven operation [1]. A particular development path, ongoing since 2000, has sought to address this issue through advancement of the ion confinement mechanism. A key development was the realization the that the single cathode accelerating mechanism is naturally defocusing to the ion stream, causing a mean ion lifetime of only a dozen or so passes through the system before impacting the cathode. Since the mean free path for fusion is on the order of a million passes, the yield for such devices is quite low [2]. It was also seen that the electrode feed stalks created large field asymmetries that contributed to rapid ion loss to the electrodes. The introduction of additional electrodes at different radial locations was found to stabilize the ion paths, even against feed stalk asymmetries, increasing their lifetime in the device 1000-fold. As the ion lifetimes grew, a coupling between the two-stream instability and the natural trap kinematics was shown to cause the ions to form long-lived diametrically opposed bunches along the channels formed by the electrode grid openings. These bunches became synchronized among the channels, all reaching the center of the device simultaneously [3]. It was theorized that by limiting the counter- streaming ion bunch interaction to the core of the device that the low-angle collisional processes that lead to rapid ion thermalization could be kept in check. For such a device to work, the ions would need to be well localized, both radially and azimuthally, perhaps using active control along the channels. They would also need to be shielded against their own space charge while in the core. A means of providing highly controllable electric and magnetic fields along the channels and confining an electron population in the core would be required, while still offering a highly transparent and unobstructed path for fusion products to escape so that direct energy conversion can take place. Thus, was born the concept of the continuous electrode (CE-) IEC.

2. Concept Overview The notional configuration of the CE-IEC can be divided into four main radial regions, as shown in Fig. 1. In radially increasing order, these are the 1) inner core, 2) outer core, 3) focusing region, and 4) power conversion region. The focusing region is where the continuous electrode structure resides. The bulk electrode structure can be thought of as a radial extrusion of the edges of a polyhedron. The cavities formed where the polyhedral faces would normally reside then become open channels through which the Fig. 1. Four distinct radial regions of the device ion bunches recirculate as they pass in and out of the core. This region is where the ion packets are continuously refocused and compressed to maintain them in a compact form against the natural spreading that results from their own space charge and low angle collision events. Although the ions are in localized bunches, the paths along the centers of these cavities from one end of the device to the other will often be referred to as beamlines. For a single species fuel (D-D for example) only two diametrically opposed ion bunches will be present along each beamline at any given time, so only one bunch per channel. For a two-species fuel (p-11B for example), four diametrically opposed packets will be present – one pair for each of the two species – and therefore there will be two bunches per channel, separated radially. The recirculating ion bunches start near the outermost edge of the SE and fall through the potential drop from the focusing region radially inward, first into the outer core. The outer core is the transition region where the ion bunches pass initially into and then out of the confined electron

47 | P a g e population on the opposite side. As they pass into the outer core, the electron population responds by being attracted to the ion bunches to neutralize their space charge. This allows the ions to then further compress along their primarily radial trajectories as they fall into the inner core. The inner core is then the central region within which the ion packets interact collisionally. The size of this region is ideally small, and is determined by the bunch sizes and trajectories. The collisional processes within the inner core include energy and momentum exchange, and of course fusion.

2.1 Slowing/Halting Thermalization Low-angle collisions among opposing bunches, which would normally result in azimuthal thermalization, instead simply reshuffle the specific radial trajectories along the beamline that the individual ions will follow as they exit the core. Upon refocusing, the azimuthal velocity distribution within each bunch should be indistinguishable from the start of the previous pass, cancelling the azimuthal momentum growth. Likewise, low angle scatters among the non-opposing packets can introduce both azimuthal and radial (energy) scattering. However, on average these scattering events will both up-scatter and down-scatter the ions equally, so again upon refocusing, the net ion energy within each packet due to low angle ion-ion collisions should remain the same.

2.2 Ion Particle and Energy Loss Mechanisms A separate effect is the drag experienced by the ions due to the electrons, transferring energy out of the ion packets. This represents a net energy loss, however continuous injection of new energetic ions into the packets may be sufficient to address this loss. This balance is to be investigated. High angle scatters present the possibility of scattering the fuel ions into the inner edge of the continuous electrode structure, therefore it is paramount to construct the electrode to be as transparent as possible as viewed from the center of the system. If the scattering angle of the ion does not cause a collision with the electrode, then the ion should simply end up within a different channel, where the refocusing process will merge the ion into the local packet. If the electrode transparency as seen from the core were 85%, a close encounter between fuel ions will only result in a possible wall collision 15% of the time. This allows more opportunity for fusion to occur. Similarly, high transparency is necessary to allow the fusion products to escape the core through the focusing region to reach the power conversion region. An 85% transparent electrode will subtend 15% of the fusion product paths, meaning that 15% of the fusion power output could end up as heat on the electrode. This will ultimately establish the operational limits on the system and will factor into system sizing.

2.3 Energy Conversion The outer edge of the focusing region represents the maximum radial extent to which the fusion fuel ion bunches must reach, with only fusion products being energetic enough to extend out into the power conversion region. The fusion products enter this outermost region with a nearly isotropic angular distribution, arriving in pulses a few nanoseconds long separated by several microseconds. Such a pulsed output may be ideal for using a technology such as Traveling or Standing Wave Direct Energy Conversion (T/SWDEC) [4].

3. Top-Down Reference Design The following presents a first cut at a self-consistent set of design and operating parameters for a full power generation system based on the continuous electrode design. The choices of parameters are not meant to be optimal, but allow for establishing a baseline from which a better point design can evolve. Detailed modeling, analysis and optimization of each of the subsystems is ongoing and will be discussed in future publications.

48 | P a g e

Continuous Electrode Geometry As mentioned, the continuous electrode can be thought of as a radial extrusion of the edges of a polyhedron. The main requirement for selection of the polyhedron is that its faces come in diametrically opposed pairs, creating the opposing channels of a beamline. So, while something as simple as a cube could work, a pyramid would not. If the walls are assumed to be thin, then the total amount of volume that all of the ion bunches have to expand into is generally the same regardless of the total number channels (faces). The thing that more channels do provide is a greater level of control over the ion bunches. The ions divided among smaller volume bunches will be closer to the channel walls on average, and therefore more affected by the electric and magnetic fields that they generate. However, as the number of channels grows, so does the number of edges, and at the inner electrode edge, a minimum achievable wall thickness will mean an ever-decreasing system transparency. For the remainder of the analysis it will be assumed for reference that the inner radius of the continuous electrode is at 푟1 = 0.5 푚, the outer radius is at 푟2 = 1.0 푚, and the wall is uniformly 푡푤 = 1.0 푐푚 thick. An entire family of highly symmetric electrode options is provided by the geometry of the fullerenes

– carbon molecules that form closed polyhedral cages [5]. Fullerenes are labeled as CN, where N is the number of carbon atoms in the molecule. Of particular interest are those of icosahedral (-Ih) symmetry, such as C20, C60, C80, C240, etc., where a necessary condition is that N must be a multiple of 20. For each of these, 12 faces are always pentagons and the rest are always hexagons. A regular truncated icosahedron (RTI) has edges of equal length, but the hexagonal faces have an area that is about 60% larger than the pentagons. This is the geometry of the C60 molecule, also called Buckminster Fullerene. However, the truncation of the icosahedron can be done in such a way that instead of ending up with the edges all the same length, one can achieve a geometry where instead the two types of faces can be inscribed by circles having the same area. This makes the resulting channels more equivalent. An image of this geometry is shown in Fig. 2, where it can be seen that the hexagons are now only 3-fold symmetric. This geometry will be referred to as the special irregular truncated icosahedron (SITI) and will be used as the baseline for design purposes.

Transparency, Volume and Mass Adequate geometric relationships are achieved by considering an RTI and approximating the total surface area of the polyhedron as being equivalent to the total curved surface area of a circumscribed sphere. This 2 surface, at a given radius (r), is equally divided among F flat faces, 12 of which are pentagonal (퐴퐹 = 1.7 푙퐸), 2 and F-12 of which are hexagonal (퐴퐹 = 2.6 푙퐸), with 퐴퐹 the area of the face, and 푙퐸 the length of an edge. The total edge area can be mapped by attributing the nearest half of the edges surrounding each face to that face, and then summing over all faces. The transparency is then approximated by taking the ratio of the total edge area to the spherical surface area, and subtracting from unity, as given by Eq. (2) 퐴퐸 3푙퐸푡푤(퐹−2) 푡푤 푇 ≈ 1 − = 1 − 2 ≈ 1 – 1.3 √퐹 (1) 퐴푆 4휋푟1 푟1 For the RTI (and approximately for the SITI) the transparency using the baseline design values is

~85%, consistent with the example value assumed above. For comparison, the C240 geometry with the same dimensions would have an inner edge transparency of only ~71%. However, while Eq. (1) is appropriate for the recirculating fuel ions, this actually represents an overestimate for the fusion products because it assumes that all of the fusion takes place at a single point at the center of the core. As the spatial extent of the fusion volume (inner core) grows, some fusion products will have trajectories that can hit the broad side of the wall surfaces with grazing incidence, reducing the effective system transparency. As the details depend on better knowledge of the achievable Fig. 2. Continuous electrode resulting from an SITI

49 | P a g e

core volume compression, this effect will not be addressed in the current analysis. The volume, and therefore the mass of material making up the electrode can be estimated by treating each wall segment as the difference between the sector of a circle with outer radius 푟2 and inner radius 푟1. Summing over all E edges of the polyhedron, the material volume can then be estimated as 2 2 푉 = 3.3 푡푤√퐹 (푟2 − 푟1 ) (2) and for the assumed parameters, this gives a total electrode volume of 0.14 푚3. The structure of the electrode will be complex, with radial segmentation, embedded feedthroughs, permanent magnets and internal structure to maintain the potential profiles. As a gross over-estimate, if the electrode were to be constructed out of solid neodymium (to provide the magnetic field – discussed later), the present electrode would have a mass of ~1000 kg (1 metric ton). Assuming that this represents a large fraction of the total system mass (say ~50%), then to achieve a target system specific mass of 2 kg/kW, the power output of the system must be at least 1MW.

Fusion Fuel Parameters As a conservative estimate, an overall power conversion efficiency of 75% will be assumed for now. Given the large energy density of fusion fuels, the impact of the conversion efficiency is less concerned with the efficient use of the fuel, and more about disposition of the wasted power. This will be addressed later in the paper. The fusion fuel that will be assumed for the baseline design is p- 11B (see Fig. 3.). Advanced fuels are notoriously challenging to burn as a result of lower fusion cross sections and higher energy requirements, however the aneutronic nature of p-11B, make it an appealing candidate for use in space. One issue with p-11B is that to burn the fuel in a thermal plasma near its peak fusion cross section (1.2 barns @ 550 keV) actually produces greater energy loss due to Bremsstrahlung within the electron population than what is generated by the fusion process [1]. It is expected that the temperature of the neutralizing electron population in the current system will be such that this loss is not significant.

Ion Energy Even targeting the peak cross-section, it may be possible that the average electron temperature in the core can be maintained below this level in the current system, since as will be shown the ions only pass through the electron core with a low duty cycle. However, for now the baseline system will avoid the issue altogether by targeting the narrow resonance in the p-11B fusion cross section that is located very near to 148 keV. This resonance offers a fusion cross section of 0.1 barns (10- 25 cm2), which is only 8% of the p-11B fusion peak and about 0.3% of the D-T fusion peak (34.3 barns @ 64 keV) [6]. However, it also reduces the cost of losing an ion by 400 keV per ion. The reason that leveraging this resonance is a possibility is that the ion focusing may be able to maintain a somewhat narrow spread in energy Fig. 3. Fusion Cross-sections for a variety of fuels that can be placed on top of the resonance. Although the required ion densities will be higher, other system losses are substantially reduced.

Duty Cycle and Power Output The radial potential profile across the device will not be parabolic, and in fact it is desirable from an ion bunch stability standpoint to have the period of oscillation increase with ion energy [7]. It is also necessary that the proton and boron bunches oscillate at the same frequency, requiring a non-

50 | P a g e parabolic profile. Nevertheless, for the purpose of estimating the period and duty cycle of the fusion output, a parabolic profile with a drift region across the core will be assumed. To achieve the necessary 148 keV center of mass energy with zero net momentum in the device frame, the speeds of the proton and boron bunches as they pass through the core of the device must be 5.1(106) m/s and 4.6(105) m/s respectively. The peak potential to confine the protons is then 136 kV. For the boron ions, the confining potential when they are fully ionized is only 2.4 kV, but when they are first introduced as singly ionized particles they must be injected at 12 kV. Injecting the boron atoms so low into the potential well is one of the many challenges. Since the potential profile is generated solely in the focusing region, the ions will drift through the core at constant speed, which will add time onto the oscillation period. Under a parabolic profile with drift, the transit time of the protons across the device is 0.7 µsec, and that of the boron atoms is 4.8 µsec, demonstrating that the profile will need to be modified to match the transit times across the system. Using the boron period as the limiter, the fusion pulses would occur at just over 208 kHz. The fusion occurs only within the inner core, where the fuel atoms collide. Ideally, the inner core volume would be highly focused, confined to a region that is perhaps no more than a few centimeters in diameter. A more conservative value might be an inner core diameter of 10 cm in the current example, exhibiting a 10:1 ion compression (in bunch radius) from the outer to the inner core. At their peak velocity, the proton bunches will pass through this inner volume in only 2 nsec, so that the fusion output occurs at a duty cycle of only DC = 2 nsec / 4.8 µsec = 4.2(10-4). This is a possible disadvantage of the current approach, as the fusion output during the pulse must be 2600 times greater to achieve the same average power output as if it occurred continuously. In general, the average power output is given by 16휋 푃 ≈ 휂 푒퐸 푛 푛 휎 푟4 (3) 3휏 퐹 푃 퐵 퐹 푖푐 where 휏 is the transit time of the fuel ions and the rest is the energy output per pulse. At constant inner core density, it can be seen that large gains can be made by increasing the inner core radius (less focusing, but larger fusion volume). However, this also means more recirculating current through the device and a lower transparency to fusion products. Resolving this trade-off will be the subject of future analyses.

Core Density and Recirculating Current For the assumed performance parameters, the density of both proton and boron atoms in the inner B-Field Lines 22 −3 core must be 푛푃 = 푛퐵 = 6.32(10 ) 푚 , assuming 휂 = 75% and 퐸퐹 = 8.7 푀푒푉. As they expand through the outer core, the ions separate into 32 individual proton bunches and 32 individual boron bunches, all moving toward their respective channels and spreading out, at least azimuthally but possibly Core also radially. As each bunch passes out of the outer core, the bunch density relative to the inner core is Permanent therefore reduced by a factor of up to 64,000 (recall Magnets the 10x radial compression) to a value of 푛푃 = 푛퐵 = 9.9(1017) 푚−3, with the protons continuing to Channel expand to the outer edge of the focusing region, where the density is again reduced by up to a factor of eight. The proton current through a given channel Fig. 4. Cut-away of CE showing B-field lines, magnets as the bunch leaves the outer core would then be 79 embedded in walls and potential profile. kA, and the boron current at the same location (1 µsec later) would be 36 kA.

51 | P a g e

Core Electron Population and Confinement When the ions are outside of the core, the electrons will spread out due to their own space charge. The electron population that is needed to fully neutralize the ions passing through the core is equal to one electron for each proton and five for each boron, assuming full ionization. When the electrons spread out, they will occupy a volume that is 1000 times larger (0.5 m outer core 20 −3 diameter), and if uniform the electron density is then 푛푒 = 3.8(10 ) 푚 . The primary means of electron confinement in the core is by a cusped magnetic field, although a reversed electric field at the inner edge of the focusing region might also be established. The effectiveness of the electron confinement will depend on the equilibrium temperature of the electrons. The magnetic field is achieved through the placement of permanent rare Earth magnets within the continuous electrode walls. The configuration will have either all North or all South poles aligned with the inner edge of the electrode. The field lines must then thread up through the channel openings to connect with the opposite magnetic poles, as shown in Fig. 4. This will create a cusped field on the inner edge of the walls, and down the middle of each channel. Recent work [8] has shown that electron confinement of this type in PolywellTM devices improves with increasing 훽, the ratio of plasma pressure to magnetic pressure. Surface currents in the electron population resulting from steep pressure gradients compress the magnetic field and constrict the electron escape paths. At 훽 = 1, the electrons are held in check by the full magnetic pressure, provided such a condition can be achieved. To estimate the field strength in the channels, consider that the entire magnetic flux leaving the inner edge of the electrode must pass through the channel opening at the inner radius and continue up the channel. Assuming a uniform field across the edge of the wall, and likewise into the channel opening, flux conservation requires that the ratio of the magnetic field strength through the channel to that on the magnet surface must be inversely proportional to the respective flux areas. This ratio is known from the transparency. At the assumed 85% transparency, the ratio of the strength of the field in the channel to that at the face of the electrode is then 15/85, or about 18% of the field strength at the wall edge. The surface field strength for an N52 grade neodymium magnet can be as high as 7400 G [9], which would mean a 1300 G peak field in the channel. The maximum electron temperature that can be confined solely using a magnetic field is found by equating the electron pressure with the magnetic field pressure 푝 훽 퐵2 푇푒푉 = = (4) 푛푒푒 2휇0푛푒푒 which for 훽 = 1 and the parameters given above will support an electron temperature of only 110 eV. While it is expected that the electron temperature will be less than the ion energies, this value seems problematic. However, it is also possible to raise the potential within the core relative to ground to provide additional confinement. Assuming the electrons to be Maxwellian distributed, the fraction of the particles that can escape a well of depth 휙 is given by 푛(휙) 2 2 = 푒푟푓푐(푥̅) + 푥̅푒−푥̅ (5) 푛0 √휋 휙 where 푥̅ = √ . As the well potential increases relative to the electron temperature (increasing 푥̅), 푇푒푉 a smaller fraction of the particle density can escape the well. If it is assumed that the electron temperature is on the order of 1 keV, the trap potential that allows Eq. 4 to be satisfied is 6 kV, whereas if the electron temperature reaches 5 keV, the trap potential must be 24 kV. Even with the pressure balance satisfied, electrons will still be lost through the cusps. Electrons that approach the cusp with a sufficiently low pitch angle (more parallel to the field line) will not be turned around before the point of maximum field strength. Therefore, some amount of electron leakage current will exist. Fig. 4 showed the magnetic field lines extending from the innermost edge of the CE to the outermost edge, however, a better configuration would be to have the outer termination point of the field lines intersect the walls farther down in the potential well. It is then possible that electrons passing through the cusp will be guided to the wall by the magnetic field and be absorbed at a potential that is closer to that of the core, reducing the power loss by escaping

52 | P a g e electrons. This would be far preferable to the electrons being accelerated to the top of the CE, where each electron lost would represent a cost of 148 keV. Additional magnetic field loops can be placed farther up the wall by alternating the North and South poles of the magnets. In the null region between each magnetic field loop, the electron velocities will tend to randomize, so making it through the first cusp will not guarantee that an electron would make it through consecutive ones, further increase the chances that the electron paths will terminate on the wall prior to reaching the anode potential.

Direct Energy Conversion Fusion products (alphas) that end up passing through the open channels will be energetic enough to escape the confining potential of the focusing region and reach the energy conversion region. Here their kinetic energies will be converted via a radio frequency direct energy conversion (DEC) system. One such system is the Standing Wave DEC (SWDEC) [10]. The operation of the SWDEC is illustrated frame-by-frame for a simplified 1-D implementation in Fig. 5. In 1-D, consider a series of ring-shaped electrodes, through which passes a localized bunch of ions. The ring electrodes are biased such that all odd numbered electrodes share the same phase, and all even numbered electrodes are 180 degrees out of phase. In frame #1, the ion bunch approaches the first ring, which is rising toward its peak Fig. 5. Frame-by-frame illustration of the SWDEC potential. The bunch therefore sees a positive potential deceleration mechanism using ring electrodes [10]. gradient and is decelerated. As the bunch passes through the center of the electrode, the phase of the electrode biases reverse, so again the ion bunch sees a positive gradient and continues to slow. By placing consecutive rings closer together to compensate for the reduced bunch velocity, this mechanism continues until most of the energy has been removed. If the electrodes are part of the capacitive element of a tuned RLC circuit, the ion bunches act as a driving force on the circuit, increasing the oscillation amplitude by pumping energy into it. This energy corresponds to the loss of kinetic energy of the bunch. The resistive element of the circuit is the load, which could be operating equipment or an energy storage device. An analysis of such a device in [10] demonstrated conversion efficiencies in excess of 90%. For implementation in the outer region of the CE-IEC, each ring in Fig. 5 would be a at a specific radius. However, instead of individual rings, each radial layer would consist of a thin walled honeycomb, offering a very high transparency, but allowing the ions to strongly couple to the electrodes. At the outermost radius of the SWDEC, the alphas would be allowed to driven into an electrode where they would be neutralized and allowed to pass out into space. The charging of this electrode due to electron loss could also potentially be used to convert the last remaining 10% of the ion kinetic energy into electricity. One challenge with the SWDEC implementation is that ideally all fusion products would be produced at the same energy, arriving at the same time and with the same velocity. In addition to some random variation, it is well-known that the three alpha particles of the p-11B reaction are not formed simultaneously with the same energy. As far back as 1936 [11] it was determined that two of the (secondary) alpha particles are formed with equal energies ranging from 3.8 MeV to 4.4 MeV each from the decay of an excited state of 8Be, with the primary alpha particle receiving typically less than 1.0 MeV. While it would be nice to extract the energy from all three alpha particles, the two higher energy alpha particles typically contain at least 88% of the available energy of the reaction. Of

53 | P a g e greater importance is designing the SWDEC so that it can convert as much of the secondary alpha energy as possible, despite the 0.6 MeV spectrum width. In addition, it is desirable that the primary alphas are able to leave the system, rather than being captured in the fuel recirculation region.

Power Dissipation and Sputtering The innermost edge of the CE will see heating due to high angle scattering of fuel ions, as well as intercepting a fraction of the fusion products. Heating of the permanent magnets is undesirable, as it may lead to de-magnetization. To mitigate this, a standoff will be constructed conformally to the inner edge of the CE, separated from it by an insulating layer. The material of this stand-off would ideally have a very high melting point and be resistant to sputtering. These requirements are related, since energetic particles impacting this surface will deposit both energy and momentum, which will cause heating and sputtering. Regarding the heating, the majority of the power deposited into the material will come from the assumed 15% of the fusion products that it intercepts on their way out of the core. At 1 MW output, 1.14 MW of ion power must reach the SWDEC, if it is assumed that only 88% of the power (100% of secondary alphas only) is extracted. This 1.14 MW must then represent the 85% of ions that pass through the channels, leaving 200 kW (15%) of power deposited onto the standoff. The area of the standoff is 0.47 m2, so to radiate this much power (assuming an emissivity of 0.8) requires a surface temperature of 1750 K. For reference, the melting temperatures of tungsten and carbon are 3700 K and 4500 K respectively, so there are materials that can likely withstand the temperatures. The radiated energy (peaking near 1 µm) will experience some absorption into other surfaces as it leaves the system, which is an effect that will have to be evaluated. Sputtering is a potential problem due to the energetic alphas, carrying energies up to 4.4 MeV. Sputtering data for alpha particles at these energies are fairly elusive, but to get an idea of expected sputtering levels, a comparison will be made to work conducted at Sandia National Labs in 2005 [12]. In this work, the focus was on the evolution of surface morphology of diamond by gallium ions with 20 KeV incident energy. The comparison is admittedly apples to oranges (the gallium atoms are singly charged initially, but can potentially reach a fully charged state of +31) but at a molecular weight of nearly 70, the momentum carried by 20 KeV Ga ions is nearly 40% of the momentum carried by 4.4 MeV alphas. The normal incidence sputtering due to Ga+ was found to be ~2.5 atoms per incident ion, so it will be assumed that the alphas will sputter material at roughly 5 atoms per incident ion. The flux of alphas to the surface (~400 kW/m2) is then ~5.6(1017) particles/m2/sec. The surface density of carbon atoms in a monolayer (assuming 154 pm bond length) is 4.2(1019) particles/m2, so the depth erosion rate is estimated to be 0.013 monolayers/second, or 63 µm/year. Even at 10 times this erosion rate, a 1 cm thick standoff could last for several years before needing replaced.

Conclusions and Future Work This paper has presented an introduction to the concept of the Continuous Electrode Inertial Electrostatic Confinement approach to fusion power generation in space. The top-down design parameters were presented assuming a nominal power output of 1 MW. Sizing of the system was arbitrary to establish a baseline, and current efforts are underway to determine the minimum system size that is required to produce a given power output. Such an analysis will then lead to an understanding of the specific mass (kg/kW) of the device as it scales to different power levels, with a desired target of less than 2 kg/kW. Successful implementation of the concept will rely on comprehensive modeling of the electron confinement, in particular as the ion bunches traverse in and out of the core region, as well as the evolution of the ion population and the effectiveness of active control. Both of these efforts are also currently underway. There are many other implementation details of the technology, such as injection of the fuel into the potential well, many of which have preliminary solutions that are yet to be fleshed out.

54 | P a g e

Acknowledgements This work has been funded in part by the NASA Space Technology Research Fellowship (NSTRF) Program (Chap – Grant #NNX13AL44H), the University Maryland Department of Aerospace Engineering AEROS Scholarship Program (Schilling), and most recently the NASA Innovative Advanced Concepts (NIAC) Program (Grant #NNX17AJ72G). The authors wish to acknowledge collaboration with the NASA Johnson Spaceflight Center Propulsion and Power Division on the topic of RF Direct Energy Conversion.

References [1] T. H. Rider, “Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium”, Physics of Plasmas 4, 1039 (1997); doi: http://dx.doi.org/10.1063/1.872556 [2] T. J. McGuire, and R.J. Sedwick, “Improved Confinement in Inertial Electrostatic Confinement for Fusion Space Power Reactors”, AIAA J. of Propulsion and Power, 2005, Vol.21: 697-706, 10.2514/1.8554 [3] C. Dietrich, L. Eurice, and R.J. Sedwick, “Experimental Verification of Enhanced Confinement in a Multi-Grid IEC Device”, 44th AIAA/ASME/SAE/ASEE JPC, 2008. [4] A. M. Chap and R.J. Sedwick, “One-dimensional semi-analytical model for optimizing the standing-wave direct energy converter”, J. of Propulsion and Power, September, Vol. 31, No. 5, pp. 1350-1361, 2015. [5] P. Schwerdteger, L.N. Wirz and J. Avery, “The topology of fullerenes”, WIREs Comput Mol Sci 2015, 5:96–145. doi: 10.1002/wcms.1207 [6] http://www.fisicanucleare.it/documents/0-19-856264-0.pdf [7] D. O. Zajfman, M. L. Heber, Rappaport, H.B. Pedersen, D. Strasser, and S. Goldberg, “Self- bunching Effect in an Ion-trap Resonator,” J. Opt. Soc. Am. B, 20 (5), pp. 1028-1032 (May 2005). [8] High beta confinement [9] https://www.kjmagnetics.com/calculator.asp?calcType=block [10] A. M. Chap and R.J. Sedwick, “One-Dimensional Semi-analytical Model for Optimizing the Standing-Wave Direct Energy Converter”, AIAA Journal of Propulsion and Power, Vol. 31, No. 5 (2015), pp. 1350-1361. doi: 10.2514/1.B35439. [11] P.I. Dee, C.W. Gilbert, Proc. R. Soc. Lond. A 154, 279 (1936) [12] T. M. Mayer D.P. Adams, M.J. Vasile, and K.M Archuleta, “Morphology evolution on diamond surfaces during ion sputtering”, J. Vac. Sci. Technol. A: Vacuum, Surfaces, and Films 23(6), 1579 (2005) doi:10.1116/1.2110386

55 | P a g e

DIRECT FUSION DRIVE FOR INTERSTELLAR EXPLORATION

S.A. Cohen1*, C. Swanson1, N. McGreivy1, A. Raja3, E. Evans1, P. Jandovitz1, M. Khodak3, Gary Pajer2, T.D. Rognlien4, Stephanie Thomas2, and Michael Paluszek2 1 Princeton Plasma Physics Laboratory, Princeton NJ, USA 2 Princeton Satellite Systems, Plainsboro, NJ, USA 3 Princeton University, Princeton, NJ, USA 4Lawrence Livermore National Laboratory, Livermore, CA, USA *Corresponding author, [email protected]

The Direct Fusion Drive rocket engine (DFD), based on the Princeton Plasma Physics Laboratory’s Princeton Field Reversed Configuration machine, has the potential to propel spacecraft to interstellar space and to nearby solar systems. This paper discusses a design for a starship that would be well suited to a variety of solar system and interstellar missions. DFD employs a unique plasma heating system to produce nuclear fusion engines in the range of 1 to 10 MW, ideal for human solar-system exploration, robotic solar-system missions, and interstellar missions. This paper gives an overview of the physics of the engine. Its innovative radiofrequency (RF) plasma heating system and the fuel choice are explained. The thrust augmentation method is described along with results of multi-fluid simulations that give an envelope of expected thrust and specific impulse. The power balance is described and the subsystems needed to support the fusion core are reviewed. The paper gives the latest results for the system design of the engine, including just-completed work done under a NASA NIAC study. A mass budget is presented for the subsystems. The paper then presents potential interstellar missions. The first are flyby missions. One is the proposed 550-AU mission that would use the Sun as a gravitational lens for exoplanet research. This mission can be done without a deceleration phase. Next, flyby missions – requiring major technological advances – to the nearest star are described. Finally we sketch a mission to orbit a planet in either the Alpha Centauri A or Alpha Centauri B systems. The mission analyses include a communications system link budget. DFD can operate in an electric-power-only mode, allowing a large fraction of the fusion power to be used for the payload and communications, enhancing the scientific return. All of the missions start in low earth orbit.

Keywords: Nuclear Fusion, Propulsion, Gravity Lens, 550 AU, Exoplanets, Alpha-Centauri, Interstellar

Nomenclature B = magnetic field -field energy density c = speed of light cs = ion sound speed E = ratio of plasma FRC plasma core length to diameter

LH = Lower-hybrid drift instability growth rate Ip = plasma current Isp = specific impulse MT = metric ton, 103 kg q = plasma safety factor rs = FRC core plasma radius s = 0.3 rs i S* = rs pi/c Th = Thrust, A = Alfvén time ~ rsE/cs, pi = ion plasma frequency

56 | P a g e

1. Introduction The idea to use fusion power for spacecraft propulsion has a long history [1, 2], with its support arising from the high energy density of the fuel and the high velocity of the fusion products. Early proponents of fusion rockets that provided steady – rather than pulsed or explosive – propulsion based their designs on the fusion devices that were then in vogue, tokamaks [3, 4], mirror machines [5] and levitated dipoles [6]. The experimental results of that period in fusion history indicated that the plasma’s anomalous transport, meaning poor plasma energy confinement, -T burning, large and powerful machines, many meters in diameter, producing over a gigawatt in power and requiring a meter or more of neutron shielding. Such large and massive devices could not be launched fully assembled; upwards of 100 launch vehicles would be needed. Such daunting and expensive proposals never proceeded beyond the conceptual stage. Recently, new designs of fusion devices, bolstered by experimental successes on prototypes, have raised optimism for the prospect of considerably smaller fusion-powered rockets that are far lighter, less radioactive, and less costly. Commensurate with their reduced size, these rocket engines would produce only megawatts of power [7], nevertheless ample for a wide variety of missions in the solar system and beyond. The common feature of these rockets is the geometry of the magnetic field that confines the plasma. The “family name” for these fusion-reactor designs is field-reversed configuration (FRC), a label derived from the original plasma-formation method, not the shape of the field, as commonly thought. for terrestrial fusion power production. -linear geometry, reduce the required peak magnetic field by about a factor of 3 compared to a tokamak’s. Lighter -called aneutronic fuels, e.g., D-3He, whose main reaction produces far fewer neutrons than D-T fusion. Accordingly, less shielding (mass) is required. One member of the FRC family – the inductively driven, liner-compression Pulsed-High-Density (PHD) device – was designed to operate in a pulsed mode with D-T, producing an average power of 70 MW. Another FRC family member is the Star Thrust Experiment (STX) [8], a 1-m plasma radius design, formed and heated by an RF technique called rotating magnetic fields [9, 10] (RMF). An STX rocket engine was predicted to be able to produce steady propulsion at a power level near ½ MW/m of length. In this paper we describe a 3rd member of the FRC family, the D-3He-fueled Direct Fusion Drive (DFD) rocket engine [11]. Similar to STX in employing RMF, the DFD differs in major ways, ones that would result in a more practical rocket engine. Important differences are: 1) the DFD RMF method has different symmetry [12] (odd-parity versus even parity, RMFo vs RMFe), providing improved energy confinement hence allowing plasmas with 4-8 times smaller linear dimensions and 100-400x smaller volume and mass; 2) The smaller radius DFD plasma is far more stable than the larger STX plasma; 3) the smaller radius of the DFD plasma allows a method to improve the 4 properties of the rocket exhaust, with specific impulse, Isp, to 2 x 10 s (and beyond) and thrust, Th, to 10 N/MW; 4) DFD operation reduces neutron wall fluxes more than a factor of 1000 compared to D- T devices, thereby reducing neutron shielding thickness by a factor of 10 and increasing engine lifetime; and 5) increased attention to the engineering details of the complete rocket engine, such as improving energy-recovery systems, raising specific power, and optimizing plasma heating and fueling systems. In section 2 of this paper we describe the physics of the DFD’s fusion core, explaining how the novel RMFo method improves energy confinement, current drive, plasma heating, and plasma stability. Section 3 described the choice of fuel, the neutron production rate, and the power balance. Section 4 describes how the energy in fusion products produced in the core is converted into directed momentum for propulsion. Section 5 describes two missions relevant to interstellar exploration.

57 | P a g e

2. The DFD Rocket Engine Core The region where abundant fusion reactions take place is the high temperature (ca. 100 keV), moderate density (ca. 5 x 1014 cm-3) plasma region named the core. For the FRC, this region is inside a magnetic separatrix, an imaginary closed surface that demarcates open magnetic-field lines, those that leave the device, from closed magnetic-field lines, ones that stay fully inside the device, see Figure 1. The open field-line region is also called the scrape-off layer, SOL. To form the closed magnetic-field lines, a strong plasma current is needed, perpendicular to the FRC’s magnetic field.

On axis, the direction of the magnetic field created by the Figure 1. FRC sketch, adapted from Ref. plasma current, Ip, is opposite to that of the open field lines which are created by external coils. If the axes of the two fields are not exactly parallel, MHD theory [13] predicts that the configuration will strongly tilt and destroy itself. In the following subsection we shall describe how RMFo generates the current and heats the plasma ions and electrons in such a way as to allow smaller devices with excellent stability, not susceptible to the tilt mode.

2.1. Macro-stability MHD theory has shown itself to be accurate in predicting the stability of plasmas that are fluid-like [14]. Fluid-like plasmas are prone to several classes of instabilities. Criteria that determine whether a magnetized plasma is fluid-like are collisionality and the ratio of particle gyro-radii to machine size. Highly collisional, that is, cold and dense, plasmas are fluid-like. Plasmas where the ion gyro- i, are small compared to the plasma radius, rs, are likely to be fluid-like. For an FRC, the size criterion is defined by two nearly equivalent dimensionless parameters: 푠 ≅ 0.3 푟푠/휌푖 and ∗ 푆 ≡ 푟푠휔푝푖/푐 pi is the ion plasma frequency and c the speed of light [15]. By choosing a small, high-temperature FRC, neither fluid criterion is satisfied and the plasma is said to be kinetic rather than fluid-like. Why a kinetic plasma is stable against the tilt mode can be understood by considering the axis-encircling orbit of a single charged particle in a magnetic field, a stand-in for a hot plasma. An axial push to the particle, in an attempt to tilt its axis, causes the particle to translate along B, not to tip over. No tilt occurs. More complicated explanations can be extracted from Steinhauer’s review [16]. It should be noted that several FRCs [17, 18, 19, 20] have achieved stable 3 5 plasmas for durations 10 to 10 A. (Stability is predicted [15] for S*/E < 3.) The plasma durations were limited by power supply capabilities not instabilities.

We now address how RMFo heats particles and allows the size of the FRC to be relatively small.

2.2. Confinement There are several reasons why energy confinement in FRCs can be good, that is, better than in tokamaks. We first discuss how to keep the FRC confinement from becoming poor! The net magnetic field caused by the external coils and the plasma current creates a nested set of closed field lines inside a separatrix; each closed field line circles the plasma current once poloidally before closing on itself. Closed field lines are good for confinement since they encourage charged particles to stay within the device. Open field lines allow particles and their energy to flow out of the device, i.e., confinement is poorer for open field lines. The addition of RMFe to an FRC causes the field lines to open, see figure 2, while application of RMFo maintains the closure of field lines, figure 3. One explanation is that the FRC, by itself, is of odd parity [21]. Mixing parities, such as by adding RMFe, causes all of an FRC’s field lines to open, hence confinement to degrade. One experimental team [22] has compared even and odd-parity electron heating on the same device and

58 | P a g e found a factor of 4 improvement in the energy confinement time. Another team [19] achieved 5 to

10-fold increases in electron temperature, Te, with RMFo compared to other machines, e.g., Reference [9], of the same size and heating power operating with RMFe.

Figure 3. Magnetic field lines when a larger amplitude Figure 2. A very small-amplitude (Bt = .005), odd-parity magnetic field, Bt = 0.04, is added to a uniform, transverse magnetic field (even Solov’ev FRC. a) Closed field lines in the y – z plane parity) is added to a Solov’ev FRC with B0 = show expansion and contraction but remain closed. b) 1. Two field lines are mapped. Though both Projection of field lines originally in the x – z plane field lines are long, they are clearly open. onto that plane show little change in shape. This FRC’s This FRC’s major axis is vertical [12]. major axis is horizontal [12].

Neoclassical theory [24] predicts that energy losses scale as (1 + q2). For tokamaks q ≥ 3 while for pure FRCs q = 0. Accordingly, FRCs should have about 10x better confinement. Sheffield prepared a survey of confinement quality in tokamaks which Kesner and Mauel updated; the results are shown in figure 4. The point denoted as C-2 represents data from a TriAlpha FRC, clearly better than the tokamak results. Whether the same improvement occurs in FRCs at higher ion temperatures needs to be tested. There are reasons to believe this improvement will occur. First, the main culprit expected [25] to cause anomalous Figure 4. Confinement quality vs ion temperature, Ti. energy transport in FRCs is called the lower- The TriAlpha C-2 FRC device has shown better hybrid drift instability (LHDI), predicted to create mm- to cm-scale turbulence that from Sheffield [23], by Mauel and Kesner.) increases transport. The LHDI growth rate,

LH, is the ratio of the electron drift speed to the ion thermal velocity. As ions get hotter

LH gets smaller and the LHDI should become less important. Secondly, Rostoker [26] and others [27] noted that hot ions and runaway electrons in tokamaks had far better confinement than thermal electrons. The reasons proposed for the large improvement was lower collisionality and less scattering by fluctuations because, like large ships in a

59 | P a g e choppy sea, the large gyro-radii of these energetic particles made them less susceptible to small- scale fluctuations.

2.3. Plasma current drive and plasma heating RMFe was proposed to drive current in the plasma, not to heat it to fusion-relevant temperatures. The current-drive mechanism was explained as being of 2nd order, specifically, the time-varying RMFe -directed electric field (along B), hence a current in that direction, Jz. From the JxB term in the fluid momentum equation, Jz interacted with Br st In contrast, RMFo current drive is 1 order because of its Bz near the FRC’s midplane. The time variation of that field

O-line magnetic null, figure 5, directly accelerating charged particles into betatron orbits near the null, figure 6a). More precisely, the trajectories are punctuated betatron orbits, separated by periods in cyclotron motion. As the particles are accelerated along the null, they gain then lose energy, figure 6b), because the direction halfway around. The more energetic Figure 5. Snapshot of the azimuthal electric field the particles get, the further away from the in the FRC’s midplane created by RMF . This o null they can circulate. In the RMF ’s rotating field rotates with the RMF . o o frame, figure 6c), these punctuated betatron- orbit electrons form a crescent, hence move, on the average, with an azimuthal velocity

equal to that of the RMFo [28]. In an FRC reactor, these current-carrying electrons will have very high peak energy, about 5 times greater than in D-T tokamak fusion reactors, consequently their collisionality will be more than 10x less. This contributes strongly to the high efficiency of RMFo for driving current. Away from the O-line null, the more massive ions will carry an appreciable part of the current and diamagnetism will also provide a substantial part of the required current.

Figure 6a). Punctuated Figure 6c). In the frame rotating betatron orbit near the FRC with the RMFo, the punctuated midplane. At the start and end Figure 6b). As the electron moves gains energy; as it moves betatron trajectory appears as of the betatron segments, the a crescent, with the betatron orbit becomes cyclotron. (Bo = the spikes in energy. segments “inside” the cyclotron 20 kG, rs RMF ci = 0.5) segments.

contribution from the RMFo-created z and r electric fields. That the RMFo frequency should not be far from the ion cyclotron frequency (at the FRC’s center) to allow quasi-resonances, particularly at

60 | P a g e higher harmonics, is seen in figure 7b). Importantly, for both electron and ion heating, the non- uniformity of the FRC’s magnetic field, especially the presence of nulls, causes orbits to lose track of the phase of the RMF, introducing stochasticity into the motion hence net energy gain [29]. Near Maxwellian distributions may develop, though usually the distributions are truncated at higher energy. Note that the required RMFo strengths, to ~ 200 G, and frequencies, 0.3-3 MHz, to achieve ion energies of 100 keV are well within the capabilities of conventional RF equipment. Of course, improvements in RF amplifier efficiency and reduction of amplifier mass would provide important benefits.

Figure 7b). Early time evolution of ion energy for two values of the RMF strength, 2 and 20 G. The quasi- resonances at higher harmonics, 3-5, are evident, as is Figure 7a). Maximum ion energy versus RMFo the stochastic nature of the heating. frequency for different RMFo strengths in a 10- cm radius, 20-kG FRC.

Having a small FRC, allowed because of the better energy confinement, makes RMFo operation better. It improves the penetration of the RMFo field to the FRC’s null line where current drive is more efficient; it requires higher RMFo frequency, which results in higher ion energies ∝ 휕퐵⁄휕푡. As we shall shortly see, other important benefits accrue, ones that result in far lower neutron wall load.

3. Fuel Choice, Neutron Production, and Power Balance The production of neutrons by fusion is particularly problematic for spacecraft propulsion. Neutrons cause damage and activation of nearby materials and structures, limiting their lifetime, necessitating maintenance, and increasing the mass needed for shielding. Neutrons are hard to “direct” hence may contribute little to the thrust required of a rocket engine. Having all the fusion products be charged particles solves these problems at the added cost of requiring higher plasma temperatures because of the lower fusion cross sections of the “advanced” aneutronic fuels. Of the two aneutronic fuels most commonly discussed, we choose D-3He instead of p-11B. The low energy release from p-11B fusion, plus the lower fuel density possible at fixed magnetic field (because of the higher nuclear charge) and the higher temperatures required, makes p-11B a dubious choice. A penalty must be paid for selecting D-3He. There are neutrons from one D-D fusion branch and possibly from the T fusion product of the other D-D fusion branch. Methods must be found to ameliorate these effects.

3.1. Reducing neutron wall load A small FRC allows solutions to these problems. The surface-to-volume ratio scales as 1/radius. For a 25-cm radius FRC, a 32-fold improvement is obtained compared to an 8-m tokamak. Additionally, fusion products born in a small FRC will have their orbits pass through the cool SOL of the FRC where the electron drag is strong. By an

61 | P a g e

“airbrake”-like effect, see figure 8a), fusion products which pass through the SOL even for a small fraction of their birth orbit, will rapidly cool, from 1 Mev to 100 keV, and their orbits will become cyclotron-like, lying fully in the SOL, figure 8b). PIC studies [30] of the slowing down indicate that this process will occur in under 10 ms, far quicker than the estimated 20-s T burn-up time. Once in the SOL, the T+ will be exhausted out the nozzle with the cooler propellant, to be described in section 4. Only those neutrons produced by D-D + fusion will remain a problem. Figure 8a). T trajectory projected on the midplane of + The third step in reducing neutron an FRC. The T slowing down by electron drag in the production is to increase the ratio of 3He to SOL is accelerated to show the transition of the orbit from betatron to figure-8 to cyclotron, the latter lying D in the plasma [31]. This does reduce the fully in the SOL, the region between the red and power density approximately linearly but green circles. the percentage of power in neutrons quadratically. From a neutron-production perspective, Figure 8b). Close-up view the net effect of these 3 measures should be in of the cyclotron segment + excess of a thousand-fold [32] reduction of of the T orbit, showing neutron power flux to the first wall. The thickness that the orbit eventually of the neutron shielding, 100% 10B, would be 10- lies fully in the SOL [30]. 30 cm, based on the duration of the mission and of the fusion-power production.

3.2. Power balance and rocket subsystems In this section we analyze a point design for a DFD rocket engine, focusing on power balance, to see if a consistent solution exists within the stability, energy confinement, and low radioactivity constraints described above. We begin by specifying the plasma density, ion and electron temperatures, plasma radius and elongation, and the external coils inner radius, rc. The latter,

2 relation, < 훽 > = 1 − 푥푠 /2, where xs = rs/rc. Table 1 presents the results of our model with rs =30 20 -3 3 cm, E = 6, Te = 30 keV, Ti = 100 keV, ne = 3x10 m , and a 2:1 He to D ratio. Flat temperature and magnetic field strength, and plasma current, Ip. The next step is to calculate volumetric losses from radiation. Though Bremsstrahlung losses may also be calculated accurately, this is not the case for synchrotron losses because of plasma absorption and wall reflections. Our model assumes full emission from a 3-cm thick shell just inside the separatrix and no wall reflection. Further into the core the magnetic field is lower, hence the frequency lower; absorption of that emitted radiation occurs in the aforementioned shell. The Bremsstrahlung and synchrotron power will be absorbed in the neutron shielding. That energy is recovered with an efficiency of 60% by a Brayton cycle cooling system. Power flow into the gas box ionizes the propellant there. The energy cost is typically 50-100 eV/ion, with higher values required at lower densities. Of that power, 80-90% is deposited on the gas box walls and recovered by the Brayton cycle system. The power flows are depicted in figure 9, which, for this DFD, is providing primarily thrust. If more electrical power is required for station keeping or communications, the thrust power can be diverted to generating electrical power. The distribution of masses is shown in figure 10. This assumes a conservative permitted neutron flux on the superconducting coils, below 1018 n/cm2 and below 10-4 DPA, resulting in a 10-cm-thick 10B

62 | P a g e shield, sufficient for 1 year at full power. Increasing the shielding thickness to 22 cm would increase the superconducting-coils lifetime to 13 years.

Table 1. Parameters for a 2-MW DFD rocket engine. Parameter DFD

rs (m) 0.3 Elongation, E 6

Ba (T) 4.3 Ip (MA) 8.0 Ion species D-3He 3He/D 2 -3 20 ne (m ) 3 x10 Te (keV) 30 Ti (keV) 100 0.84

PRMF (MW) 0.5 6 R (radians/s) 1.6x10 BR/Ba 0.003 Figure 9. Power-flow diagram of a 2-MW DFD. Pf (MW) 2.13 Psynch (MW) 0.7 PBremss (MW) 0.32 PGB (MW) 0.1 classical Ei E 2.7 s (T+) 2.3 s (4He++) 2.2 S*/E 2.8

LH 0.02 RMF penetration 34 Isp (s) 2.3x104 Thrust (N) 12.5

Bnozzle (T) 20 % power in neutrons 1.1 Wall load (MW/m2) 2x10-3

Figure 10. Mass budget of the DFD engine.

We now examine the consistency of this design point with energy confinement, stability, and propulsion. The ratio of the classical confinement time, classical Ei, to the required energy confinement time is 2.7, consistent with the improvement in energy confinement seen by C-2 and PFRC-1. The two stability criteria are also satisfied: the LH micro- LH, is < 1 and macro-stability RMF penetration, is that for RMF field to penetrate in the core of the FRC. This parameter was derived for RMFe not RMFo, so its applicability is questionable. For RMFe RMF penetration must be greater than 1 for penetration. For the DFD, this parameter is above 30, an encouraging margin in light of the possible lack of direct applicability. The neutron wall load for this plasma is 2500x below that specified as acceptable in D-T tokamaks, a sizeable improvement. The amount of thrust power lost in the neutron channel is small, 1%, though could be lowered by increasing the 3He/D ratio.

63 | P a g e

The Isp predicted for the DFD depends on the propellant species and injection rate into the gas box. For Table 1 we have selected a low propellant injection rate, one that produces an Isp above 4 2 x 10 s. For higher propellant flow, Isp would drop and the power required in the gas box would increase along with the thrust, topics we describe in more detail in section 4. A pictorial representation of the subsystems is shown in figure 11 and an artist’s rendition of a DFD module is in figure 12.

Figure 11. Block diagram of DFD major subsystems.

Figure 12. Artist’s rendition of a 2-MW DFD module.

4. The Scrape-Off Layer (Sol) and Rocket Exhaust The SOL of the DFD is quite different than that of any other fusion device. In tokamaks, for example, the SOL is heated and populated by diffusive transport across the separatrix of both energy and particles. The heat transport into it is local, that is, described by Fick’s law, by the local flux- surface-normal gradient in pressure. Because this diffusive transport is slow compared to the flow along the magnetic field, the SOL is onion-skin thin, 훿푆푂퐿, compared to the plasma’s radius. For example, ITER’s SOL is predicted to be ½-cm thick while the plasma outer radius at its midplane is 9

64 | P a g e

훿 푆푂퐿⁄ ≅ 6푥 10−4 m, 푟푠 . It the DFD, the density profile of the SOL is determined by the orifice to the gas box and the field expansion between the gas box and the plasma midplane. For the DFD in Table 훿 푆푂퐿⁄ > 0.2 1, the SOL would be about 7 cm thick, 푟푠 . Energy is deposited across the entire SOL cross section by the large gyro-radii fusion products. Thus the DFD, the SOL + FRC, is more like a navel orange, with a very thick rind. The energy is deposited in the SOL directly from the fusion products via a non-local process and is predominantly transmitted to the electrons via fast-ion drag. The random thermal energy in the SOL electrons is transferred to the cool SOL ions through a double layer at the nozzle and via expansion downstream, thus being converted into directed flow. Because of the relatively low temperature (< 100 eV) and high density (> 5x1019 m-3) of the SOL, resulting in a collisional mean-free-path of the thermal (majority) electrons less than 50 cm, it is appropriate to use a fluid model for the SOL between the gas box and the nozzle. Results from one UEDGE [33] fluid-code simulation are shown in figure 13. In each, the gas box is 1-m long, at the far left, the electron heating occurs in the central 2 m, and the nozzle is located at z ~ 2 m. The inputs were Pi =1 MW of power and 푚̇ = 0.08 g/s of D2 gas into the gas box. (The gas input is equivalent to a current, Ie = 푚̇ 푁퐴 e/amu ~ 3.85 kA, where NA is Avogadro’s number and e the charge on an electron.) From Emax = Pi/Ie, one can then readily estimate the upper limit of ion energy to be 260 eV. As figure 13c) shows, only half that value is reached. The culprits are radiation and ionization losses and plasma energy brought to the gas box walls by plasma transport. The results of an extensive number of simulations are presented in figure 14, showing thrust reaching 10 N/MW.

Figure 13a). Electron Figure 13b). Electron Figure 13c). Ion energy density, n , contours. e temperature, Te, contours. contours.

Figure 14a). Thrust vs gas feed for Figure 14b). Exhaust velocity vs gas feed for powers of 0.25 to 7 MW. powers of 0.25 to 7 MW.

65 | P a g e

5. Missions We describe two missions, one to place a 1-m telescope at 550 AU where it can use the sun as a gravitational lens to image exoplanets and the second to deliver a 1 MT payload to Alpha Centuri.

5.1. 550-AU mission The 550-AU mission will carry a camera and other instruments to a distance of 550 AU (and beyond) from the Sun. At that distance, unique interstellar and solar system observations can be conducted. Using the Sun as a gravitational lens for imaging exoplanets is the one considered here. Conventional rocket technology would result in a 30-year transit to 550 AU; data collection would start in 2060. Using the Direct Fusion Drive (DFD), the transit time to 550 AU would be 13 years. Even accounting for development time, data collection will start 15 years earlier than with conventional technology, in 2045 rather than 2060. In transit and on arrival, the DFD would provide a megawatt of power for science, communication, and station-keeping. Furthermore, DFD allows a much smaller launch vehicle to be used, reducing mission costs substantially. The mission objectives include the objectives of the Innovative Interstellar [34] and the 550 AU mission [35, 36]. One instrument is an infrared telescope capable of looking back toward the Sun to assess the solar system dust that causes IR extinction as we look outward from Earth. It was too heavy for the Innovative Interstellar Explorer mission. The instruments are given in Table 2. The Exoplanet Imaging instrument would be a 1-m telescope with a large focal plane with a 0.4° field-of- view. The baseline communications system is a 40-GHz, Ka-band system with a 4-m-diameter transmit dish and 500-kW power. The data rates as a function of distance are shown in figure 15, sufficient to return a 1080p HDTV image every 6 seconds. (A 1- 100-fold.)

Table 2. Instrument packages [37]. The power is that necessary to operate the instrument, not for communications. Acronym Instrument Mass (kg) Power (W) Data rate (bps) MAG Magnetometer 8.81 5.30 130.00 PWS Plasma wave sensor 10.00 1.60 65.00 PLS Plasma parameters 2.00 2.30 10.00 EPS Energetic particle spectrometer 1.50 2.50 10.00 CRS- Cosmic-ray spectrometer: anomalous 3.50 2.50 5.00 ACR/GCR and galactic cosmic rays CRS-LoZCR Cosmic-ray spectrometer: 2.30 2.00 3.00 electrons/positrons, protons, helium CDS Cosmic dust sensor 1.75 5.00 0.05 NAI Neutral atom detector 2.50 4.00 1.00 ENA Energetic neutral atom imager 2.50 4.00 1.00 LAD Lyman-alpha detector 0.30 0.20 1.00 EXOI Exoplanet Imager 20 100 3 x 106 IRD Infrared camera for solar system dust 10 100 3 x 106 Total resources 35.16 229.40 6 x 106

The exoplanet telescope focus extends semi-infinitely. A 1-meter telescope, with coronagraph components, could resolve 3-km features on a planet 30 parsecs away. The light from the exoplanet appears as a ring around the sun, whose disc of light is blocked. There are many complexities [38] to the data analysis: pointing; focal properties of the sun are different in the radial

66 | P a g e and azimuthal directions; signal to noise; the exoplanet moves across the field of view; etc. The spacecraft is translatable perpendicular to the focal length vector to produce an image. High-spectral-resolution spectroscopic data is available for every 3-km pixel. The unprecedented spectral resolution allows LANDSAT-like characterization of the exoplanet surface. Geological and material features of the 3 km x 3 km areas can be determined. Weather patterns can be tracked in real time. If the target exoplanet were Earth, the extent of industrial and agricultural use would be available for each 3 km x 3 km area.

Figure 15. Data rate for a Ka-band communication Figure 16. Example of what the system. telescope might be capable of resolving from 30 parsecs [39].

A list of select spacecraft specifications is shown in Table 3. The fuel mass does not include that for the outgoing spiral. The “efficiency” is the fraction of power that goes into thrust; the fuel “tank fraction” is the ratio of its mass to that of the fuel. Once the spacecraft departs from Earth, it takes 13 years to reach 550 AU. The same spacecraft could be put into solar orbit at 550 AU in 18 years. The additional time is due to deceleration. Orbiting at 550 AU could not be done with a solar sail or laser light sail. Launch windows for gravity-assisted missions can be decades apart while a direct flight does not require any particular launch window since it does not employ any flybys of the planets. It can be launched as soon as it is ready. Figure 17 shows a transfer (flyby) trajectory. The Earth departure spiral requires 400 kg of fuel from an ISS orbit and is shown in Figure 18. The spacecraft total mass of 5282 kg is low enough to be launched on any currently available launcher, as shown in Table 4. The spacecraft is in the inner radiation belt for 11.7 days. Achieving the spacecraft performance values listed in Table 3 will be challenging. The specific impulse corresponds to 2.6 keV deuterons. In the lab [40] magnetic nozzles have produced only ~100 eV ions, though at considerably lower power (density) than the DFD. Higher Isp studies would require kinetic codes rather than fluid ones because of the reduced collisionality.

67 | P a g e

Table 3. Select spacecraft specifications for the 550 AU flyby mission.

Parameter Value Units

Final position 555.6 AU

Final velocity 479.1 km/s

Final time 13.0 yr

Fuel 3217.6 kg

Mass Total 5282. kg

Mass Engine 1700. kg

Mass 300. kg Payload Figure 17. Flyby trajectory parameters [41].

Exhaust 510. km/s Velocity

Power 1.7 MW

Thrust 4.0 N

Specific 1.0 kW/kg power

Efficiency 0.30

Tank fraction 0.02

Table 4. Launch vehicles to put spacecraft into LEO.

Family Launch Vehicle LEO (kg) ISS (kg)

Atlas 401 9800 8910

411 12030 10260

431 15260 13250

501 8210 7540

511 11000 10160

Figure 18. Earth departure spiral [39].

68 | P a g e

531 15530 14480

551 18850 17720

Delta IV Medium 9190 8510

Medium+ (4.2) 12900 12000

Medium+ (5.2) 11060 10220

Medium+ (5.4) 13730 12820

Heavy 28370 25980

Falcon 9 Block 1 9000 8500

Block 1.1 13150 12420

5.1.1. Spacecraft Design The spacecraft design is shown in figure 19. The 4-m-dia Ka-band high gain antenna dominates the spacecraft. A single DFD engine is used. While a second engine would give the system some redundancy, it may be better just to fly two spacecraft. For other missions, multiple engine modules offer strong benefits, noted later. The solar panels are for the spacecraft LEO checkout phase. The deuterium (propellant) tank is the larger of the two and is cryogenic. It has a cryo-cooler to recirculate boil-off. Figure 19. Spacecraft design. The large tank is for Helium-3 is stored as a gas in the smaller liquid D, the smaller tank is for gaseous helium- tank. The antenna, small blue vertical 3. panels) and radiators (large black horizontal panels) are deployable.

5.2. An interstellar mission Interstellar missions require much longer burn durations, and higher Isp and specific power than the 550 AU mission. Figure 20 shows the rendezvous distance as a function of specific power and thrust for a 325-year-duration mission. The power is fixed at 100 MW. The exhaust velocity is found by solving the power equation,

69 | P a g e

2휂푃 ((1) 푢 = 푒 푇 where 휂 is the power to thrust efficiency, ~ 0.3. Figure 21 shows the same but for a flyby. The maximum distance at each specific power is achieved for different thrust levels. At low specific powers, higher thrusts send the spacecraft further. This is not true at high specific powers. At a specific power, the maximum distance is achieved with 4 N thrust, not 8 N. There will be an optimal thrust for every duration and specific power. The exhaust velocity assumed is a sizeable fraction of that of the full energy of the fusion products. The distance as a function of time for intercept is

푚푠 푚̇ 푚 푚0 ̇ 푚̇ 푑 = 푢푒 [(휏 − ) 푙표푔 (1 − 휏) (1 − ) − (푡푠 − ) 푙표푔 (1 − 푡푠) + 푡푠 − 휏] + 푣푠휏 푚̇ 푚푠 푚푠 푚̇ 푚푠

(2) where 푚푠 is the mass at switch time, 푚̇ is the mass flow rate, 푢푒 is the propellant exhaust velocity, 휏 = 푡푓 − 푡푠, 푚푠 = 푚0 − 푚̇ 푡푠, and 푣푠 is the velocity at switch time, 푚̇ 푣푠 = 푢푒푙표푔 (1 − 푡푠) 푚0 (3)

The switch time is found from the quadratic equation 2 푡푠 − 2훾푡푠 + 훾푡푓 = 0 (4)

푚 where 훾 = 0 . The solution for 푡 that is less than 푡 is the correct solution. 푚̇ 푠 푓

Figure 20. Rendezvous distance in 325 years Figure 21. Flyby distance after 325 years of for different thrusts and specific powers constant thrust [39]. [39].

Entry into the star system is similar to entry into a planetary orbit within the solar system. The approach geometry is shown in figure 22. The final orbit adjust maneuver is shown in figure 23. By the time such a mission is launched, accurate information about planetary orbits should be available so that the maneuvers can be planned in advance. Once in orbit the spacecraft would have up to 100 MW of power to transmit data back to earth. The data rate from interstellar space using a 95 MW laser transmitter is shown in figure 24.

70 | P a g e

Alpha-Centauri Orbital Plane B From Earth

Thrust Normal to Orbital Plane

VFP A ! = 17 deg

VFP

Figure 22. Approach to Alpha-Centuri [39]. Figure 23. Final orbit adjust [39].

If the engine burns for 500 years it could go further, reaching Alpha-Centauri, with specific power of 25 kW/kg, in 500 years. This is shown in figure 25 for a rendezvous. Currently our best estimates of attainable specific power are from 0.3 to 1.5 kW/kg, woefully inadequate for these missions. To achieve the high numbers in these plots would require a number of revolutionary improvements, such as:

 Replace the Brayton cycle heat engine with a method of direct conversion from x-rays and waste heat to radio-frequency power. Direct conversion of heat to electricity is done now but is only about 5% efficient. Direct conversion of x-rays is done in x-ray machines but the efficiency is very low.  Use DFD staged modules - consume then jettison. This is similar to chemical rockets today, with the significant difference that all remaining DFD modules provide thrust until they and their propellant tanks are jettisoned. Figure 24. Data rate from interstellar space for The performance improves with the logarithm a 95-MW transmitter. of the mass of the extra stages [42]. Employing 100 DFD units, a flyby of Alpha-Centuri within 350

71 | P a g e

years is then achievable at a specific power of 5 kW/kg, an improvement compared to requiring 30 kW/kg for a single 100 MW DFD, as depicted in figure 21.  Make superconductors that can last 300-500 years in the face of neutron bombardment.  Make superconductors that retain their superconducting properties at higher temperatures, to reduce the need for cryo-coolers.  Lower mass structures.  Increasing 3He supply, perhaps by T-suppressed D-D fusion reactors. The currently available 3He supply is (x1000) inadequate for a 100-MW-power, 300-year mission.  Closed cycle method for recycling propellant/coolant during electrical power generation mode of operation, to reduce the system mass.

Figure 25. Rendezvous distance after 500 Figure 26. Mass of a 100 MW power plant as years [39]. a function of specific power [39].

Figures 27 and 28 show example trajectories for the 325-year rendezvous and flyby missions. The parameters for these cases are: a constant thrust of 4 N; a specific power of 100 kW/kg; engine power of 160 MW; and an exhaust velocity of 24,000 km/s. Note the switch time is beyond the halfway point as the spacecraft continues to become less massive. Using multiple engine modules, and jettisoning them and empty propellant tanks along the way, could reduce the required specific power a factor of 10 while keeping the trip duration and payload the same. These jettisoned modules could act as relay stations for communications, increasing the data rates enormously.

72 | P a g e

Figure 27. Sample flyby trajectory for T = 4 N [39]. Figure 28. Sample rendezvous trajectory for T = 4 N [39].

Conclusions The physics basis for low-radioactivity, FRC fusion reactors has steadily grown over the last two decades, with innovative contributions from theory, modeling, and experiments. Importantly, stability limits, once thought to be a major issue, have been exceeded by a factor of 105 and energy

ine fusion reactor designs. Scaling predictions to hotter FRC plasmas is favorable. More recently, attention has been given to technical and engineering aspects, such as reducing the weight of subsystems, increasing electrical efficiency, and identifying components with high resistance to radiation damage. From this foundation, we extrapolate to a Direct Fusion Drive rocket engine that would permit high scientific-return interstellar research missions in the 2030 time frame, provided advances are made in achieving fusion and producing the predicted thrusts and specific impulse levels. A DFD-powered spacecraft could be used for the 550-AU gravitational lensing mission. An Alpha Centauri flyby and orbital mission would require a ten-fold increase in mission duration and place far more difficult demands on the technical components. DFD has the potential to reduce the cost and increase the scientific return for most solar system robotic missions and human missions to nearby planets. The paper illustrates, once again, the critical relationship between specific power and mission performance. The current estimated DFD specific powers are between 0.3 and 1.5 kW/kg. Far higher specific powers are desired for missions to other star systems, ones that will also require much better methods of recycling waste energy and components that are far less sensitive to neutron irradiation. Near-term work includes the completion of the PFRC-2 ion heating experiment, detailed mission analysis, and subsystem designs for the engine components. Design work on higher efficiency RF heating systems and on superconducting magnets is underway. Design of PFRC-3 will begin once the ion heating experiments are complete. This will be about 50% larger than PFRC-2 and aims at higher plasma temperatures and pressures. The succeeding facility, the PFRC-4, is aimed at demonstrating fusion power generation with D-3He. Additional work will be done on the integration issues of multiple engine modules, including the effect of one engine's field on another. A critical point is that the engineering challenges in the DFD design, though large, are greatly reduced, compared to all previous fusion rocket engine concepts, because of its small, clean, steady-state,

73 | P a g e and high- s ambitious missions throughout and outside the solar system. Direct Fusion Drive has the potential to revolutionize space exploration. Near term research and development aim to move the technology to operational status by 2030.

Acknowledgements This work was supported by the US Department of Energy Contract No. DE-AC02-76-CHO-3073 and NASA grant NNX16AK28G.

References [1] N. R. Schulze, "Fusion Energy for Space Missions in the Twenty-First Century," Technical Memorandum 4298, National Aeronautics and Space Administration (Aug. 1991). [2] J. A. Angelo and D. Buden, “Space Nuclear Power,” Orbit Book Company, Malabar, FL, (1985). [3] C. Williams, S. Borowski, L. Dudzinski, and A. Juhasz, “Realizing 2001: A Space Odyssey: Piloted Spherical Torus Nuclear Fusion Propulsion,” Tech. Rep. NASA/TM 2005-213559, NASA Glenn Research Center, (2005). [4] N. Gorelenkov, L. Zakharov, P. Bhatta, and M. Paluszek, “Magnetic Fusion Engine,” 43rd AIAA/ASME/ SAE/ASEE Joint Propulsion Conference (2007). [5] F. Romanelli, C. Brunob, and G. Regnolia, “Assessment of Open Magnetic Fusion for Space Propulsion,” Tech. Rep. 18853/05/NL/MV, The European Space Research and Technology Centre, (2005). [6] E. Teller, A.J. Glass, T.K. Fowler, et al., “Space propulsion by fusion in a magnetic dipole,” Fusion Technology 22, 81 (1992). [7] J. Slough, D. Kirtley, A. Pancotti, et al., “A Magneto-Inertial Fusion Driven Rocket”, ICOPS 1P-125 (2012). [8] K. Miller, J. Slough, and A. Hoffman “An overview of the Star Thrust experiment,” AIP Conference Proceedings 420, 1352 (1998). [9] H. A. Blevin and P.C. Thonemann, “Plasma confinement using alternating magnetic field,” Nucl. Fusion: 1962 Supplement, Part 1, 55 (1962). [10] W. N. Hugrass and R.C. Grimm, “A numerical study of the generation of an azimuthal current in a plasma cylinder using transverse rotating magnetic field,” J. Plasma Physics 26, 455 (1981). [11] Y. S. Razin, G. Pajer, M. Breton, et al., “A direct fusion drive for rocket propulsion,” Acta Astronautica 105, 145 (2014). [12] S. A. Cohen and R.D. Milroy, “Maintaining the closed magnetic-field-line topology of a field- reversed configuration with the addition of static transverse magnetic fields,” Phys. Plasmas 7, 2539 (2000). [13] M. N. Rosenbluth and M.N. Bussac, “MHD theory of the spheromak,” Nucl. Fusion 19, 489 (1979). [14] J. Friedberg, Ideal MHD, Cambridge University Press (2014). [15] A. Ishida, H. Momota, and L. C. Steinhauer, “Variational formulation for a multifluid flowing plasma with application to the internal tilt mode of a field-reversed configuration,” Phys. Fluids 31, 3024 (1988). [16] L. C. Steinhauer, “Review of field-reversed configurations,” Phys. Plasmas 18, 070501 (2011). [17] I. R. Jones, “A review of rotating magnetic field current drive and the operation of the rotamak as a field-reversed configuration and a spherical tokamak,” Phys. Plasmas 6, 1950 (1999). [18] Y. Petrov, X. Yang, Y.Wang, and T-S Huang, “Experiments on rotamak plasma equilibrium and shape control,” Phys. Plasmas 17, 0112506 (2010). [19] S. A. Cohen, B. Berlinger, C. Brunkhorst, et al., “Formation of collisionless high- plasmas by odd- parity rotating magnetic fields,” Phys. Rev. Lett. 98, 145002 (2007). [20] H. Y. Guo, M.W. Binderbauer, T. Tajima, et al., “Achieving a long-lived high-beta plasma state by energetic beam injection,” Nature Communications, |6:6897| DOI: 10.1038/ncomms7897

74 | P a g e

(2015). [21] Private communication, E. Lieberman. [22] H. Y. Guo, A.L. Hoffman, and L.C. Steinhauer, “Observations of improved confinement in field reversed configurations sustained by antisymmetric rotating magnetic fields,” Phys. Plasmas 12, 062507 (2005). [23] J. Sheffield, “Physics requirements for an attractive magnetic fusion reactor,” Nucl. Fusion 25, 1733 (1985). [24] J. Wesson, Tokamaks, Oxford University Press, 4th edition, Oxford (2011). [25] N. A. Krall and P.C. Liewer, “Low frequency instabilities in magnetic pulses,” Phys.Rev. A. 4, 2094 (1971). [26] N. Rostoker and A. Qerushi, “Classical transport in a field reversed configuration,” Plasma Physics Reports, 29, 626 (2003). [27] C. W. Barnes, J.M. Stavely Jr. and J.D. Strachan, “High-energy runaway electron transport deduced from photonuclear activation of the PLT limiter”, Nucl. Fusion 21, 1469 (1981). [28] A. H. Glasser and S.A. Cohen, “Ion and electron acceleration in the field-reversed configuration with an odd-parity rotating magnetic field,” Phys. Plasmas 9, 2093 (2002). [29] S. A. Cohen, A.S. Landsman, and A.H. Glasser, “Stochastic ion heating in a field-reversed configuration by rotating magnetic fields,” Phys. Plasmas 14, 072508 ((2007). [30] E. S. Evans, et al., “Particle-in-cell studies of fast-ion slowing-down rates in cool tenuous magnetized plasmas,” to be submitted to Phys. Plasmas (2017). [31] J. F. Santarius, “Role of advanced-fuel and innovative-concept fusion in the nuclear renaissance,” Bull. Amer. Phys. Soc. 51, 147 (2006). [32] S. A. Cohen, M. Chu-Cheong, R. Feder, et al., “Reducing Neutron Emission from Small Fusion Rocket Engines,” IAC 2015, October, 2015, Jerusalem, Israel. [33] T. Rognlien, J.L. Milovich, M.E. Rensink, and G.D. Porter, “The UEDGE Code”, J. Nucl. Mat., 196– 198, 347 (1992). [34] R. L. McNutt Jr, R.E. Gold , T. Krimigis, et al., “Innovative interstellar explorer”, Physics of the Inner Heliosheath, CP858, 2006. [35] L. Alkalai, N. Arora, M. Shao, et al., “Mission to the Solar Gravity Lens Focus: Natural Highground for Imaging Earth-like Exoplanets”, Planetary Science Vision 2050 Workshop, No. 8203, (2017). [36] P. Gilster, “The FOCAL Mission: To the Sun's Gravity Lens”, http://www.centauri-dreams.org, “Centauri Dreams Imagining and Planning Interstellar Exploration,” (2006). [37] R. L. McNutt, R. E. Gold, S. M. Krimis, et al., “Innovative Interstellar Explorer,” Proc. Workshop on Innovative Systems Concepts, The Netherlands, (2006) and McNutt, R.L., Gold, R.E. Krimis, S.M., et al., “Innovative Interstellar Explorer,” Physics of the Inner Heliosheath, J. Heerikhuisen et al., ed., Am. Inst. Phys. 978-0-7354-0355-0/06 (2006) [38] G. A. Landis, “Mission to the gravitational focus of the sun: A critical analysis,” arxiv.org/abs/1604.06351 [39] E. Stone, L. Alkalai, L. Friedman, et al., “Science and Enabling Technologies for the Exploration of the Interstellar Medium: Final Report,” Science and Enabling Technologies to Explore the Interstellar Medium conference, (2014). http://kiss.caltech.edu/new_website/programs/Final%20KISS%20ISM%20Report.pdf [40] X. Sun, S. A. Cohen, E.A. Scime, and M. Miah, “On-axis parallel ion speeds near mechanical and magnetic apertures in a helicon plasma device,” Phys. Plasmas 12, 103509 (2005). [41] Simulations performed with The Spaceraft Control Toolbox, see Paluszek, M., Thomas, S. et al., “The Spacecraft Control Toolbox for MATLAB v2016.1,” Princeton Satellite Systems, 2016. [42] H. S. Seifert and K. Brown (editors), Ballistic missile and space vehicle systems, New York Wiley, (1961).

75 | P a g e

HIGH BETA CUSP CONFINEMENT: A PATH TO COMPACT FUSION

Regina Sullivan, PhD Revolutionary Technology Programs Lockheed Martin Aeronautics

In this talk the author discussed the motivations for compact fusion. They also discussed the background to High Beta Cusps. They discussed the path of their laboratory using Linear Encapsulated Ring Cusps and then the application to a nominal reactor design. The conclusions of their presentation were:

• To minimize magnetically confined fusion reactor size, want highest β possible. • Tokamaks – limit on β means coils must be large (or you need to develop compact, high field coils). • High β cusps: combine stability of cusp with improved confinement (cusp loss area shrinks as β -> 1). • Lockheed Martin compact fusion experiment seeks to answer several open questions related to cusp physics at high β. • Current status: – Experiment: generating a plasma target that will be heated with high energy (15-25 keV) neutral beams – Simulation: initial sims support predictions of cusp/inflation behavior at high β – Analytical reactor model predicts a reasonably sized 200 MWth class reactor.

[No Abstract submitted since last minute addition]

76 | P a g e

POSITRON PROPULSION FOR INTERPLANETARY AND INTERSTELLAR TRAVEL

Ryan Weed 1*, Bala Ramamurthy1, Josh Machacek1, Dante Sblendorio1, Mason Peck2

1 Positron Dynamics Inc, Livermore, CA 2 Sibley School of Mechanical and Aerospace Engineering, Cornell University, NY

[email protected]

Current state of the art in-space propulsion systems fail to meet requirements of 21st century space missions. Antimatter propulsion has been identified [1] as a candidate mechanism that could safely transport humans and/or robotic systems with drastically reduced transit times, providing quicker scientific results, increasing the payload mass to allow more capable instruments and larger crews, and reducing the overall mission cost. Propulsion systems based on antimatter have been considered in several manifestations [2, 3]. Despite the substantial performance advantages, significant technical barriers have kept the cost of usable antimatter well outside the realm of propulsion applications. Each design is a trade-off between mass and complexity, but they all share high specific impulse (Isp) well above those obtained from even the most ambitious electric ion-propulsion. We describe a positron-based propulsion system utilizing radioisotope positron sources combined with annihilation catalyzed fusion and include a basic design for a propulsion demonstration employing the CubeSat architecture as well a scaled propulsion system that utilizes an ‘on-board’ radioisotope breeding technique.

Keywords: Antimatter, Positrons, Fusion propulsion

1. Introduction The primary challenge of an antimatter propulsion system is conversion of the annihilation products into propulsive force. One way to do this is by catalyzing a fusion reaction(s), resulting in fast charged particle products that can be guided to produce thrust [4]. Traditional laser or particle fusion-driver systems have high mass and power requirements that are not practical for any near- term space applications [5]. Positrons are the easier form of antimatter to obtain - over the past 20 years the cost of usable positron production has decreased, and the techniques have become more widely known [6]. Our solution to antimatter propulsion is based on using electron/positron annihilation induced fusion reactions, first proposed in the 1990’s [7], but never experimentally measured. Recent advances in cold positron production [8], creation of dense deuterium clusters on metallic substrates [9], and measurement of positron catalyzed fusion reaction cross section [29] show that a Na-22 radioisotope positron catalyzed fusion propulsion system is possible, capable of >100mN thrust with 6 >10 secs Isp. Initial design of an in-orbit demonstration flight spacecraft utilizing the Cubesat architecture is presented. Using commercial GPS, better than 10m orbital-position accuracy can be obtained, ensuring 99.99% confidence in the measurement of 1 deg. inclination change, decoupled from any in-track perturbations (e.g. atmospheric drag). While radioisotope sources are sufficient for missions within the Solar System, a regenerative source of positrons will be required to reach thrust levels and transit times required for interstellar travel. We present initial analysis of a positron

77 | P a g e source generation concept based on Deuterium-Deuterium (DD) fusion neutron capture reaction 78 79Kr [10, 32, 36]. This is a type of radioisotope ‘breeder’ fuel cycle would allow for much higher positron source intensities and thrust levels required for an interstellar mission.

Why Positrons? Antiprotons have been the antimatter particle of choice for most propulsion system studies over the last several decades [37-39]. While antiproton annihilation does release approximately 2,000 times more energy per annihilation, a large accelerator (e.g. CERN, FermiLab) is required to reach the energies required for pair production of antiprotons. Such large systems are unrealistic in a spacecraft, therefore, antiproton propulsion concepts rely on storage of these charged particles in magnetic bottles (e.g. Penning traps). These charged particle traps run up against fundamental number density limits (Brillouin limit) that require large mass and volume to trap a tiny amount of antimatter, leading to poor propulsion system performance. The positron, or anti-electron, is the antimatter counterpart of the electron. It has the same mass as an electron but opposite charge. Positrons are the ‘easier’ form an antimatter and are produced by several readily available radioisotopes (e.g. Na-22, Co-58) in large number and broad energy spread. A radioisotope such as Na-22 has a specific activity of 6,243 Ci/gram. Five micrograms of Na-22 produces a billion ‘hot’ positrons per second. In condensed matter, an energetic positron, like those produced from a radioisotope, will rapidly Figure 1. Original ‘Photonraket’ design of Sanger. thermalize (cool) through inelastic collisions. Reproduced from [28] Eventually, the positron annihilates with an electron in the material and emits several gamma rays. When a positron annihilates with an electron in free space to produce gamma rays, these gamma rays are emitted (approximately) back-to-back, but in any orientation. Using photons directly for propulsion, as envisioned by Sanger in the 1950’s [11], requires the ability to efficiently reflect photons (see figure 1). No currently known material is known to be capable of reflection of gamma-rays, like those emitted from antimatter annihilation. In general, the absorption of photons scales with the mass of the material. Thus, it is likely that a gamma-ray mirror would be prohibitively massive for a spacecraft. Without a gamma ray mirror, the only mechanism known to produce a well collimated beam of gamma-rays is the gamma-ray laser [12]. This requires the production and control of a Bose-Einstein Condensate (BEC) of positronium atoms (a bound state of a positron and an electron). To-date, efforts have yet to produce a BEC of positronium [17].

Propulsion Mechanism Positron catalyzed fusion propulsion works by injecting cold positrons onto a region of high deuterium density. Typically, the deuterium is located on the metal surface or inside vacancies and other point defects or surface states of the metal lattice as shown in Figure 2 (C).

78 | P a g e

Figure 2 (A) Radioisotope source of hot positrons (red). (B) positron moderator produces high flux of cold positrons. (C) Deuterium loaded metal. Deuterium clusters (blue) have formed in vacancy type point defects or surface states. Injected cold positrons will diffuse into the same defect sites before annihilation. (D) Fusion reaction products (red) are magnetically guided to produce thrust along magnetic field line direction.

A radioisotope positron source produces isotropic ‘hot’ positrons which are cooled by an array moderator to near thermal energies (~eV). The resulting ‘cold’ positron beam is guided and focused into the deuterium-loaded fuel material at the appropriate density to catalyze fusion. A permanent magnet array provides the field required for each section, ultimately forming a nozzle to direct the fusion particles. The fusion process (described below) produces charged particles with ~3 MeV energy, travelling at nearly 10% of the speed of light, which are magnetically guided to the engine exit producing thrust.

The Fuel Recent work on dense states of deuterium in metal substrates could lead to a further increase in the positron/deuterium overlap and therefore fusion rate, leading to a corresponding increase in thrust. Ultra-dense deuterium (UDD) states on the surface and subsurface of Palladium have been reported by two groups, and correspond to a number density between 1027 and 1029 cm-3. [21-24]. In fact, the University of Gothenburg group reported on laser induced fusion events in UDD states on the surface of metals [25]. This work on dense deuterium and UDD, in addition to earlier work on laser-initiated Coulomb explosion in D clusters [26] inspired us to investigate the existence of a regime of positron flux that can produce similar coulomb explosion fusion process in dense D clusters and surface states. Utilizing these ultra-dense states results in significantly higher thrust for a given amount of positron radioisotope by relaxing the conditions necessary to produce a fusion burn.

2. Theory It has been postulated that positron-electron annihilation could induce fusion reactions in hydrogen isotopes. In this process, the positron-electron annihilation couples to a lattice-trapped deuteron giving it a kinetic energy kick [7]. This 'knock-on' process provides a mechanism to accelerate deuterium ions using positrons. The accelerated deuteron, in some cases, has sufficient kinetic energy to fuse with other deuterons in the substrate. Other mechanisms for transferring energy from annihilating positron/electrons to the atomic nuclei have been investigated. Figure 3 (left) shows the Feynman diagram for nuclear excitation of nuclei via an inelastic (non-resonant) channel. This energy transfer mechanism is similar to positron nuclear excitation process described by Raghavan and Mills [13] and has been shown experimentally to produce excited metastable states of surrounding nuclei, with the cross section increasing with increasing atomic number of the absorbing atom [14-16].

79 | P a g e

Figure 3. Feynman diagrams for Inelastic Nuclear Excitation Process (left) and the Morioka Process (right). Qint describes the sudden momentum transfer interaction with the surrounding crystal (analogous to the Mossbauer effect).

Figure 3 (right) shows the Feynman diagram for a similar nuclear excitation process, whereby a virtual photon imparts a large amount of kinetic energy to a trapped deuteron, theorized by Morioka. In the case where positron and Deuterium atoms are co-located in the potential well of the lattice point defect, we consider the knock-on Deuteron process induced by the annihilating positron inside the metal vacancy. Typically, the fusion rate is defined by 휆퐹 = 휎퐷휐퐷 Where 휐퐷 and 휎퐷are the velocity and cross section of the deuteron-deuteron system. However, in the case where we consider momentum transfer from the annihilating positron to the surrounding 퐷 Deuteron the fusion rate becomes 휆퐹 = 푅휆퐹 Where R is the non-relativistic spin averaged differential cross section for the momentum transfer process described above. Although the value for R will depend on the substrate material characteristics, it has been calculated at R~10-3 for reasonable atomic parameters [7], giving a fusion 퐷 −19 + rate proportional to Deuterium and positron number density, 휆퐹 ≈ 10 /퐷푒 /푠. It is important to note that the fusion rate depends only on the overlap in the positron and Deuteron number densities. In order to ensure sufficient overlap with reasonable fuel geometries the positrons must be cooled, or moderated.

Fig. 4 Planar Array moderator extraction concept (single Fig.5 Silicon Carbide Moderator Array. element)

When positrons are born, they are extremely energetic or ‘hot’ (mean energy ~250keV) and thus, difficult to control. One significant challenge to date is the ability to control these very hot positrons using realistic electric and magnetic fields. Before the positrons can be used as such, they must be cooled down to

80 | P a g e process to date has been <1%. Through a grant from the Thiel Foundation’s Breakout Labs, Positron Dynamics has developed new methods to increase moderation efficiency by several orders of magnitude [8], combining a technique called Field-assisted-moderation [18-20] in wide bandgap semiconductor (Silicon Carbide) arrays with a charged particle extraction technique using crossed electric and magnetic fields (ExB drift). Using such an efficient moderator will allow for production of intense and focused pulses of positrons that are able to deposit substantial amounts of power into fuel targets.

3. Spacecraft Design and Performance Estimates Using measured value for momentum transfer probability R of 10-2 [29] we estimate that a 20um diameter, ns pulse of 1012 positrons could deposit >1023W/cm3 onto a thin film substrate surface covered in 50 nm of UDD material of number density 1029/cm3, leading to hot spot ignition [40]. Using a conservative estimate for burn fraction (10%) in the implantation volume, this leads to a thrust of approximately 2mN/Ci. Thrust produced by the 3MeV DD fusion protons is given by 퐹 = 퐼푆푃푚̇ 푝푔0 Where 푚̇ 푝 is the mass flow rate of the protons. The specific impulse is related to the exhaust velocity of the protons, which in an ideal case will be ~.08c, leading to a specific impulse of ~2.5 x106 seconds. Total impulse will be limited by the half life 휏 of the radioisotope and the reduction in Deuterium 퐷 density as the fuel is burned, described by decay rate 휆 = 휆퐹 ∗ 휉 ∗ 휀. Where 휉is the initial positron flux and 휀 is the moderation efficiency. 푡푓 1 −푡[ +휆] 퐼푡표푡 = ∫ 퐼푆푃푚̇ 푝푔0푒 휏 푑푡 0 We consider an example propulsion system using a Na-22 source with a half-life of 2.6 years and activity of 14 Ci /cm2 [27] over a 4 cm2 surface. This gives an initial total thrust of 132 mN and total 5 impulse of ~9.4x 10 Ns over a mission duration of 푡푓. We define the mission duration as the time at which thrust has dropped to 5% of initial thrust, which, depending on the mission thrust profile requirements and can range from 0.7 to 6 years for a Na-22 positron source.

Fig 6. Thrust available for positron catalyzed fusion propulsion system based on Na-22 source of 56 Ci activity. The reduction in thrust in the solid line (100% duty) is mainly due to burn-up of the Deuterium fuel, while the thrust decay in the dotted line (5%) is primarily due to the half-life of the positron source.

Cubesat Demonstrator In order to validate this concept, a small propulsion subsystem (<3kg) will is being designed in partnership with PD and the Space Systems Design Studio at Cornell. The propulsion unit will be housed inside a 3U CubeSat (a standardized small satellite form factor) weighing approximately 6kg. Initial estimates show this mass and volume is sufficient for a six-month demonstration mission. Launch, ascent and orbit environments are well-characterized and flying fragile science hardware is not a unique challenge. Standard methods to test and mitigate damage (vibration table, thermal- vacuum testing, etc) during these phases of flight test are well understood and will be utilized.

81 | P a g e

Figure 7. Rough sketch of Cubesat design for positron source and moderator subsystem.

The spacecraft will change its inclination over the course of the six months using the positron- catalyzed propulsion subsystem. The volume and mass of the flight demonstration spacecraft will require a 10 Ci Na-22 positron source, with a half-life of 2.6 years, to provide a sufficient number of positrons for approximately 20mN of instantaneous thrust. The Na-22 source would be classified as radiotoxicity group III “minor sources” according to the FAA’s Office of Commercial Space Transportation [30]. Recent advances in composite shielding materials will be utilized in order to minimize additional spacecraft weight due to shielding requirements [31]

Scaling to Alpha Centauri The Alpha Centauri mission would require to scale thrust levels between 10N-100N. Due to limits in specific activity and lifetime of positron emitting radioisotopes, these higher thrust levels require on- board production of positrons. Such a system would allow for an approximately ~50 year transit to Alpha Centauri, with the spacecraft reaching nearly 10% of the speed of light.

79Kr Breeding* (on-board positron source) Fortunately, the Deuterium-Deuterium fusion process produces an abundance of fast neutrons. In this case, we may devise a radioisotope breeding technique that utilizes a high neutron capture cross section [28] in Krypton-78 to produce Krypton-79, a positron emitting radioisotope (see figure 8). This fuel cycle will allow for scaling of Thrust to approaching 100N. The fuel cycle [36] is summarized in Figure 9. Hot positrons are generated from layers of Krypton (79Kr-rich) frozen onto metallic surfaces in an array Figure 8. Production channels for 79Kr, including the structure described in section 2. Fortunately, neutron capture cross section 78Kr(n,g)79Kr considered Krypton not only serves as the source of positrons, it for breeding positron emitting radioisotope 79Kr. also makes an excellent positron moderator [33]. In Reproduced from [28] the engine core, large positron pulses generate fusion reactions on the fuel target substrate, generating a high flux of fast neutrons. It is estimated that 10-100atm blanket of pressurized Kr will be sufficient to thermalize these hot neutrons within a reasonable length scale (<1m). At some point in the fuel cycle, the Br79 contaminated coolant will need to be

82 | P a g e

Figure 9. The 79Kr breeding cycle. chemically filtered out. The extreme reactivity of Bromine compared to Krypton will help in this separation step. The Krypton then passes into the cryogenic isotope enrichment stage. This allows for source specific activities (Ci/g) high enough to generate the number of positrons required for higher thrust levels. A candidate isotope separation method is described by Mills [10,31], where 79Kr created in the engine core is preferentially separated from the Kr78 using a liquid nitrogen immersed tube with an array of heater elements and a carrier gas that oscillates pneumatically. A numerical solution to the Krypton breeding fuel cycle is shown in Figure 10. This model assumed a total initial Krypton mass of 10kg, including 100ug of 79Kr. The model also includes an artificial ‘limiter’ that maintained 79Kr total mass below 100g and thrust at a constant level. In practice, this would be accomplished by controlling the repetition rate of the pulsed positron beam. The 79Kr source moderator assumes 20 micron thick layers deposited on a 10cm x 10cm, 100 element moderator array.

*A traditional fission breeder reactor creates more fissile material than it uses. Here, in the context of a fusion reactor and with the addition of an intermediate step (positron production/annihilation) we will use the same term ‘breeder’ to indicate that the fusion reactions generate neutrons that produce more positron emitting radioisotope, which in turn produce more fusion reactions.

The reference design including a rough mass budget and delta-V estimates is included in Table 1 below. The mass fraction for this design is 0.7, slightly lower than 0.8 mass fraction of the retired Space Shuttle system. The total mass of the reference design at approximately 1.5mT could be launched into LEO by a small or medium lift launch vehicle (Minataur-C, Falcon 9, Delta II, etc) and would not require in orbit assembly (approximate size 6m length x 2m diameter). The fast neutron flux in Table 1 is high enough to cause damage to surrounding materials (hardening / embrittlement / creep / phase instability). However, such a high neutron flux is seen in the core of high flux fission reactors [32] without catastrophic structural failure over the course of a decade.

Figure 10. A numerical solution to the 79Kr breeding cycle over approximately 10 years. The initial 79Kr breeding period lasts ~2 months.

Table 1 and Figure 11. Reference design for scaled propulsion system based on 79Kr breeding. Krypton Deuterium Structure/Payload Thrust Fast neutron flux Delta-V Alpha Cen 10kg 950kg 400kg 60N 5E15 n/s×cm2 2.4E7 m/s 50 years

83 | P a g e

Conclusions Interstellar travel within the span of a human lifetime is perhaps the greatest technological challenge that humanity faces. The vast distances, incredible cold, harsh radioactive & micro particle environment requires novel solutions if we are to venture outside of our Solar System. Conquering these challenges will prove to be difficult, but the rewards are profound. Unlike beam-powered propulsion, this propulsion concept would allow a spacecraft to carry large scientific or mission payloads and would also allow the spacecraft to slow down once it has reached its target destination. The fuel cycle described in section 4 could also provide abundant source of thermoelectric power to run avionics, communications, sensor and other payloads. Antimatter based propulsion is a game-changing propulsion technology for this application. We have laid out the path to an antimatter propulsion technology demonstration based on an available radioisotope positron source that does not require long term antimatter trapping and can be demonstrated in the near term. This concept is scalable to fast transit, high delta-V missions with small to medium sized spacecraft.

References [1] 2015 NASA OCT Roadmap TA02: In-Space Propulsion Technologies (http://www.nasa.gov/offices/oct/home/roadmaps/index.html) 2.3.5 Antimatter Propulsion [2] G. Smith, NIAC Phase I Final Report “Positron Propelled and Powered Space Transport Vehicle for Planetary Missions” [3] A. McNutt, “Realistic Interstellar Explorer”, NIAC 7600-039 Final Report, 2002 [4] R. Keane, “Beamed Core Antimatter Propulsion”, Journal of the British Interplanetary Society 2012 [5] J. Lindl, et al. "Review of the national ignition campaign 2009-2012." Physics of Plasmas 21.2 (2014): 020501. [6] R. Krause-Rehberg, “Positron Annihilation in Semiconductors: Defect Studies”, 1999 [7] S. Morioka, “Nuclear Fusion Triggered by Positron Annihilation in Deuterated Metals”, Il Nuovo Cimento, Vol107a,1994 [8] R. Weed, et al, “Array Structures for Field Assisted Positron Moderation and Corresponding Methods”, WO Patent App. PCT/US2012/042,049 [9] B. Shahriar, P. U. Andersson, and L. Holmlid, "High-energy Coulomb explosions in ultra-dense deuterium: Time-of-flight-mass spectrometry with variable energy and flight length." International Journal of Mass Spectrometry 282.1 (2009): 70-76. [10] A. P. Mills Jr, "Suitability of 79 Kr as a Reactor-Based Source of Slow Positrons." Nuclear science and engineering 110.2 (1992): 165-167. [11] E. Sanger, “Zur Theorie der Photonenrakteten”, Ing. Arch. 21, 213, 1953.

84 | P a g e

[12] D. B. Cassidy and A. P. Mills, (2007), Physics with dense positronium. Phys. Status Solidi C, 4: 3419–3428. [13] R. S. Raghavan and A. Mills, “Nuclear Excitation by positron annihilation: Comments on theory vs experiment” Physical Review C Vol 24 Num 4, October 1981 [14] R. D. Present, S. C. Chen, "Nuclear Disintegration by Positron-K Electron Annihilation," Physical Review, Vol 85, Num 3, February 1952 [15] D. B. Cassidy et al, "Resonant versus nonresonant nuclear excitation of 115In by positron annihilation," Physical Review C, Vol 64 054603, October 2001 [16] A. Ljubičić, “Nuclear excitation in 176Lu by positron annihilation on K-shell electrons” Journal of Radioanalytical and Nuclear Chemistry V 272 2007 [17] K. Shu et al, "Study on Bose-Einstein condensation of positronium." Journal of Physics: Conference Series. Vol. 791. No. 1. IOP Publishing, 2017. [18] K. G. Lynn and B.T.A. Mckee, “Some Investigations of Moderators for Slow Positron Beams”, Applied Physics, 1979. 19(3): p. 247-255. [19] Al-Qaradawi, I.Y., P.A. Sellin, and P.G. Coleman, “Tests of a diamond field-assisted positron moderator”, Applied Surface Science, 2002. 194(1-4): p. 29-31. [20] J. P. Merrison, et al., “Field Assisted Positron Moderation by Surface Charging of Rare-Gas Solids”, Journal of Physics-Condensed Matter, 1992. 4(12): p. L207-L212. [21] A. Lipson, B. J. Heuser, C. Castano et al, “Transport and Magnetic Anomalies below 70K in a Hydrogen Cycled Pd Foil with a Thermally Grown Oxide”, PHYSICAL REVIEW B 72, 212507 2005 [22] F. Winterberg, “Ultra-dense deuterium and cold fusion claims”, Physics Letters A, Volume 374, Issue 27, 14 June 2010, Pages 2766-2771 [23] L. Holmlid, “High-charge Coulomb explosions of clusters in ultra-dense deuterium D(−1)”, International Journal of Mass Spectrometry, Volume 304, Issue 1, 15 June 2011, Pages 51-56 [24] P. Andersson, “Ultra-dense deuterium: A possible nuclear fuel for inertial confinement fusion (ICF)”, Physics Letters A, Volume 373, Issue 34, 17 August 2009, Pages 3067-3070 [25] L. Holmlid, “Laser-induced fusion in ultra-dense deuterium D(−1): Optimizing MeV particle emission by carrier material selection”, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Volume 296, 1 February 2013, Pages 66-71, [26] T. Ditmire, J. Zweiback, V. P. Yanovsky et al, “Nuclear fusion from explosions of femtosecond laser-heated deuterium clusters”, Nature, 398, pp.489-492, 08 April 1999. [27] M. Skalsey and J. Van House. "Proposed new reactor-activated positron source for intense slow e+ beam production." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 30.2 (1988): 211-216. [28] R. Hoffman et al. “Neutron and charged-particle induced cross sections for radiochemistry in the region of bromine and krypton”, No. UCRL-TR-205563. Lawrence Livermore National Laboratory (LLNL), Livermore, CA, 2004. [29] R. Weed, et al., Positron catalyzed fusion reactions in deuterated palladium, Unpublished work, Livermore, CA [30] Space Applications of Radioactive Materials, Office of Commercial Space Transportation Licensing Programs Division, Federal Aviation Administration, 1990 [31] S. Chen, M. Bourham, A. Rabiei. “Attenuation efficiency of X-ray and comparison to gamma ray and neutrons in composite metal foams” Radiation Physics and Chemistry, 2015 [32] A. P. Mills Jr, "Physics with many positrons." Rivista del Nuovo Cimento della Societa Italiana di Fisica 34.4 (2011): 151-252. [33] J. P. Merrison et al. "Field assisted positron moderation by surface charging of rare gas solids." Journal of Physics: Condensed Matter 4.12 (1992): L207. [34] W. L. Bohm, “Propulsion by light: visions of the German pioneer Eugen Saenger”, Proc. SPIE 5777, XV International Symposium on Gas Flow, Chemical Lasers, and High-Power Lasers, 986 (April 01, 2005)

85 | P a g e

[35] R. D. Cheverton and T. M. Sims. “HFIR CORE NUCLEAR DESIGN”, No. ORNL--4621. Oak Ridge National Lab., Tenn., 1971. [36] R. Weed et al, “Positron-emitting Noble-gas Fusion Breeder Reactor, Patent date Filed”, Dec 8, 2016 US 52254426 [37] G. Schmidt, H. Gerrish, J. J. Martin, "Antimatter Production for Near-term Propulsion Applications," 1999 Joint Propulsion Conference. [38] R. L. Forward, "Antiproton Annihilation Propulsion," Journal of Propulsion, 1 (5), 370-74 (1985). [39] G. A. Smith, G. Gaidos, R. A. Lewis, K. Meyer and T. Schmid, "Aimstar: Antimatter Initiated Microfusion for Precursor Interstellar Missions," Acta Astronautica, 44 183-86 (1999) [40] M. D. Rosen, "The physics issues that determine inertial confinement fusion target gain and driver requirements: A tutorial." Physics of plasmas 6.5 (1999): 1690-1699.

86 | P a g e

COMBINED THERMAL DESORPTION AND ELECTRICAL PROPULSION OF SAILCRAFT USING SPACE ENVIRONMENTAL EFFECT

Elena Ancona1*, Roman Ya. Kezerashvili2 1 Telespazio VEGA Deutschland GmbH, Darmstadt, Germany 2 New York City College of Technology, City University of New York, Brooklyn, USA

*Corresponding author, [email protected] [Abstract Only]

Abstract For extrasolar space exploration it is suggested to use space environmental effects such as solar radiation heating and a proton component of the solar wind to accelerate a solar sail coated by materials that undergo thermal desorption at a particular temperature. The solar radiation consists of two parts: electromagnetic and corpuscular radiation. Typically, when considering solar sails, the interest is in the electromagnetic radiation, since photons can transfer momentum to the sail and guarantee a continuous thrust. But what if also the corpuscular part of solar radiation could be exploited for the sailcraft propulsion? In this study we investigate the advantage related to the electrical propulsion of a solar sail by the solar wind plasma, a mixture of protons and electrons that moves away from the Sun. Due to the fact that the proton mass is almost two-thousand times bigger than the electron's, the total momentum carried by the proton flux is significantly higher than that of the electron component. Besides electrical repulsion, another mechanism could be convenient to accelerate the sailcraft: thermal desorption, a physical process of mass loss which can provide additional thrust as heating liberates atoms, embedded on the surface of a solar sail [1,2,3]. We propose the following scenario: the sail is carried as a payload to a relatively small heliocentric distance (0.1 - 0.3 AU); once at the perihelion, the sail is deployed and accelerated by thermal desorption. When the desorption process ends, the sail is electrically charged by a device. The sail experiences additional propulsive force due to the strong repulsion of the positive charged sailcraft with the solar wind protons. Neutralization phenomena are also addressed in the present study [4]. Particularly we are considering the following scenarios: i. Hohmann transfer, plus thermal desorption, plus electrical propulsion. In this scenario the sail would be carried as a payload to the perihelion with a conventional propulsion system by a Hohmann transfer from Earth’s orbit to an orbit very close to the Sun and then be deployed there. Then desorption occurs, which provides a thrust and boosts the sailcraft to its escape velocity. When the desorption acceleration ends, the positively charged sail is accelerated by photon pressure and, due to the electrical propulsion, by extracting the momentum from the proton component of solar wind ii. Elliptical transfer plus Slingshot, plus thermal desorption, plus electrical propulsion. In this scenario the transfer occurs from Earth’s orbit to Jupiter’s orbit. A Jupiter’s fly-by leads to the orbit close to the Sun, where the sail is deployed when it reaches the perihelion. After that the sailcraft is accelerated as in the previous case. We demonstrate that thermal desorption and electrical propulsion come as an additional source of sailcraft acceleration, beside traditional propulsion systems that provide to a sailcraft the speed of about 0.001c for extrasolar space exploration.

Keywords: Electrical propulsion, Propulsion due to thermal desorption, Hohmann transfer, Slingshot

87 | P a g e

References [1] G. Benford and J. Benford, "Acceleration of sails by thermal desorption of coatings", Acta Astronaut. 56, 593-599 2005. [2] R. Ya. Kezerashvili, Space exploration with a solar sail coated by materials that undergo thermal desorption, Acta Astronautica 117, 231-237 2015. [3] E. Ancona, R. Ya. Kezerashvili, Orbital dynamics of a solar sail accelerated by thermal desorption of coatings, arXiv:1609.03131v1 [physics.space-ph], Sep 2016; Paper IAC-16-C1.6.7.32480, IAC 2016. [4] R. Ya. Kezerashvili and G. L. Matloff, Solar Radiation and the Beryllium Hollow-Body Sail: 2. Diffusion, Recombination and Erosion Processes, JBIS, 61, 47-57, 2008.

88 | P a g e

Session 2: Sails and Beams

The following is a report from the Sails and Beams session. The Chairman for this session was Professor Roman Kezerashvili. The purpose of this session was to bring together papers which discussed any concepts which involves the transfer of momentum via photons or particle beams, e.g. solar sails, laser sails, microwave sails, particle beamers, stellar wind pushers. The session was a nod towards the identified physics and engineering challenges of the Breakthrough Initiatives Project Starshot. Specific problems identified for possible focus were to include:

(1) Achieving a stable structure and light-sail geometry for beam riding (2) Mitigating the effects of interstellar dust and ionization (3) Dissipation of heat build-up on sail from a laser beam or high velocity close solar flyby (4) The design of low mass, thin, materials for (high g) sail concepts (5) Systems architectures, fabrication and construction methods for ground and space based beaming methods.

89 | P a g e

SOLAR SAIL PROPULSION: A ROADMAP FROM TODAY’S TECHNOLOGY TO INTERSTELLAR SAILSHIPS

Les Johnson, 1* Edward E. Montgomery2 1 Tennessee Valley Interstellar Workshop 2 MontTech, LLC [Abstract Only]

Abstract Solar sail propulsion systems are maturing rapidly and will soon enable science and exploration missions that are simply impossible to accomplish by any other means. Solar sail technology is rapidly advancing to support these demonstrations and missions, and in the process, is incrementally advancing one of the few approaches allowed by physics that may one day take humanity to the stars. Continuous solar pressure provides solar sails with propellantless thrust, potentially enabling them to propel a spacecraft to tremendous speeds—theoretically much faster than any present-day propulsion system. The next generation of sails will enable us to take our first real steps beyond the edge of the solar system, sending spacecraft out to distances of 1000 Astronomical Units, or more. In the farther term, the descendants of these first and second generation sails will augment their thrust by using high power lasers and enable travel to nearby stellar systems with flight times less than 100 years – a tremendous improvement over what is possible with conventional propulsion systems. By fielding these first solar sail systems we are actually developing a capability to reach the stars. Maturing these systems from today’s state-of-the- art as exemplified by The Planetary Society’s LightSail [1], the Japanese Aerospace Exploration Agency’s IKAROS [2], NASA’s Near Earth Asteroid Scout [3], and the proposed Earth-to-Orbit Beamed Energy eXperiment (EBEX) [4] will not be quick or easy and the development paths for solar photon sails and beamed energy sails will quickly diverge. Each order of magnitude improvement in sail size (for solar photon sails) and performance (for both) will require advances in materials science; spacecraft attitude dynamics and control during deployment and flight; flight guidance, navigation and control; and, eventually, in-space sail fabrication capability. A notional solar and beamed energy sail technology maturation plan (with performance metrics) will be outlined. A discussion of the real-world engineering challenges facing today’s first generation missions and the design and development challenges for those in the next generation will be described. Finally, a step-by-step approach for developing sails of increasing capability and performance will be proposed – leading to the sailcraft required for true interstellar travel. Keywords: Solar Sail, Beamed Energy Sail

References [1] R. Ridenoure, et al, “Testing the LightSail Program: Advancing Solar Sailing Technology Using a CubeSat Platform”, Journal of Small Satellites, Vol. 5, No. 2, pp 531-550. [2] Y. Tsuda, et al, “Flight Status of IKAROS Deep Space Solar Sail Demonstrator,” IAC-10-A3.6.8, presented at the 61st Int. Astronautical Congress, Prague, Czech Republic,2010. [3] L. McNutt, et al, "Near-Earth Asteroid (NEA) Scout", AIAA SPACE 2014 Conference and Exposition, AIAA SPACE Forum, (AIAA 2014-4435). [4] M. Montgomery and L. Johnson, "Feasibility Study for a Near Term Demonstration of Laser-Sail Propulsion from the Ground to Low Earth Orbit", Advanced Maui Optical and Space Surveillance Technologies (AMOS) Conference /USAF AFRL RDSM and Maui Economic Development Board (MEDB); 20-23 Sep. 2016; Wailea, HI.

90 | P a g e

ENABLING THE FIRST GENERATION OF INTERSTELLAR MISSIONS

Philip M. Lubin1

1Physics Dept, UC Santa Barbara, Santa Barbara, CA 93106

[Abstract Only]

Abstract If we want to reach the nearest stars in flight times that are within a human lifetime we must achieve relativistic flight which means we must radically change the ways in which we both propel spacecraft and the way in which we design them. Conventional propulsion systems used for interplanetary travel will not work for this purpose. Any mass ejection propulsion system including nuclear has to confront the issue of the very large mass ratios needed for relativistic flight. The only other alternative is to discover and develop new physics. In this talk we will discuss the fundamental issues of what does and does not work in currently known physics and technology as well as the many challenges we face. Within the realm of known physics we are led to three options with the assumptions above. First is very high efficiency fusion engines with extremely large mass ratios given the relatively low yield of fusion (<1%). Second is to develop an annihilation engine using large scale antimatter production which faces unknown technological hurdles to minimize the secondary mass required to store and react the materials and third is to use directed energy (DE) with the DE drive system left at "home" or some hybrid of the above. With recent advances in photonics and directed energy systems we can now seriously envision and design a large scale DE system that will allow us to reach the nearby stars and exo-planets. We are currently in a NASA Phase II program that is supporting our effort to explore this option and further the development of the underlying technology. With spacecraft from fully-functional gram-level wafer-scale systems (“wafer sats”) capable of speeds greater than ¼ c that could reach the nearest star in 20 years to spacecraft for large missions capable of supporting human life with masses more than 105 kg (100 tons) that could reach speeds of greater than 1000 km/s this technology offers a radical change going forward. With this technology spacecraft can be propelled to speeds currently unimaginable with existing propulsion technologies. In addition to larger spacecraft, that travel slower, we focus on “spacecraft on a wafer” that include integrated optical communications, imaging and spectroscopy systems, navigation, photon thrusters, radiation and magnetic field sensors combined with “standoff” directed energy propulsion. Since the propulsion system stays “at home” the costs can be amortized over a very large number of missions. Interplanetary shuttle missions, to Mars for example, could be enabled if a second unit were built at the target planet. In addition, the same photon driver can be used for planetary defense, space debris vaporization and de-orbiting, beaming energy to distant spacecraft, beaming power for high Isp ion engine missions, asteroid mining, sending power back to Earth for high value needs, stand-off composition analysis, long range laser communications, SETI searches, and terra-forming. Such systems would transform and enable many other space applications. In April 2015 NASA Phase I funding started. One year later on April 12, 2016 the Breakthrough Foundation announced that they would support this idea with a 100M$ Research and Development program to explore the fundamental technology. On May 12 NASA announced Phase II funding. On May 23 the FY 2017 congressional appropriations request directs NASA to study the feasibility of an interstellar mission to coincide with the 100th anniversary of the moon landing quoting our NASA funded directed energy program as an option to enable this. We will discuss our "roadmap" and show the latest laboratory data. While this program faces enormous challenges, the rewards for mastering this technology will enable truly radical and transformative capabilities.

91 | P a g e

Keywords: Directed Energy, Relativistic flight, Interstellar Medium

References

For technical information on this program see our website:

[1] http://www.deepspace.ucsb.edu/projects/directed-energy-interstellar-precursors

[2] http://arxiv.org/abs/1604.01356

[3] http://www.deepspace.ucsb.edu/projects/implications-of-directed-energy-for-seti

[4] http://arxiv.org/abs/1604.02108

92 | P a g e

THE ANDROMEDA STUDY: A FEMTO- SPACECRAFT MISSION TO ALPHA CENTAURI

Andreas M. Hein, Kelvin F. Long, Dan Fries, Nikolaos Perakis, Angelo Genovese, Stefan Zeidler, Martin Langer, Richard Osborne, Rob Swinney, John Davies, Bill Cress, Marc Casson, Adrian Mann, Rachel Armstrong

[email protected] Initiative for Interstellar Studies, The Bone Mill, New Street, Charfield, Gloucestershire, GL12 8ES

This paper discusses the physics, engineering and mission architecture relating to a gram-sized interstellar probe propelled by a laser beam. The objectives are to design a fly-by mission to Alpha Centauri with a total mission duration of 50 years travelling at a cruise speed of 0.1c. Furthermore, optical data from the target star system is to be obtained and sent back to the Solar system. The main challenges of such a mission are presented and possible solutions proposed. The results show that by extrapolating from currently existing technology, such a mission would be feasible. The total mass of the proposed spacecraft is 23g and the space-based laser infrastructure has a beam power output of 15GW. Further exploration of the laser – spacecraft trade-space and associated technologies are necessary. This work was completed as an alternative architecture for the Breakthrough Initiatives Project Starshot.

Keywords: laser sail propulsion, interstellar studies, Project Starshot.

1. Introduction Concepts for beam-propelled interstellar missions have been proposed notably by [1] for a microwave-propelled gram-sized probe and [2] for a laser-propelled fly-by probe with a 333 kg payload, propelled by a 65 GW space-based laser infrastructure. The spacecraft would be accelerated over a distance of 0.17 light years. More recent laser sail concepts such as [3], [4] and [5] have proposed the use of dielectric materials, which have a reflectivity larger than 99% and melting temperatures of between 2000-3000K for the laser sail. Furthermore, they propose much higher accelerations of hundreds to thousands of g that are enabled by the higher temperature limit of the sail material. Besides dielectric materials, [6]–[8] have proposed the use of Graphene-based sails that have a melting temperature above 4000K and a very low density. However, one drawback is the low reflectivity of the material. Although [1] has proposed a probe with a total mass of one gram, such low masses seemed to be infeasible by that time. However, recent developments in micro- electronics has led to the emergence of small spacecraft such as CubeSats [9] with masses between 1 to a dozen kg, FemtoSats with masses below 100g [10], and AttoSats with masses below 10g such as ChipSats [11]. CubeSats have extended their applications from educational purposes to scientific and industrial applications. Recently, interplanetary CubeSats have been proposed as a means for low-cost exploration of outer space [12]. Landis [13] has already explored the prospects of decreasing the payload mass for a laser-propelled fly-by probe in 1995 by extrapolating from mass decreases at that time. He argues that a decrease to 8kg might be feasible by 2030. One recent proposal [5] has explored the trade-space for gram-sized interstellar probes. However, details regarding the subsystems and the overall architecture of spacecraft and the space-based laser infrastructure have been left open.

93 | P a g e

Extrapolating from these trends, this paper addresses the question, how far a FemtoSat-scale interstellar probe would be feasible, exploring a variety of technology options and proposing a baseline concept. The problem is defined to address the scenario of a 10-100 gram interstellar probe sent to the Alpha Centauri star system in a total mission time of 50 years, travelling at a cruise speed of 0.1c. Data is to be obtained at the target system and returned back to the solar system. The propulsion system is to be laser based. A set of questions were tasked, of which this brief note sets out multiple solutions. It is necessary to first scope the problem.

The distance to the Alpha Centauri system is 4.3 Light Years, or approximately 272,000 AU. Travelling at 0.1c (30,000 km/s) over this distance would take 43 years, allowing for up to 7 years for the acceleration phase, implying a lower acceleration bound of 0.136 m/s2. Table 1 below shows several acceleration scenarios for a 100 gram probe assuming a reflectivity of unity, and the distances obtained end of boost assuming that 0.1c is the cruise target speed. These calculations are non- relativistic but are presented as a starting point for the analysis.

For this brief study it was necessary to also make some basic assumptions in the absence of information. These are briefly defined: 1. Flyby mission only (no deceleration) 2. Launch date 2025-2035. 3. No consideration is given for launch costs, which are considered a separate matter.

Table 1: Example Probe Scenarios for an interstellar mission (100 grams) Acceleration (m/s2) Power (MW) Boost duration (years) End of Boost distance (AU)

0.136 2.04 7 (2,555 days) 22,230.9

0.190 2.85 5 (1,825 days) 15,788.7

0.317 4.75 3 (1,095 days) 9,483.2

0.951 14.26 1 (365 days) 3,161.0

1.903 28.53 0.5 (183 days) 1,581.4

3.805 57.07 0.25 (91 days) 790.5

9.513 (~1g) 142.69 0.1 (37 days) 316.2

19.026 285.39 0.05 (18 days) 158.1

38.052 570.78 0.025 (9 days) 79.05

It needs to be acknowledged that a 50 year mission to the stars is extremely challenging whatever the propulsion system being utilised and many example studies to address this are well documented [14]. This would become even more so if it was also desired to effect some form of deceleration, although it is assumed not to be the case for this study. Yet, at 0.1c the encounter time at the target will be days. If we assume a typical 100 AU stellar system diameter, then at 0.1c the probe would have passed through the entire system in 0.0158 years or around 6 days. For this reason, it might be worthwhile for any future iteration of this work to look at ways of slowing the probe down as it approaches the target.

94 | P a g e

Forward [15] has examined the idea of decelerating by electrically charging the probe to turn using the Lorentz force in the interstellar magnetic field [16], reversing the sail velocity so that the laser can decelerate it. He concludes that there is sufficient doubt about the strength of the interstellar magnetic field that we do not know if this is possible.

Andrews and Zubrin [17] discuss several difficulties relating to maintaining a focused beam on the sail over interstellar distances. They conclude that for the two-stage LightSail, the mirror must maintain surface quality to a non-plausible tolerance as it decelerates the second stage. They also discuss the fact that the laser dispersion due to beam quality, jitter, etc. must be considerably better than beam qualities of existing state of the art beams. Hence, they propose braking interstellar ships using drag from the interstellar medium or the solar wind by using magnetic sails. More recently, the concept has been evaluated with respect to laser-propelled interstellar missions [18], [19]. Perakis and Hein [19] propose combining a magnetic and electric sail for quicker deceleration than each of the sails alone.

Another possible option to effect some deceleration of the sail is to provide for a central concentric ring in the sail, enough for gasses to be ejected, and then to use the incoming particle stream hitting the sail as an energy source for a photovoltaic mini-electric (ion) engine. Such a concept was described by Landis [4]. It is not likely that this would provide sufficient thrust to decelerate to orbital velocity but the combination of the sail pressure and ion drive may be enough to increase the encounter time from days to weeks.

In the remainder of this paper we will lay out the various technical issues that are relevant to the probe design and therefore set out the necessary program of work that needs to be conducted in order to make a flight feasible. Where possible we provide more than one solution to some of the technical problems so as to provide options and inform the design reference point.

2. Specific Technical Challenges Several technical challenges are briefly addressed. Some additional issues are covered for completion.

2.1 Deep Space Navigation It is expected that due to the small size of the probe it will have limited ability to cause directional changes to its trajectory after the acceleration phase. It is possible to eject gas so as to change the pointing but this will have little effect compared to the directional velocity of the vehicle travelling at 0.1c. If it were possible however, with a larger probe mass, then navigation by pulsars and the known brightest stars within the stellar neighbourhood would be key. For pulsar navigation, a miniaturized X-ray telescope would be required, which are under development for CubeSat missions today [20]–[22]. Another possibility is to use miniaturized star trackers with star maps for various locations along the trajectory [23], [24].

Another, passive approach is to use the orientation of a laser beam locked on to spacecraft or orientation of incoming photons from the communication system in conjunction with the red-shift of incoming photons from the communication system or from the reflected photons of the beam-lock to calculate the distance. The precision of this approach is limited by the precision of red-shift measurements (current equipment has errors <1%) [25] and the laser beam diameter at the position of the probe. The best case is thus probe arrival at Alpha Centauri. Initial considerations lead to the following results:

The distance can be determined very precisely, while the position within the beam spot is known with a confidence of up to ±0.004% of an AU. Moreover, the probe needs to be equipped with very

95 | P a g e accurate pointing capabilities, but not only for navigation. When passing through the target system at 0.1c very high tracking and pointing accuracy is required as well, otherwise any images will be useless, especially when trying to approach an object more closely. The LISA targeting system is very large for what we are trying to achieve, but it uses technologies that can be miniaturized and achieves nano-radian accuracy. The James Webb space telescope also achieves nrad pointing (~24 nrad), so that there is interest and progress in this field. Miniaturized gyros and accelerometers (MEMS) to aid in the pointing motion and measurement of the orientation are a requirement too. Due to the delay in receiving signals on both ends the position of the spacecraft will be merely predicted at some point and deviations from the nominal trajectory can hardly be corrected in real time, requiring almost full autonomy of the spacecraft or group of spacecraft.

2.2 Communications between the Probe and Earth For the communications systems, we look at several options. This includes radiofrequency and optical communication. We consider the following communication architectures:  Radiofrequency (RF) communication via antenna on spacecraft and receiver in Solar system  Laser communication via laser on spacecraft and receiver telescope in Solar system  Radiofrequency communication via the Sun’s gravitational lensing effect.  Optical occultation communication as back-up solution: Opto-electrical parts of sail occult the target star. Changing occultation results in a “morse-code” signal.  Trailing communication: Trailing spacecraft are launched that serve as relay stations. Either radiofrequency or laser systems are used in conjunction.

As an example for communication requirements, we look at the Robert Forward Starwisp paper [1] that assumes 8 × 106 bits for an image taken by the spacecraft with a resolution of 1000×1000 pixel (8 bit per pixel for 256 shades of grey). At 80 bits per hour, it would take 100 hours to finish transmission of one file on the spacecraft side. Considering the communications delay at interstellar distances (several lightyears) this might not be an issue, however, sufficient power must be available and the downlink cannot be interrupted during transmission and receiving operations, respectively.

Messerschmitt [26] considered the theoretical limits of low power information transmission in the radiofrequency regime. The author argues that contrary to terrestrial and near-earth communication where bandwidth availability is limited, interstellar communication is energy limited and the underlying equations suggest that maximizing the utilized signal bandwidth is beneficial. Considering the limiting case of an infinite bandwidth, he calculated 8 photons per 0.46 Wh as the fundamental energy limit, i.e. with 4.6 W 80 photons per hour can be sent. The fundamental limit for received energy per bit is calculated as 7.66 × 10−23 J/bit (page 227 of Messerschmidt’s thesis), assuming a total noise temperature of 8 K.

For our own link budget calculations we make the following common assumptions: a) the maximum distance is 4.3 lightyears (Alpha Centauri); b) the output power of transmitter is 1W; c) the bandwidth is 1 Mhz, which can be seen as representative for a large bandwidth RF sytem and a typical laser linewidth; d) the receiver antenna is 70 m in diameter, which is equivalent to the currently largest antennas in the DSN.

Moreover, we assume an antenna efficiency of 65% with the gain profile of pencil beam antennas, no channel coding and the downlink as the worst-case scenario since it is reasonable that more power is available on the receiver side in the solar system. Constant improvements and developments in the communications sector are likely to only improve upon our estimates.

96 | P a g e

The resulting RF link budget assuming K-band utilization is shown in Figure 2. Since we want to miniaturize the spacecraft, thus, limiting the available transmitter power, transmitter antennas have to approach diameters of hundreds of meters to allow for the transmission of just 1 bit/s. Even larger antennas are necessary if positive Signal-to-Noise ratios are required to separate the signal from background noise. A solution could be an ultrathin foldable antenna, based on graphene sandwich material, similar to the material used for the laser sail. Satellite antennas with diameters of close to 20m in diameter have already been flown on geostationary satellites, for example, on the ETS-VIII mission. Hence, a 100 m antenna is deemed to be feasible by extrapolating existing technology.

Figure 2: RF link budget calculations at the fundamental limit

Optical communication is another option, where lasers are used instead of radiofrequency antennas. The higher frequency of lasers allows for a higher data rate. However, since lasers are highly directional, accurate pointing of the beam is required to avoid excessive losses. Lasers for interstellar probe communication have been proposed by [8] and Lubin [5]. Reference [5] proposes to submit the data via short laser power “bursts” to achieve high data rates over short periods of time. Moreover, the development for chip sized photonic phased laser arrays is actively pursued [27]. For our optical link budget at 500 nm (green) wavelength laser is considered. We assume a pointing accuracy of at least 1 nrad, which is about an order of magnitude better than what currently seems feasible [28][29]. Thus, it is within the realm of possibilities considering future developments in the area. A Gaussian beam with a divergence of 6.1 µrad is assumed, the path loss is mainly due to spill over the receiver while pointing loss is based on pointing accuracy and an estimated standard deviation. We further postulate that ≥1 bit/photon data encoding is possible since different methods working in this direction have already been presented [30][31]. With a 1 cm laser beam transmitter on the spacecraft side the resulting link budget is shown in Figure 3.

Losses pertaining to the optical communication system that have not been considered are related to optical emissions from the telescope/ array, emissions from our solar system dust both scattering sunlight and emitting thermal radiation and the Cosmic Infrared Background [5]. For terrestrial receivers the atmospheric scattering and emissions present further complications.

To give an impression of the RF and optical antenna sizes needed for a specific downlink speed Figure 4 and Figure 5 are presented. It gives the achievable data rates at a distance of 4.3 light years

97 | P a g e and a transmitter power of 1W as a function of both transmitter and receiver antenna diameter assuming 65% antenna efficiency. At first glance, the plots suggest that optical communications are far superior in terms of achievable data rate for a given setup. However, assumptions have been made regarding pointing accuracy, jitter and bit/photon capacity that might be too optimistic, and, as mentioned above, some losses have not been considered. Thus, more detailed analysis is required to establish a truly reliable optical communications trade space.

Figure 3: Optical link budget calculations

To improve the gain at the receiver end [32], the Sun’s gravitational lens could be used as a gigantic receiver station, as Drake discovered [33]. The electromagnetic signals are amplified by the Sun’s gravitational field and a receiver spacecraft at the Sun’s focal point 550 AU away can pick up the signal [34]. Technical challenges are to position the spacecraft at a straight line with the Sun and the interstellar probe over these distances and to keep track of the signal from the probe.

Figure 4: RF communication design space at 4.3 Figure 5: Optical communication design space at 4.3 lightyears distance using the same assumptions lightyears distance using the same assumptions stated in the text above with 1W transmitter power. stated in the text above with 1W transmitter power and 1 bit=1 photon.

An option to maximize gain on the transmitter end and to avoid additional mass/spacecraft components is to utilize the laser sail itself as the antenna, for both RF and optical communication.

98 | P a g e

A completely different, unconventional communication method is to directly use environmental features for communication. Like exoplanet search, where the occultation of the stellar disk is used for detecting planets via the transit method, we can imagine that a probe flying towards Alpha Centauri occults one of the two bright stars. By using electro-chromic patches on the laser sail, the sail can change its optical transparency. Given the natural variation in luminosity of the star, we can imagine artificial luminosity changes via the sail that are strong enough to be detected from the Solar system. Such a communication system would transmit a form of Morse code and would have a very low data rate. However, it might be possible to transmit basic telemetry data.

Using trailing spacecraft as relay stations for communication the distance for communication would be reduced, however, the mission complexity overall increases due to the sequential launch of the spacecraft.

As this section shows, there are several options for communication over interstellar distances that are in principle feasible with technologies likely to be available during the next 10-20 years. Moreover, there is potential for several augmentations that can be made to classical communication system to make such systems work at the gargantuan scales we are considering.

2.3 Spacecraft Probe Size (Miniaturization) The sorts of electronics that can be packed into a small probe was analysed. Our starting point was ChipSat (sprite) technology [11], [35].

Figure 5: Chipsat Probes

Future trends in miniaturization may enable unprecedented spacecraft, mission architectures, and laser infrastructures:

 Swarm lenses, created by spacecraft swarms such as proposed in the NASA NIAC “Orbiting Rainbow” concept, as introduced in Section 2.18.1. Such a concept could allow for launching a large number of “swarm” spacecraft in the gram-range and still send data back. Required laser power could be significantly reduced that way. Furthermore, massive redundancy could be established [36]. Another approach was proposed by Underwood et al. [37] by assembling a large optical telescope from small autonomous telescope elements. Each element is a CubeSat, equipped with the basic satellite subsystems.  3D-integrated electronics: Circuits and sensors could be further integrated via 3D- integration, further reducing the mass of the spacecraft [38], [39].

99 | P a g e

 Miniaturization: Further miniaturization in electronics and the use of NEMS (nano) components could allow for even smaller spacecraft sizes [40], [41]. Fundamental physical limits for optical instruments still exist [42], however, such instruments could be formed by distributed small spacecraft, such as chip-sized satellites forming a lens and another spacecraft carrying a detector [43]–[46]. Intuitively one would expect that the miniaturization of electronic components would increase its vulnerability to the interstellar radiation environment, as the damage from the impact of a single radiation particle would affect a higher number of components. However, recent advances in Field-Programmable Gate Arrays (FPGAs) and latch up protection have considerably reduced the vulnerability of electric circuits to in-space radiation in general.

2.4 Stability of Sail to ride the Beam Passive sail stability can be achieved by a conical shape of the sail, as [47]–[49] have shown analytically and experimentally for microwave sails. The resulting force vector moves the sail automatically to the centre of the laser beam. However, such a sail geometry does not seem to be appropriate for sails that are subject to high acceleration loads. Hence, more recent results [50] have proposed a spherical sail geometry. As the authors have remarked, such a geometry would increase the cross section of the spacecraft in flight direction, increasing the amount of interstellar matter impacting the sail and the risk of a catastrophic dust particle impact. Further open questions are which geometries are optimal for laser sails, depending on the laser and sail material characteristics, as [5] has demonstrated for different laser array geometries.

2.5 Thrust Vector Control of Sail Several attitude determination and control system (ADCS) options exist during and after the acceleration phase. Attitude control refers to the change in attitude of the spacecraft. Determining the attitude of the spacecraft is often a necessary condition for attitude control. By contrast, changes in position are referred to as “trajectory modifications”. Attitude control during acceleration can be accomplished via several technologies: Electro-chromic surfaces such as used for the Japanese space probe Ikaros is one option, displacing a mass on a boom, and small flaps at the outer edges of the sail are alternatives [51]–[53]. Electro-chromic surfaces change their optical properties by changing electric potential [54]. A darker part of the sail reflects less and absorbs more; hence a momentum is generated if the symmetric opposite part of the sail is not darkened. Displacing a mass on the boom results in generating a momentum, as the centre of mass of the sail changes the direction of the resulting force vector on the sail [52]. Small steerable flaps on the edges of the sail create small forces on the sail that induce torque and a momentum [51].

Options during acceleration phase:  Electro-chromic surfaces on sail [54], [55]: The area with the electro-chromic coating changes its optical property. Usually the electro-chromic surface decreases its reflectivity. This means that the resulting force acting on the side with the coating is lower than on the opposite side of the sail. The resulting torque turns the sail around the x-axis.  Mass on boom [52]: Another option for inducing a torque is to displace the centre of mass of the sail. The change in centre of mass results in a larger angular momentum on the left side of the sail in the illustration than on the right. In consequence, a torque is generated that turns the spacecraft around the axis perpendicular to the plane of this document.  Flaps [51]: Using small flaps at the edges of the solar sail generates a torque on the sail by changing the angle of the sail. Contrary to the two former options the flaps enable to induce a rotatory movement to the sail by creating a torque around the axis going through the centre of the sail, similar to a windmill.

100 | P a g e

Options after acceleration phase Controlling the spacecraft after the acceleration phase is challenging but still possible. A classic approach is to use thrusters with a high specific impulse in order to save fuel and at the same time a low mass. One option is the field-emission electric propulsion (FEEP) that is already being developed for CubeSat’s [56], [57]. FEEP specific impulses range from 4,000s to 8,000s and thrusts in the μN range. Propulsion-less systems are, for example, electromagnetic tethers and electric sails [58], [59]. By deploying tethers or wires asymmetrically, a torque can be induced via the momentum of incoming interstellar electrons and protons. A further option is the use of the galactic magnetic field, which was rather proposed for trajectory modifications in the past [15], [16]. Due to the low field strength of the magnetic field of an average of 1nT compared to 30μT for the Earth magnetic field [60]–[62]. Assuming a wire with a diameter of 1m and 1 to 1000 windings and a 0.1A current, an angular momentum on the order of 10-10 to 10-7 Nm can be generated. The induced angular momentum would be one to several orders of magnitudes lower than for the FEEP thruster. As another option, [5] proposes photon propulsion. It would create thrusts in the nN range.

Table 2. Propulsion Methods Technology Propellant needed? Thrust range

FEEP Yes 10-6 – 10-5

Electromagnetic tether No Depends on current and length

Electric sail No Depends on current and length

Magnetorquer No 10-7 – 10-10

Photon thrusters No 10-9

2.6 Spacecraft Instrumentation and Sensors Recent advances in MEMS technology have resulted in a plethora of miniaturized sensors for space applications [63]–[66]:  Printed electronics [27]: There are a range of sensors such as temperature sensors that can be printed via technologies commonly used in the area of printable electronics. These electronics are usually limited by their complexity and voltage. Whereas standard space electronics operates at 3 V or 5 V, printed electronics would operate at higher voltages such as 30 V. Furthermore, due to limitations in printing resolution, more complex components such as microprocessors cannot be fabricated with this technology. However, the main advantage of printed electronics is its low weight. In a NASA NIAC study [27], a basic miniature planetary probe prototype was designed with a total mass of 4 grams.  Micro Electric Mechanical Systems (MEMS) sensors: A large variety of MEMS sensors exists such as: - Magnetometers [67], [68] - Gyroscopes [69]–[71] - Accelerometers - Sun sensors [72] - Star tracker [23], [73], [74] - Sun sensor [72]

It is clear that there are basic physical limits to miniaturization for certain instruments such as the aperture size for optical instruments. An overview of possibilities for miniaturization for CubeSat applications is given in Selva et al [42].

101 | P a g e

For our spacecraft, we propose the following set of instruments: - MEMS spectrometer [75]–[77] - Optical MEMS camera with aperture: Used as star tracker and camera. The aperture is made of a graphene sheet structure that is extremely light but is still a good stiffness characteristic. - Camera: standard CMOS technology - MEMS particle detector - MEMS magnetometer

Miniature Gamma Ray Spectrometer It is proposed to use a Sodium Iodide (Thallium doped) scintillating crystal, wrapped for protection with PTFE tape on 5 faces, and having the 6th face bonded to a large area photodiode. This is then connected to a sensitive amplifier. High energy impacts with the crystal will result in scintillation, and this scintillation will be seen by the photodiode. A spectrum will be produced. This is a known method for use in small space spectrometers.

Optical Camera (doubling up as star tracker) A smartphone camera module will be used to reduce mass, since these modules have masses as little as a few grams. Using a camera sensor with the largest Megapixel count, however, would not be the most effective solution. What is required is a camera module which has less noise than other modules, whilst still producing an adequate resolution image. It is anticipated that a camera module of about 8 to 12 Megapixels will be chosen for this reason, and because of the mass constraints, a lens system based on the lenses used as external lenses for smartphones would be optimised for this purpose.

IR Camera The IR camera would consist of a smartphone camera module, similarly to the optical camera. It would only include the necessary filter for use in the near IR.

Light Intensity sensor A Light Intensity sensor measures the intensity or brightness of light. In this application, it can be used as a way to determine the brightness of a target object being pointed at. A Light Intensity sensor capable of detecting as little as 188 uLux up to 88,000 Lux, and with a 600,000,000:1 dynamic range has been identified. This sensor has a mass of 1.1g

UV sensor The UV sensor proves another emission detecting sensor which would be pointed at the appropriate target with the other sensors. The baseline UV sensor is a UV-B Sensor with a 240nm - 370 nm range, and with a mass of 0.7g.

Temperature sensor There are numerous surface mount temperature sensor solutions, and it is proposed to use one of these temperature sensors, with a suitable operating range.

Radiometer It may be possible to incorporate a compact radiometer, however work is ongoing to determine the packaging constraints for this sensor.

Inertial Navigation The Inertial Navigation System consists of:

102 | P a g e

3solid state gyros (X, Y and Z-Axis) 3 solid state accelerometers (X, Y and Z-Axis) 3 solid state magnetometers (X, Y and Z-Axis) Star Tracker (the optical camera) Sun sensor (used for tracking the target star during fly-by) The well-known problem of drift can be mitigated by using the star tracker and a Kalman filter, along with the temperature sensor. These will enable the drift of the gyros to be zeroed out.

Sensor Positioning All imaging or related sensors would be orientated in the same direction, to ensure they are all imaging the same target. This would include the optical camera, IR camera, light intensity sensor and UV sensor.

2.7 Interstellar Dust and High Energy Particle Bombardment The probe is subject to the interstellar medium it traverses during its flight. The effects of the interstellar medium on the spacecraft have been previously explored by [78] and [79]. Three types of effects of the interstellar medium on the spacecraft can be distinguished: Galactic cosmic rays, particles, and dust [80]. The galactic magnetic field has already been previously introduced.

The first is high-energy cosmic rays which derive from either solar energetic particles or galactic cosmic rays. Of this, 85% are high-energy protons, 14% are alpha particles, and the remainder is small portions of positrons and antiprotons (<1%). The peak of this energy spectrum tends to be at around 0.3 GeV. High-energy cosmic rays can alter the states of electronic circuits. The mitigating options to manage this include physical shielding (e.g. radiation hardening), magnetic shielding or some combination of both. A spacecraft in interstellar space is subject to a higher flow of heavy particles as inside the Heliopause [81], [82]. On the other hand, Solar protons are absent. For an interstellar probe, it is essentially impossible to protect against galactic cosmic rays, except by more than a meter of hydrogen or lead.

Interstellar particles predominantly consist of hydrogen and electrons. Hydrogen occurs in either a neutral or ionized state. The protons can have significant affects at velocities greater than 0.01c, where energy is dissipated into the structure through atomic ionisation leading to emission of radiation and structural heating through absorption. At very high energies these collisions may cause plastic deformation and local melting, leading to a degradation of the spacecraft structure. The electrons from the interstellar space will lose their energy by emission of radiation as an electron passes close to the nucleus, and radiation is absorbed by the material structure via the photoelectric effect, Compton scattering and pair formation. The impact of the electrons may also lead to the emission of Bremsstrahlung radiation as soft x-rays, which further heat the structure. Estimates for the interstellar hydrogen, proton, and electron density have been presented in [80] and are depicted in Table 1.

Table 1: Interstellar hydrogen and electron density ranges [80]

Interstellar medium element Conservative density range [particle/cm³]

Atomic hydrogen 0.10 – 0.23

Electrons 0.05 – 0.21

Neutral and ionized hydrogen 0.15 – 0.44

103 | P a g e

Interstellar dust grains are substantially smaller than interplanetary dust grains. A typical grain size is 0.1μm. Interstellar dust comprises about 1% of the mass of the interstellar medium, where 99% are hydrogen and electrons. However, the energy of an impacting dust grain on the structure is much higher than for protons or electrons. When the particle slows down into the material to subsonic speeds, the kinetic energy is deposited into a volume larger than the particle itself. Hence the energy density and its temperature are much higher, around 1012 K. This is high enough to vaporise and cause mass loss through ablation. For a typical grain size 10-16 kg the impact energy of order 1011 – 1012 MeV at 0.15c. Two processes will then result from such bombardment, which includes heating of the material but no permanent damage, and processes which will cause permanent damage.

As examples to study we considered three types of geometries, which we call model 1, 2 and 3 and all are assumed to be cylinders. Model 1 has a radii of 1 mm and a length of 10 mm (aspect ratio 2: 10) which we call the ‘small model’. Model 2 has a radii of 10 mm and a length of 100 mm (aspect ratio 20: 100) which we call the ‘slim model’. Model 3 has a radii of 20 mm and a length of 100 mm (aspect ratio 40:100) which we call the ‘fat model’.

One of the considerations is simply the temperature rise due to the incoming protons and electrons, but permanent changes in the material will only occur if the temperature is sufficiently high. For the three geometries considered we find that the temperature is in fact not high and amounts to 192.7 K for the 1 mm radii design and 108.38 K for the 10 mm and 20 mm radii designs. The surface temperature is mainly a function of the frontal area geometry and the incoming energy flux.

It is necessary to assess the mass loss and therefore frontage shielding requirements on our mini- spacecraft. To do this we can adopt the Benedikt [83] relation or the Langton [84] relation and we will use to make an approximate assessment for how much shielding is required. We will look at three different areal geometries for our 280 gram probe. We will also look at three different temperatures for comparison, which includes 600 K, 1,000 K and 1,500 K.

The Benedict relation is an equation to model the mass loss due to material erosion from an incoming particle stream. It is defined by several parameters including the fraction of the energy that is transferred from the medium, which will result in permanent changes in the material of the vehicles – this is assumed to be 0.25. It is also derived from the heat flow required to destroy a unit mass of the material. The latent heat of sublimation defines the characteristic property of the chosen material. The equation is also a function of the velocity relative to the speed of light. The frontal area of the probe also features in this relation.

Some calculations were conducted to assess the mass loss from the probe under the assumption of a 0.1c velocity for a 50 year mission profile. A crucial factor in these calculations is the assumption of interstellar medium density. Note that the conservative upper and lower bounds for the density of hydrogen and electrons is 2.49 – 7.30×10-22 kg/m3. The results of these calculations for the three model geometries are shown in tables 4 and 5 and these are conducted assuming a Beryllium frontal shield material.

Overall these numbers look very encouraging in terms of our aim and for the reference design we recommend studies start with the assumption of a 20 grams shield provided the length of the probe is much greater (×10) than the radii on the frontal area. For comparison it is worth noting the heat of sublimation rates of some standard materials that are potential shield candidates. This includes Lithium (2.57×106 J kg/m), Beryllium (35.53×106 J kg/m), Boron (53.6×106 J kg/m), Graphite (60×106 J kg/m), Aluminium (12.1×106 J kg/m). Some examination of the material aerogel is also recommended which could have ideal applications as a heat shield given its lightweight structure.

104 | P a g e

Table 2: Particle Shield Calculations for a Beryllium material over a 50 year flight at 0.1c. Model 2.49×10-22 kg/m3 7.3×*10-22 kg/m3

1 dm/dt=3.125×10-12 kg/s, 5 g mass dm/dt=9.162×10-12 kg/s, 14.6 g mass ablated ablated

2 dm/dt=3.125×10-10kg/s, 493 g dm/dt=9.162×10-10 kg/s, 1445 g mass mass ablated ablated

3 dm/dt=3.125×10-10 kg/s, 1972 g dm/dt=9.162×10-10 kg/s, 5781 g mass mass ablated ablated

Table 3: Particle Shield Calculations for a Graphite material over a 50 year flight at 0.1c. Model 2.49×10-22 kg/m3 7.3×10-22 kg/m3

1 dm/dt=1.850×10-12 kg/s, 2.95 g dm/dt=5.425×10-12 kg/s, 8.65 g mass mass ablated ablated

2 dm/dt=1.850×10-10kg/s, 292 g dm/dt=5.425×10-10 kg/s, 856 g mass mass ablated ablated

3 dm/dt=1.850×10-10 kg/s, 1168 g dm/dt=5.425×10-10 kg/s, 3423 g mass mass ablated ablated

One important assumption of the above analysis is n, the fraction of energy converted from impacts that does permanent damage. We assumed a high value of 0.25 but this was very conservative as a worst-case model so there does appear to be plenty of scope for reducing the shield mass overall.

It is assumed that the distribution of interstellar dust size follows the power law distribution [85]. Hence, there is a chance that the probe might collide with a dust particle that would instantly destroy it. This risk can be mitigated by redundant probes. In that it is not one probe that is sent but many, and this way if any are lost it would not matter.

So with our small probe one of the problems is, how to get smaller and still protect sufficiently against lattice displacement. We recommend the adoption of an ablative material on the front of the probe. This should be a material that is extremely light but would still absorb the impacts. The key requirement for any material is that they are very lightweight but also subject to mass ablation so they can be eroded away by the constant stream of particles.

However, this ablative front shield will only mitigate the incoming high-energy particle impacts. What about the radiation protection given that any electronics will likely have a krad radiation limit beyond which they will not work? For this it may be necessary to explore the option of generating a self-induced magnetic field around the probe, as a form of mini-magnetosphere. But this will not mitigate the most energetic of particles. Also this comes at the cost of increasing the mass to the vehicle. Again, playing the statistics game by having many probes as a form of redundancy should take care of that and the objective would be to get a large percentage of the probes to complete the journey.

In addition, the on board computer should be coded up with fault-tolerant software, which would decouple damage done to the hardware from leading to software errors. Third, we advise that the

105 | P a g e electronics is switched off most of the time so that any flip switching will not have any effect on the probe.

There are developments today in relation to CubeSats that will be immune to a lot of radiation. It is possible to implement any processor on an FPGA, with the benefit of being able to re-route your FPGA in space and therefore “reset & heal” your own main processor. If you then mix that with some radiation hardened memory (maybe MRAM, maybe phase change memory, maybe FRAM or something else) and you can run your system for a long time, because you are able to re-route your processor on the FPGA. There are small FPGAs that have already been developed and these may have enough processing power to run a really low level program for us. And maybe we can use some radiation hardening manufacturing process on them (against SEL, SEB, and all the hard errors). We can also implement a lot of strategies to cope with radiation effects through software. Especially the MRAM with the critical information can be secured. Overall we recommend the implementation of a hybrid protection system that includes radiation hardening, self-healing capability and corrective software. As this will add mass to the system so trade-studies will need to be constructed.

2.8 System Reliability over Mission Time An obvious approach to reliability and redundancy is simply to propel multiple (thousands or millions) of probes towards the nearest stars as illustrated in Figure 6. This also has the advantage of a potential long distance space communications option, in terms of utilising optoelectronics to encode information on the return wave of a reflected beam. The array, would present an effective reflection disc.

Figure 6: Illustration of multi-sail array for reliability, redundancy and enhanced communications link

We assume that the spacecraft remains in hibernation mode for most of its trip. Due to the power limitations imposed by the nuclear battery and the supercapacitor, subsystems are activated selectively. Note that hibernation protects from life-time issues from operation but does not prevent effects that are independent of the component operating. For example, radiation degradation takes place irrespective of component operation.

Apart from hibernation, the following mitigation strategies are used, as already introduced in an earlier section:

106 | P a g e

 Minimize mechanical components that are subject to wear: magnetically levitated MEMS gyros  Redundancy: Although we assume that one spacecraft is a single-string system, we assume the launch of several spacecraft of the same type.  FPGA: For protecting against software errors induced by radiation, we rely on FPGAs, which are very tolerant to radiation effects on the hardware. The software can be executed even with damages inflicted to the hardware.

2.9 Spacecraft Thermal Issues Use of radioisotope battery (power subsystem) to keep spacecraft heated. The nuclear battery generates 1 We with an efficiency of 5% [86]. The remaining 95% of the energy generated is released as heat. This is about 19 W of heat which is transmitted via heat conductors such as copper circuits to components that need to be kept above certain minimum temperatures. As a more recent technology, carbon nanotubes could be used for transporting heat [87], [88]. Whenever components need to be operated and woken up from hibernation, the heat from the battery could be selectively transmitted to these components allowing for a rapid wake-up from hibernation. The On Board Data Handling (OBDH) system is located close to the battery in order to allow for a radiative heat transfer independent of heat conducting circuits.

2.10 Power Supply for the Probe In consideration of the power supply for the probe we have identified several options which will need further examination. These options can be divided into options relying on power sources external and internal to the spacecraft. Internal power sources are devices which are brought on board of the spacecraft and produce energy without any external inputs. One of the technologies suitable for the interstellar probe could be a scaled down RTG utilising Americium-241. This element has a radioactive half-life of 432 years, which is longer than the one of Plutonium 238 (87.7 years), but comes at a cost of a reduced power density of 0.13 kW/kg, which is low compared to the standard Pu-238 having a power density of 0.54 kW/kg. However, Americium-241 also produces more penetrating radiation through decay products so increased shielding may be required. There are prototype RTG designs that can be examined which give output of 2-2.2 We/kg for 5 We RTG designs. Landis et al. [89] have investigated the use of alphavoltaics in space. Contrary to RTGs that are based on thermoelectric conversion, alphavoltaics convert the ionization trail of alpha particles into electricity. Commercially available alphavoltaic cells have a specific power of about 0.33W/kg [89] which is three orders of magnitude less than for RTGs. Landis et al. [89] have also recently investigated the use of betavoltaic cells for small space missions. Betavoltaics use a direct conversion approach by exploiting elecone-hole pairs that are generated by electrons emitted from the radioactive material. The main shortcoming of betavoltaics is the use of low power density and the short half-life of the used radioactive substances such as Tritium and Promethium-147. Furthermore, the use of nuclear D-cell battery is an option. A 5-20 We range is being developed by the Centre for Space Nuclear Research [90]. In contrast to alphavoltaics and betavoltaics which directly make use of the emitted radiation of a radioactive source, radioisotope thermophotovoltaic cells convert the radiation from a radioactive material via photovoltaic cells in the infrared spectrum [91]. The main advantage is the higher efficiency, compared to other nuclear batteries. Teofilo et al. [92] report an integrated specific power of 14We/kg for thermophotovoltaic cells with efficiencies between 19-25%. Hence their specific power is about two orders of magnitude higher than for RTGs. Another example worth mentioning is the possibility of developing a tiny battery powered by micro-organisms. Microbial fuel cells will rely on some kind of organic matter and would have limited lifespan – and currently we do not know how long microbes can metabolise in extreme environments. Yet, they can generate small amounts of electricity. Such a system could be biofilm

107 | P a g e powered [93], [94]. Recently developed miniature microbial fuel cells generated electric power on the order of 10-6W at a volume of 0.0026mm². Using the density of Carbon (the fibers used are made of Carbon) yields a specific power of 788W/kg. The specific power is therefore about the same order of magnitude than for radioisotopic thermal generators. However, some drawbacks are the expected lower stability of the power source over long durations, and the need for consumable mass. A comparison of the aforementioned technologies is presented in Table 4. For this feasibility study, the Strawman requirements are used, leading to the assumption of 0.05% transfer time and 99.95% charging time for the power system. With a 5W transmitter power and an efficiency of 50%, the required input power is 10W and this yields a 0.02 W continuous power need. The nuclear D-cell battery is identified as the most promising technology with higher feasibility due to the low mass. Table 4: Comparison of internal power sources.

Technology Feasible? Power density

RTG No (too heavy: ~0.01 kg) 2-2.2 We/kg

Alphavoltaics No (too heavy: ~0.06 kg) 0.33 We/kg

Betavoltaics No (too heavy, too short half-life of - Tritium, Promethium 147)

Microbal battery No (stability, temperature) -

CubeSat Nuclear D-cell Yes (~0.0013-0.0017 kg) 12-16 e/kg battery (thermophotovoltaics)

Options with power sources external to the spacecraft can either rely on artificial or natural sources. Artificial sources imply beaming electromagnetic waves from the solar system to the sail as a remote power source, as proposed by Forward [1]. Either a laser beam or a microwave beam could be utilised. In the case of beamed-laser power, getting 0.1 W/m2 to the spacecraft over a distance of 4 light years would require 10 GW of laser power when assuming a wavelength of 1000 nm and nrad pointing accuracy. For a 1000km spot size, a 90km aperture at the solar system would be needed. For the beamed microwave-power (Starwisp), very high power levels and receiver antenna are needed. Due to the large wavelength, the size of the aperture is also prohibitive making the option rather unattractive. Various natural sources are also available in the interstellar space. Stellar luminosity, i.e. residual light from nearby stars could be captured by solar cells. The areal power density of these light sources is likely on the order of 10-7 to 10-6W/m², if it is assumed that 5 stars illuminate the spacecraft from a distance of 100,000AU. Use of an ultrathin and lightweight organic solar cell could be made for capturing the rays. Current research [37] claims 0.1 kg/kW so that for a 100 W system you would only need 10 g of solar cells when close to a star. The resulting captured energy of the starlight is rather low and it would take months for harvesting 1 Ws with a 1m² surface area. The large diffusion of this light makes inefficient for powering the probe. Fluctuations in the galactic magnetic field could also be exploited: Due to the turbulent and anisotropic structure of the galactic magnetic field, changes in the field strength could be exploited for generating a current via the Lorentz force. The field strength is close to 0.1-0.6 nT. However, the gradient of the field strength does not seem to be known today and it is difficult to estimate how much power could be generated from a system exploiting it. Galactic cosmic rays, protons, and electrons could be used for creating an electric current. This could be done by transforming the kinetic energy of the incoming particles and rays into electric energy with the help of betavoltaics.

108 | P a g e

Assuming that the kinetic energy of incoming charged particles could be completely converted into electric energy, at 10%c, a surface area of 1cm², a power between 10-15 and 10-16 W could be harvested. In reality, the power is likely orders of magnitude below these levels. Hence, using interstellar particles as an energy source does not seem to be a viable option, unless a significantly larger area is covered. Finally the use of an electromagnetic tether as proposed by Matloff is quite promising. We can supply some 5 W during flight with a 100 m tether by capturing interstellar electrons. The tether can be broken up into 10×10 m tethers. The current generated is about 3.3 Amp. The mass of the tether is below 0.1 gram. The whole system could be built for a mass close to 0.1 gram [59]. A summary of the technologies is shown in Table 7, where it is evident that the electromagnetic tethers and the beamed laser power are the most mature options.

Table 7: Comparison of external power sources.

Technology Feasible? Power density

Solar cells (Stellar light) No (yes close to star) 10-6 – 10-7W/m² @interstellar space

Galactic magnetic field No Unknown fluctuations

Cosmic rays with beta No 10-11-10-12 W/m² @0.1c voltaics

Electromagnetic tether Yes 5W @10×10 m tethers; (Charged interstellar 0.1gram particles)

Beamed laser power Yes 0.001 W/m² or higher, depending on spot size

Beamed microwave No power

Clearly a small research program will be required to work out the best system for the interstellar probe but what is encouraging is that there are lots of options that already exist or are emerging to supply the on board power. This issue does not appear to be a show stopper.

2.11 Data and Telemetry Management Data from the sensors is temporarily stored in the memory within the OBDH system. Once the communication downlink to the Solar System is established, the stored data is then forwarded to the communication system. Currently, no on board-treatment of the data is planned, as this would probably exceed the hardware and software capabilities. However, with future advances in computing and electronics, data treatment on-board could be envisaged in order to reduce the amount of data transmitted by selecting the most relevant data.

2.12 Sail Material and Design The laser sail material is a crucial element for the success of a small interstellar probe as its temperature limit determines the maximum laser power per surface area and its areal density determines the mass of the sail. The maximum temperature depends on the optical characteristics of the material. Hence, the areal density and the optical characteristics are the most important

109 | P a g e parameters. The values from Matloff, 2012 are shown in Table 8 [7]. The analysis conducted by the team from the Technical University of Munich [95] during the Project Dragonfly design competition resulted in the choice of a graphene sandwich sail due to its superior thermal characteristics for resisting the laser beam and its extremely low density. One disadvantage of graphene-based sail materials is the low reflectivity compared to materials such as Aluminized Mylar. However, the extremely low density compensates for this shortcoming.

Table 8: Comparison of Aluminized Mylar, Grahene Monolayer and Graphene Sandwich according to Matloff, 2012 [7]

A technology which can significantly improve the performance characteristics of an interstellar sail is the one of dielectric materials. The main benefit of dielectric materials lies in their ability to have their reflecting properties “tuned” at a specific wavelength. By alternating between high index and low index dielectrics, the reflectance at a specific wavelength can be increased close to unity (Forward 1985 [1]). Their high emissivity, low absorption and high-temperature properties makes them suitable for high laser intensities (Landis 1999 [3]).

The reflectivity of a dielectric material reaches a maximum when the thickness of the film 푡 is equal to one quarter of the light’s wavelength within the film (휆/푛). This is when constructive interference can occur and the condition reads:

휆 푡 = (1) 4푛

The reflectivity 푅 of the quarter-wave layer film is then given by [3]:

2 푛2−1 푅 = ( ) (2) 푛2+1

A summary of promising dielectric materials based on oxides is given in Table 9.

110 | P a g e

Table 9: Dielectric sail material properties

Material Reflectivity [-] Density Emissivity [-] Max. Max [kg/m3] Temperature intensity [K] [W/m2]

Al2O3 0.26 3960 0.9 2500 2.7 10^6

Ta2O5 0.52 8750 0.25 2140 6.2 10^5

ZrO2 0.42 5500 0.95 3000 7.5 10^6

The values for reflectivity, density and maximal temperature are taken from [3]. With the values found in literature for the emissivity, the maximal intensity was calculated.

Further increasing the number of layers of the dielectric film can lead to even higher reflectivity, which leads to two effects: the force on the sail increases and the absorbed energy becomes lower, leading to less strict requirements for the thermal management. At the same time however, the total mass of the sail is increased leading to an optimum for the number of layers.

Lubin has proposed the superposition of multi-layer dielectrics on metalized plastic film, leading to reflectivity close to 99.995 %. The dielectric layers are comprised of SiO2 and TiO2, whereas for the metalized film Ag and Cu have been tested. For multi-layer dielectric on metalized glass reflectivity values up to 99.999% have been achieved. These values refer to a short bandwidth around 1.06 microns of laser wavelength.

A summary of the tested materials and their respective properties is given in Table 10.

Table 10: Dielectric multi-layer sail material properties

Material Reflectivity [-] Density Emissivity [-] Max. Max [kg/m3] Temperature intensity [K] [W/m2]

Ag, SiO2, TiO2 5 0.9961 1400 0.03 1235 1.0 10^6 layers

Ag, SiO2, TiO2 15 0.9999535 1400 0.03 1235 8.5 10^7 layers

Cu, SiO2, TiO2 15 0.9999294 1400 0.07 1360 1.9 10^8 layers

The sail has a slightly conical shape in order to make it self-stabilizing when propelled by the laser beam. If the sail is subject to perturbations and is displaced from the laser maximum, it would automatically create a thrust force to realign with the beam maximum. This principle has already been introduced in an earlier section. Table 11 shows the main parameter values of the sail.

111 | P a g e

Table 11: Laser sail characteristics Characteristic Value

Material Graphene Sandwich

Areal density [kg/m²] 7.4×10-7

Radius [m] 183

Mass [g] 81.6

2.13 Assembly in Space 100 m kg/ 10× Space Station The assembly of large structures in space is a challenging task. The largest structure assembled in space to date is the international space station ISS. However, advances in on-orbit manufacturing might soon change the state of the art. The US Company “Made in Space” has announced end of 2015 that it will demonstrate the in-space manufacturing of large booms [96]. The project has been selected by NASA in the context of the Tipping Point Technologies Program. Expected truss lengths are up to 7 km and ring structures with a diameter of 555 m.

Furthermore, Tethers Unlimited is currently developing a system for manufacturing large truss structures in space [97]–[100]. A first demonstrator on a 6 unit CubeSat platform is planned to be launched until 2017 [97]. Its objective is to mature the technology to TRL 4-5.

To summarize, there are serious attempts underway to construct large truss and boom structures in space that have the potential for constructing kilometre-size structures in-situ. The technology has reached a prototypical level and is soon going to be tested in space.

2.14 Mass Reduction of Laser Beam Assembly One of the elements of the laser beam assembly that heavily contributes to the mass of the beam system is primary power generation. The most obvious technology is photovoltaic cells. We leverage on current advances in photovoltaic cells such as organic cells that have a rather low efficiency of <10% but an extremely low areal mass compared to high-efficiency solar cells. Latest developments resulted in a specific-mass 0.1 kg/kW for a terrestrial application [101]. We expect that further advances in photovoltaic cell technology will lead to further increase in mass-specific power output. One disadvantage of organic solar cells is their vulnerability to space radiation. However, degradation issues have been addressed in order to adapt organic cells to space environment [102]– [104].

2.15 Beam Assembly Cooling Heat on the order of several dozens of MW has to be rejected via radiators. High performance radiators are crucial for space exploration, in particular for nuclear-electric propulsion systems. Hence, increasing the mass-specific heat rejection rate has been one of the main objectives of space radiator research. For example, radiators using graphene are expected to reduce the mass by 80- 90% with the same heat rejection rate, as it conducts heat five times better than a carbon fibre- reinforced composite sheet [51].

2.16 Pointing of Beam Segment at Launch The pointing requirements for the laser aperture can be calculated by basic trigonometry. There are two effects that affect pointing:  Laser diffraction, which increases the spot size and decreases the power density of the laser beam on the sail.

112 | P a g e

 Jitter: Vibrations usually induced by equipment on a spacecraft such as reaction wheels.

Both aspects have been dealt with in the existing laser sail literature such as [2] for diffraction and [105]

2.17 Laser Beam Delivery Laser beam divergence becomes an issue at interstellar distances as too much laser power will eventually spill over the sail and cannot be used for propulsion anymore. While the lens system used to steer and focus the laser beam plays an important role, as discussed in the next subsections, the beam itself can be manipulated to decrease the divergence. Specifically, instead of using a Gaussian beam, which is produced by most laser systems, the beam can be converted to an almost diffraction- less Bessel beam, at least over a limited distance [106][107]. Ideally, one would create a zeroth order Bessel beam using, for example, an Axicon. This beam would propagate with diffraction over a certain distance before returning back to a Gaussian profile. The maximum Bessel-like propagation distance is given by the equation

2 푧푚푎푥 = 푅⁄푡푎푛휃 = 푅 2휋⁄(2.405휆) where 푅 is the aperture radius of the laser emitting system, 휆 the laser wavelength and the factor 2.405 is given by the location of the first root of the Bessel function. The advantage gained by such a system is illustrated in Figure 7. Since an Axicon is a conical prism optical element, however, there are some issues and losses associated with it. For the application in an interstellar lasersail system, the Axicon would have to be big, which in turn makes it heavy using standard manufacturing techniques. Moreover, exact pointing is required. Finally, the optical losses through the Axicon have to be traded off against losses caused by light spilling over the lasersail to choose the optimal solution.

50 45 40 35 30 25 Bessel beam 20 15 Diffraction-limited 10 5 Distance Distance 10m for spot size [AU] 0 0 200 400 600 800 1000 1200 Aperture radius [m]

Figure 7: Focusing capabilities of a purely Gaussian vs. a Bessel-Gaussian beam. 2.18 Lens Configuration In his 1989 paper [52] Geoffrey Landis looked at the idea of a segmented lens configuration as illustrated in the Figure 8. This means that there would be multiple lenses spread out between the laser and the spacecraft that will facilitate enhanced collimation and pointing accuracy. The table

113 | P a g e below shows some examples of the beam segmentation architecture and the various options for how it could be staggered.

For the conventional Fresnel lens-based architectures that were originally studied by Robert Forward, high mass ratios are avoided by using a stationary energy source. But this requires a large lens and the high lens/target distance results in an extremely high optical magnification, which presents alignment and positioning difficulties. Some advantage can be gained by using a lightsail reflective in a shorter wavelength regime. The method of lens segmentation however is to use many intermediate lenses spaced between the probe and the source. It is acknowledged however that these will still present pointing, positioning, and deployment challenges.

Figure 8: Use of multiple intermediate lenses to propel a light sail.

Table 12: Example scaling of Robert Forward Fresnel Lens via Landis Segmentation Scheme Total System Mass Number of Lenses Individual Lens (tons) Mass (tons)

560,000 1 560,000

112,000 5 22,400

56,000 10 5,600

22,400 25 896

11,200 50 224

5,600 100 56

1,120 500 2.24

560 1,000 0.56

Examining this type of segmented architecture, we estimate that the interstellar mission discussed in this report can be achieved with multiple N lenses instead of a single giant lens, and that the mission could be completed with 6 lenses each with a 5 km diameter spread out to around 70 AU.

114 | P a g e

2.18.1 Distributed mirror/lens system To lower the overall mass and simplify the deployment, instead of using solid lenses, mirrors and other optical elements (e.g. an Axicon) a distributed or inflatable system can be imagined. The orbital rainbow study [108] and DARPA’s Membrane Optic Imager Real-Time Exploration (MOIRE) are examples of such concepts. One class of such systems for refractive optics can be described by the “Bruggeman effective medium” approximation. Instead of a space filling medium, particles in a certain size range, with certain shapes and with a certain refractive index are used (e.g. ice crystals) to fill the volume of a prescribed shape by some amount (fill fraction). The changes in refractive index between the background medium (in our case the vacuum of space) and the particles causes refraction to occur with light beams that pass through it. The collective shape can be enforced using a laser trapping system or an inflatable structure. The focal length of such an effective medium can be approximated as

푓 = 2푅/(푛푒 − 1) (3)

where 푅 is the aperture radius and

2 2 (푛푒 − 1) = 3/2퐹(푛 − 1)/(푛 + 2) (4)

is the effective index of refraction, with 퐹 being the fill fraction and 푛 being the refractive index of the particles. It should be noted that these equations are derived from more general theories describing the propagation of electromagnetic waves through an effective medium and that an inherent assumption is that the refractive index of space is equal to one. A conceptual sketch showing how such a refractive optic would work is shown in Figure 6.

Some advantages and disadvantages of such a system are listed in Table 13 [108]. The precise light propagation properties and efficiencies of such an effective medium need to be studied further to assess their feasibility.

Table 13: Advantages and disadvantages of a large distributed optical systems

Advantages Disadvantages

1. Less sensitive to degradation 1. Danger of orbital debris creation by lost particles 2. Easier to maintain (repair of hull, readjustment of 2. Coherence of very large distributed structures is laser trap and injection of new particles) challenging 3. Possible use of in-situ resources (e.g. water) 3. Precise positioning is challenging 4. Significant mass and cost savings 4. Light loss due to particles not being completely space-filling

115 | P a g e

Figure 6: Conceptual design of a refractive optic using the principle of an effective medium

2.19 Conversion Efficiencies of Beamer According to Lubin [5] current fibre-fed lasers can have efficiencies near 40%. For example, the DARPA Excalibur program’s laser has a specific power of 5kg/kW with prospects of reaching 1 kg/kW near term. Brashears et al. further assume that laser efficiency will increase to 70% with the specific mass decreasing to 0.1 kg/kW in 10-20 years.

2.20 Cost of Mission Fixed cost: - Development & test of components (sail, communication, energy generation & storage, navigation) - Developing of specific manufacturing technologies (e.g. in-space manufacturing of large tethers or bubble-blow-up-technologies or mylar-unroll-technologies for the sails) (more needed if many probes should deployed)

Variable cost: - Transport cost of sail & components to space - Possible in space final assembly of the sail Variable cost depending on the number of sails, lenses used and the power requirements of the lasers (relating to the space solar power voltaic system size).

116 | P a g e

Used NASA Advanced Mission Cost Model and known values to estimate cost of spacecraft development [109].

Assumptions: ● Estimated payload, bus and sail separately ● Wrap factor in spacecraft cost model includes: Adv. Development, Phase A conceptual studies, Phase B definition studies, based on space shuttle program (worst case?) ● Assumed unmanned, exploratory science mission ● Final margin includes: operations capability development, program management and integration, program support wraps, based on space shuttle program (worst case?) ● Assume at least 3 spacecraft and 2 sails are required for development, test and launch ● Technology readiness in 2030 ● AMCM includes material, personal, risk, program, development cost ● Does NOT include launch cost, The summary of the development cost is shown in Table 14. It results in a total development cost of about 11M$, including production cost of the first spacecraft units.

Table 14: Development cost for interstellar probe Mio US-$

Total cost 11.28

Wrap Margin 1.38

Total cost + Margin 15.54

Inflation correction from 1990 to 2015 28.82

Phase A and B 0.72

Table 15: Detailed cost breakdown

For any future analysis, the overall mission cost using projected transportation should take account of cost decreases (as projected by SpaceX rocket reuse scenario) and this will need to be considered.

117 | P a g e

2.21 National and International Policies/Treaties on use of Directed Energy Devices in Space It is necessary to conduct a brief survey of the key laws, conventions and treaties which will be relevant to such an innovative laser sail mission given the use of directed energy sources. We do flag up that is not clear to this team whether lasers are considered to be conventional weapons or not. The Geneva Convention bans the building of lasers under a special conventional weapons treaty but we are unsure of the clear definitions which are covered. Another point to make is that some of the recent activities on treaties could potentially be in favour of such a mission, such as the recent addition of rights to utilize space resources and the right to keep control of launched objects. The following are some of the relevant articles which this team feels are relevant to such a mission as proposed for Andromeda. Outer Space Treaty  Article 8: The State that launches a space object retains jurisdiction and control over that object  Article 7: The launching state is absolutely liable for damage caused on Earth's surface or to aircraft in flight; if the damage is caused elsewhere (e.g., in space), the launching state is liable only if the damage is due to its fault or the fault of persons for whom it is responsible  Article 4: Limits the use of the Moon and other celestial bodies to peaceful purposes and expressly prohibits their use for testing weapons of any kind, conducting military manoeuvres, or establishing military bases, installations, and fortifications. However, the Treaty does not prohibit the placement of conventional weapons in orbit. → Lasers seem to be conventional weapons  Agreement Governing the Activities of States on the Moon and Other Celestial Bodies:  Exploration and use of the Moon shall be carried out for the benefit and in the interest of all countries, and due regard shall be paid to the interests of present and future generations and to the need to promote higher standards of living and conditions of economic and social progress and development in accordance with the U.N. charter.  States Parties bear international responsibility for national activities on the Moon, whether by governmental or non-governmental entities. Activities of non- governmental entities must take place only under the authority and continuing supervision of the appropriate State Party.  All space vehicles, equipment, facilities, etc. shall be open to other States Parties so all States Parties may assure themselves that activities of others are in conformance with this agreement. Procedures are established for resolving differences. Space Resource Exploration and Utilization Act of 2015  Sec 2:  Discourage government barriers to the development of economically viable, safe, and stable industries for the exploration and utilization of space resources in manners consistent with the existing international obligations of the United States  Promote the right of U.S. commercial entities to explore outer space and utilize space resources, in accordance with such obligations, free from harmful interference, and to transfer or sell such resources. Defines "space resource" as a natural resource of any kind found in place in outer space. → Solar power a space resource?

Outer Space Treaty and Weapons in Space

118 | P a g e

We argue that a laser is not a non-discriminatory weapon, as it is targeted, therefore no weapon of mass destruction (WMD). Deployment in Earth orbit or the "outer void space" of non-prohibited weapon types is allowed under the terms of the Outer Space treaty. Deployment on the moon and other celestial bodies is prohibited.

Interpretation: Lasers are no WMD (even so they can be deemed as weapons) and we do not plan to deploy on them on the Moon or any other celestial body but in Earth orbit; so according to the paper by Minero (2008) it would be legal to install Lasers in orbit under the Space Treaty.

See also information on the definition and discussion of conventional/discriminatory weapons [55].

3. Concept Design for Andromeda Probe Here we briefly lay out a concept for a probe design based on all the considerations discussed above. This concept is not the final design, and a greater level of sub-system fidelity is required to fully sketch out the performance. A graphic of the possible probe design is shown below as a configuration layout.

Figure 9 shows an overview of the components of the spacecraft. The probe is fitted with a camera (star tracker) and has a foldable aperture. It can be folded onto the main plate structure of the spacecraft. A CMOS camera is integrated into the spacecraft structure. A nuclear battery is positioned as a circular object on the back. The excess heat is used for heating the spacecraft components. Hence there are very thin copper circuits running from the battery to the critical components.

Figure 9: Orthographic Layout Drawing for Interstellar Probe

Graphene based supercapacitors are positioned at the side of the nuclear battery. The battery then loads the supercapacitors, and then they supply power to selective components such as the

119 | P a g e antenna, OBDH etc. The spacecraft structure has distributed MEMS sensors such as magnetometers etc. The antenna is a phased array, which is folded at the bottom of the spacecraft, approximately 1 m on each edge when unfolded.

A graphene whipple shield is used at the front of the spacecraft for protecting the spacecraft from the interstellar matter that is incoming. The whipple shield consists of multiple layers of shield material. Each laser is intended to extract energy from the incoming particle. Part of the energy is released via radiation, when a plasma is generated upon impact. The plasma cools down immediately, releasing its energy via radiation during its transit to the next layer in the shield. Hence, the multiple layers of the shield are more effective than a bulk shield. Alternative materials such as Beryllium are also possible. The shield is approximately 1 mm thick and 5 cm to 10 cm wide, depending on the width of the spacecraft. The spacecraft flies in the direction of the graphene shield, once it has completed its acceleration phase. Note that the graphene sail provides additional shielding before it is eroded away.

The spacecraft has actuators. These are MEMS actuators (gyros) that are distributed on the spacecraft for providing attitude control. There are also MEMS propulsion units for desaturating gyro’s occasionally. During the acceleration phase, the spacecraft is attached to the sail via graphene wires. The sail has optomechanical elements for steering. The sail has furthermore a slightly conic shape in order to self-adjust to the laser beam maximum

Figure 10: Overview of spacecraft components

120 | P a g e

Figure 11: Spacecraft with folded camera aperture for protecting against interstellar matter

Figure 12: Spacecraft with deployed antenna panels

Figure 13: Spacecraft with deployed antenna panels

121 | P a g e

Figure 14: Illustration of Interstellar Probe

Figure 15: Spacecraft with deployed antenna panels

Figure 16: Spacecraft with deployed antenna panels

122 | P a g e

Figure 17: Spacecraft in flight

Possible architectures with mass budget The mass budget for the spacecraft is shown in Table 16. Most of the component masses seem to be exceptionally low. However, we believe that advances in miniaturization will soon attain a level where these low masses are actually feasible. For several components, such as the OBDH, we have taken values for existing components. The total mass is 280g without the mass margin. If a 50% margin is added, this mass increases to 420g. However, in the rest of the report, we use the lower 280g value, as we think that the component masses we assumed are rather conservative with respect to future advances in electronics.

Table 16: Mass budget for spacecraft Mass [g]

Payload

Sensor package 4

Nano FPGA-based OBDH 30

Power

Graphene supercapacitors 25

Nuclear battery 40

Structure 5

Communications RF 26

ADCS 10

Startracker / camera + telescope 20

123 | P a g e

Radiation protection (Polyethylene) 20

Interstellar dust protection 20

Bus mass 200

Sail 80

Total mass 280

50% margin 140

Mass with margin 420

The data below shows the output from an in-house laser-sail physics code written in Fortran 95 which calculates the mission profile for a desired scenario. The calculations show that the probe will accelerate at 22 m/s2 for 16 days until it reaches a distance of 140.5 AU, hitting a cruise velocity of 30,408 km/s or 0.1c getting to its target destination Alpha Centauri at 4.3 light years after 42 years of flight. The total laser power required to propel this vehicle is around 1.12 GW assuming a 500 nm wavelength laser.

Table 17. Fortran code output for Sail calculation Centauri A, Destination distance (LY, AU): 4.30000019 271926.156 One way flyby mission ======Data for out route Sail ======Sail material is Graphene Sail geometry is circular Sail diameter (m): 366.000000 Sail mass (kg): 0.280000001 Sail loading (g/m2): 2.66137440E-03 Lens distance from Light Source (m, AU): 2.24399983E+12 15.0000000 Solar irradiance at launch (W/m2): 6.03709412 Sail density (g/cm3): 2.20000005 Sail thickness (nm): 16.0000000 Sail areal density (g/m2): 0.100000001 Sail Reflectivity: 0.819999993 Sail Emissivity: 5.99999987E-02 Sail Absorption Coefficient: 0.135000005 Sail Temperature: 600.000000 Acceleration (m/s2): 22.0000000 Earth Gravities (1/ge): 2.24260950 Lightness number (m/s2): 3709.94946 Laser Wavelength (m): 4.99999999E-07 Sail Power requirement (GW): 1.12604964 ======Mission Performance ======Cruise velocity (km/s, %c): 30408.9023 10.1433182

124 | P a g e

Boost time (Years): 4.38299999E-02 Boost distance (m, AU, LY): 2.10159419E+13 140.480896 2.22144090E-03 Beam spot size at boost cut-off (km): 2.52191313E-02 Cruise distance (m, AU): 4.06591368E+16 271785.688 Cruise time (Years): 42.3985291 Total mission distance (m, AU, LY): 4.06801521E+16 271926.156 4.30000019 Total mission duration (Years): 42.4423599 ======

To conclude, extrapolating from current trends in microelectronics and their use in CubeSats and Femtosats, we can assume that an interstellar probe as presented in this section could become feasible within a timeframe of 10 to 20 years.

4. I4IS Laser Sail Demonstrator Mission The Initiative for Interstellar Studies has recently begun work on plans for a CubeSat mission into space that deploys the world’s first laser-sail. The philosophy of this mission is “keep it simple, cheap, get to flight readiness quickly and de-risk the physics and engineering” by maximum ground validation and certification pre-flight. The current plan is to aim for a launch in the 2017-2020 timeframe in celebration of the 60th anniversary of the Sputnik 1 mission which kickstarted the space race. Our aspiration is to kickstart a new era of space exploration but with laser-sail technology and by demonstrating it is possible.

Our probe design is small, of order 9 cm2 in area for the sail and 1 cm2 in area for the ChipSat that is deployed with it. We estimate that at LEO such a sail could receive around 1 W of power just from solar energy alone, although the Earth albedo and atmospheric drag may reduce this if the launch altitude is not high enough. This power would be sufficient to push a 10s gram probe to 100s m/s. The calculations below show examples for such probes over variations in sail parameters and probe mass.

Table 18: Calculations for 0.16 W ChipSats

125 | P a g e

Table 19: Calculations for 0.54 W ChipSats

Table 20: Calculations for 1.22 W ChipSats

126 | P a g e

Yet, instead, our plan is to deploy our sail system from a CubeSat, and then to push it with a 1-2 W laser, and then to capture it on film and video. The mission has several key objectives:  Goal 1: Successful deployment of a sail from a CubeSat.  Goal 2: Successful demonstration of laser-push of sail.  Goal 3: Successful demonstration of a turning manoeuvre by moving the laser position by say 10° to effect a directional change.  Goal 4: Provided the first three goals are achieved and the altitude high enough, our ambition is to successfully conduct one 90 minute orbit of the Earth.

An illustration of the i4is laser-sail concept is shown in the graphic below which shows a sail being propelled by a laser housed on the main CubeSat. For reliability it would be desirable to launch several and with different unfolding mechanisms and sail designs, so as to improve the chances that one will demonstrate proof of concept. The i4is is looking for direct sponsorship to fund this mission which we estimate is in the range $250,000+.

Figure 18: Illustration of Laser-Sail CubeSat mission that i4is wants to conduct in 2017-2020 timeframe as a mission demonstrator

The possible mission is summarised below.

Mission statement: The first in-space demonstration of laser sail propulsion

Key mission requirements: To increase the orbit semi-major axis of the laser sail spacecraft in low earth orbit (LEO) by at least 5 km via a laser beam from a CubeSat. 5 km are selected, as it is a measurable change in the orbit parameters.

127 | P a g e

Mission architecture: A CubeSat is launched into an 800 km orbit (lower orbits have higher drag, which requires a much bigger laser power to overcome it), Sun-synchronous, with a Right Ascension of the Ascending Node (RAAN) angle perpendicular to the Sun’s position, as shown here:

Figure 19. Schematic of orbit

This has two advantages: the first is that the CubeSat, which has to carry the laser system, will almost always be in the view of the Sun, and therefore can get the required energy with the solar panels, without any eclipse time. The second is that, due to the perpendicular configuration, the Sun does not exert almost any force on the sail. The sail (20 cm x 20 cm) is deployed from the CubeSat. It has a total mass of 50 g (sail + ADCS + transmitter), as we need to send the position of the sail, and also actively control the sail attitude with some magnetic coils.

The CubeSat has an on-board electric micro-propulsion system, so it can chase the sail all the time and provide constant thrust, the distance from the sail is always kept constant, thereby having a constant pointing accuracy requirement. After 29 days of laser illumination, the required orbit increase of 5 km for the sail has been achieved.

Maturity of used technologies: All components have a TRL of 7 or higher. The CubeSat can be provided by FOTEC, Austria, a company for which i4is has links [56, 57, 58, 59].

Estimated cost / schedule: The cost can be estimated in less than 1 million US-$. Depending on the funding, this mission can be assembled in 18-24 months.

128 | P a g e

5. Minimal Interstellar Mission

In addition, our program included consideration for a minimal interstellar mission which will now briefly be described. Mission statement: The first interstellar mission of Mankind (the Voyager probes are not directed to any particular star) and first private spacecraft to leave the Solar System. It intends to motivate future missions to overtake this spacecraft. Key mission requirements: The objective of this mission is to beat the speed record of Voyager 1, the fastest space probe built by Mankind (17 km/s), arrive at Alpha Centauri, 4.24 light years away, in less than 25,000 years.

Mission architecture: Mission architecture consists of an interstellar probe, based on a 4U Cubesat, launched at solar system escape velocity by a suitable launcher. The probe is then propelled by a cluster of ion microthrusters, which are powered by an advanced Radioisotope Thermoelectric Generator.

Figure 20 shows an artist´s concept of the interstellar probe. The first Cubesat unit houses an array of ion microthrusters of the type Indium Field Emission Electric Propulsion. The Indium FEEP microthruster has the required specific impulse (4000 s) and the most efficient way of carrying propellant (Indium stored in solid state). Each thruster can provide a nominal thrust of 0.35 mN. A thrusting time of 20 years is needed for a ∆v of 25 km/s which is enough to fulfill the flight time requirement of 25,000 years (as Alpha Centauri has a radial velocity of 25 km/s towards the Sun, the spacecraft velocity relative to AC will be 50 km/s). As the expected lifetime of an Indium FEEP microthruster is less than 5 years, a cluster of at least four or five microthrusters is needed to perform the mission. The Indium mass required for a thrusting time of 20 years is about 6 kg, which corresponds to a reservoir as large as a 1U CubeSat. Hence, the Indium FEEP propulsion system takes two CubeSats, leading to a 12 kg 4U interstellar probe (2 CubeSats for propulsion, 1 CubeSat for the power source and 1 CubeSat for the payload, see Table 1).

The propulsion system input power is about 30 W. The power source is an Advanced Radioisotope Thermoelectric Generator with an electrical power output per unit mass of 10 W/kg; this leads to a power source mass of at least 3 kg. The thermal power dissipated by the ARTG can be used to keep the thruster reservoir at an operational temperature above the Indium melting point.

Figure 20: an artist´s concept of the spacecraft. The first CubeSat houses an array of micro-thrusters, the second contains a miniaturized radioisotope thermal generator with affixed radiators, the third contains the payload. In this picture the 1U unit for the Indium propellant reservoir is missing.

129 | P a g e

Table 21: Preliminary mass budget

Propellant 6

Advanced RTG Power 3

Total Engine Assembly 1

Payload (instruments, comms…) 1

Spacecraft Structure 1

Total Mass ~ 4U CubeSat 12 kg

Alternatives and key parameter values for alternatives: A ballistic launch with hyperbolic excess energy C3 of 250 km2/s2 could give a Δv of 15 km/s in excess to the Solar System escape velocity. This launch energy should be achievable with a Falcon Heavy or SLS. A Jupiter gravity assist could add a Δv of 10 km/s. Adding up these velocities with the 25 km/s provided by the ion micro-thrusters leads to a final speed relative to the Sun of 50 km/s (10 AU/year). That is 500 AU in 50 years and Alpha Centauri in less than 20,000 years, accounting for the relative AC velocity.

If the advanced RTG is not available in time, the mission can be performed with a more standard RTG with a specific power of 5 W/kg, and compensating the lower ∆v provided by the ion propulsion system with a more energetic launch and/or a Jupiter gravity assist.

Maturity of used technologies: The Indium FEEP microthrusters are under development at FOTEC, Austria, in the framework of an ESA contract (The i4is has links to FOTEC). The present TRL is 6 [60, 61, 62]. The advanced RTG is at a lower TRL.

Estimated cost / schedule: The cost of the interstellar probe can be estimated to be less than 5 million US-$. Depending on the funding and on the availability of an advanced RTG, the interstellar probe can be developed in 3-5 years.

6. Andromeda: Ultra-light Interstellar Flyby Mission

Ultimately, our aim is to conduct a full interstellar mission and launch it within the next 20 years. We briefly describe what such a system may look like, and with a cut-down mass budget.

Mission statement: To perform a fly-by mission to Alpha Centauri and return at least a photo of the star or potential exoplanets.

Key mission requirements:

- Maximum mission duration of 50 years - Return at least one photo of the star and/or exoplanet

130 | P a g e

- Perform a fly-by mission Mission architecture: Mission architecture consists of the interstellar probe and the space-based beaming infrastructure. The beaming infrastructure accelerates the probe via a laser or microwave beam. After acceleration, the probe enters the cruise phase. During target system encounter, pictures of the star and/or exoplanet are taken and sent back to the Solar System.

Table 22: Alternative Architecture Options

Architecture element Option 1 Option 2 Option 3

Beaming infrastructure Laser Microwaves

Spacecraft

- Power Electromagnetic tether + Nuclear battery + graphene capacitors graphene capacitors

- Communication Radiofrequency Laser Star occultation

- Navigation Pulsar / quasar navigation Enhanced star tracker

- Interstellar dust Graphene whipple shield Beryllium protection - Radiation Radiation-tolerant protection electronic components

- On-board data FPGA-based handling microprocessor

Our preferred design is highlighted in green in the table above.

Baseline architecture: A laser infrastructure is selected as a baseline. In order to decrease the lens size, ten sequential Fresnel lenses with a radius of 95 m are used. Circular structures of this diameter are currently conceived by Tethers Unlimited for in-orbit manufacturing. A potential Fresnel lens material is Graphene sandwich. Graphene lenses have been demonstrated in the lab in 2016. The lens infrastructure is shown in the image below:

Figure 21. Illustration of Segmented Lens System

131 | P a g e

Table 23: Description of Lens System

Laser infrastructure power [MW] 1150

Lens radius [m] 95

Number of lenses 10

Acceleration distance [AU] 1.8

Cruise velocity [%c] 10

Table 24: Estimated spacecraft mass budget

Spacecraft subsystem Technology [g]

Payload MEMS camera + aperture, various MEMS 2,4 sensors

OBDH FPGA-based microcomputer 1

Power Graphene supercapacitors (storage) and 6.5 electromagnetic tethers (power generation)

Structure Rigid Graphene matrix 0,1

Communications RF Foldable phased-array antenna + transceiver 3

ADCS Momentum wheels, MEMS FEEP thrusters 1

Navigation Use of camera -

Interstellar dust protection Graphene Whipple shield 2

Bus mass 15

Sail 4-layer Graphene sandwich (Radius: 34m) 8

Total mass [g] 23

Due to the miniaturization, common mass-based cost estimation models do not seem to be applicable to the spacecraft. We therefore select cost estimates for currently developed interplanetary CubeSats and multiply these costs by a factor of 5 in order to represent the increased difficulty of the mission. With a rough cost of 20 million dollar for an interplanetary CubeSat, we

132 | P a g e assume that developing the interstellar spacecraft may be comparable to that or several times higher in the 10s million US-$. The cost of the laser power generation infrastructure strongly depends on synergies between potential space power satellite systems. However, using near-term ultrathin solar cells with a specific power of 6 kg/kW we expect a cost of development, production, and launch to be in the billions US-$. The advantage of a space-based infrastructure are a factor 10 higher PV power output and laser efficiency compensating for high transportation cost. Conclusions In this report we have briefly considered the scenario of sending a small probe towards the Alpha Centauri system in a 50 year total mission time travelling at an average cruise velocity of 0.1c. We find that this idea is plausible and may be attempted within the next 10-20 years provided adequate investment is made and also that key laser technology is permitted into the space environment. The specific probe design down selected has a total spacecraft mass of 280 grams propelled by a 1.1 GW 500 nm beam, or a smaller design at 28 grams in mass.

On a final note, the Initiative for Interstellar Studies team would like to conduct a space mission attempt during the 2017-2020 time-frame which demonstrates the first laser-sail in space using ChipSat technology. We estimate that such a mission cost would be in the range of $250,000+ and this concept is directly on the technology roadmap towards the grander concept described in this report. We are looking for funding to support this attempt as a way of kickstarting global efforts towards laser-sail propulsion. Our philosophy for this mission is to keep it simple, cheap, do it quickly and to minimise risk by ground validation and physics demonstration. Our team is ready to go and is looking for sponsorship.

Figure 22. Project Andromeda mission patch

133 | P a g e

Acknowledgements In addition to the Interstellar Probe Team the following are thanked for their contributions to this study: Gregory Matloff, Peter Milne, Sam Harrison. The authors would also like to thank the members of the Breakthrough Initiatives Project Starshot, for which this work was initiated in early 2016.

References

[1] R. Forward, “Starwisp-An ultra-light interstellar probe,” Journal of Spacecraft and Rockets, 1985. [2] R. Forward, “Roundtrip interstellar travel using laser-pushed lightsails,” Journal of Spacecraft and Rockets, vol. 21, no. 2, pp. 187–195, 1984. [3] G. Landis, “Beamed energy propulsion for practical interstellar flight,” Journal of the British Interplanetary Society, 1999. [4] G. Landis, “Optics and materials considerations for a laser-propelled lightsail,” 1989. [5] P. Lubin, “A Roadmap to Interstellar Flight,” Journal of the British Interplanetary Society, vol. 69, no. 2–3, 2016. [6] G. Matloff, “Graphene Solar Photon Sails and Interstellar Arks,” Journal of the British Interplanetary Society, 2014. [7] G. Matloff, “Graphene, the Ultimate Interstellar Solar Sail Material?,” Journal of the British Interplanetary Society, 2012. [8] A. M. Hein, K. F. Long, G. Matloff, R. Swinney, R. Osborne, A. Mann, and M. Ciupa, “Project Dragonfly: Small, Sail-Based Spacecraft for Interstellar Missions,” submitted to JBIS, 2016. [9] H. Heidt, J. Puig-Suari, A. Moore, S. Nakasuka, and R. Twiggs, “CubeSat: A new generation of picosatellite for education and industry low-cost space experimentation,” 2000. [10] T. R. Perez and K. Subbarao, “A Survey of Current Femtosatellite Designs , Technologies , and Mission Concepts,” Journal of Small Satellites, vol. 5, no. 3, pp. 467–482, 2016. [11] Z. Manchester, “Centimeter-Scale Spacecraft: Design, Fabrication, And Deployment,” PhD thesis, Cornell University, 2015. [12] R. Staehle, D. Blaney, and H. Hemmati, “Interplanetary CubeSats: opening the solar system to a broad community at lower cost,” … Workshop, Logan, UT, 2011. [13] G. Landis, “Small Laser-propelled Interstellar Probe - Google Scholar,” in 46th International Astronautical Congress. [14] K. Long, “Deep Space Propulsion: A Roadmap to Interstellar Flight,” Springer, 2011. [15] R. FORWARD, “Zero thrust velocity vector control for interstellar probes-lorentz force navigation and circling,” aiaa Journal, 1964. [16] P. Norem, “Interstellar Travel: A Round Trip Propulsion System with Relativistic Velocity Capabilities,” AAS paper, vol. 69, p. 388, 1969. [17] D. ANDREWS and R. ZUBRIN, “Magnetic sails and interstellar travel,” British Interplanetary Society, Journal, 1990. [18] C. Gros, “Universal scaling relation for magnetic sails: momentum breaking in the limit of dilute interstellar media,” Jul. 2017. [19] N. Perakis and A. M. Hein, “Combining Magnetic and Electric Sails for Interstellar Deceleration,” Acta Astronautica, vol. 128, pp. 13–20, 2016. [20] L. Winternitz, K. Gendreau, M. Hasouneh, and J. Mitchell, “The Role of X-rays in Future Space Navigation and Communication,” 2013. [21] R. Hudec, L. Pina, and A. Inneman, “Applications of lobster eye optics,” SPIE Optics+, 2015. [22] L. Pina, R. Hudec, and A. Inneman, “X-ray monitoring for astrophysical applications on Cubesat,” SPIE Optics+, 2015. [23] C. McBryde and E. Lightsey, “A star tracker design for CubeSats,” Aerospace Conference, 2012 IEEE, 2012.

134 | P a g e

[24] T. Segert, S. Engelen, M. Buhl, and B. Monna, “Development of the pico star tracker ST-200– design challenges and road ahead,” 2011. [25] A. Meshcheryakov, V. Glazkova, and S. Gerasimov, “High-accuracy redshift measurements for galaxy clusters at z< 0.45 based on SDSS-III photometry,” Astronomy Letters, 2015. [26] D. Messerschmitt, “End-to-end interstellar communication system design for power efficiency,” arXiv preprint arXiv:1305.4684, 2013. [27] J. Hulme, J. Doylend, and M. Heck, “Fully integrated hybrid silicon free-space beam steering source with 32-channel phased array,” SPIE, 2014. [28] W. M. Folkner, “LISA orbit selection and stability,” Classical and Quantum Gravity, vol. 18, no. 19, pp. 4053–4057, Oct. 2001. [29] A. Boccaletti, P.-O. Lagage, P. Baudoz, C. Beichman, P. Bouchet, C. Cavarroc, D. Dubreuil, A. Glasse, A. M. Glauser, D. C. Hines, C.-P. Lajoie, J. Lebreton, M. D. Perrin, L. Pueyo, J. M. Reess, G. H. Rieke, S. Ronayette, D. Rouan, R. Soummer, and G. S. Wright, “The Mid-Infrared Instrument for the James Webb Space Telescope , V: Predicted Performance of the MIRI Coronagraphs,” Publications of the Astronomical Society of the Pacific, vol. 127, no. 953, pp. 633–645, Jul. 2015. [30] T. B. H. Tentrup, T. Hummel, T. A. W. Wolterink, R. Uppu, A. P. Mosk, and P. W. H. Pinkse, “Transmitting more than 10 bit with a single photon,” Sep. 2016. [31] D. J. Geisler, T. M. Yarnall, W. E. Keicher, M. L. Stevens, A. M. Fletcher, R. R. Parenti, D. O. Caplan, and S. A. Hamilton, “Demonstration of 2.1 Photon-Per-Bit Sensitivity for BPSK at 9.94- Gb/s with Rate-½ FEC,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, 2013, p. OM2C.6. [32] P. Galea, “Project Icarus: Solar sail technology for the Icarus interstellar mission,” 2nd International Symposium on Solar Sailing, New, 2010. [33] F. Drake, “Stars as gravitational lenses,” Bioastronomy—The Next Steps, 1988. [34] C. Maccone, “Interstellar radio links enhanced by exploiting the Sun as a gravitational lens,” Acta Astronautica, 2011. [35] Z. Manchester, M. Peck, and A. Filo, “Kicksat: A crowd-funded mission to demonstrate the world’s smallest spacecraft,” 2013. [36] M. B. Quadrelli, S. Basinger, and G. Swartzlander, “Orbiting rainbows: Optical manipulation of aerosols and the beginnings of future space construction,” Final Report of NASA Innovative Advanced Concepts (NIAC) Phase 1 Task 12-NIAC12B-0038, 2013. [37] C. Underwood, S. Pellegrino, V. Lappas, and C. Bridges, “Using CubeSat/micro-satellite technology to demonstrate the Autonomous Assembly of a Reconfigurable Space Telescope (AAReST),” Acta Astronautica, 2015. [38] A. Javey, S. Nam, R. Friedman, H. Yan, and C. Lieber, “Layer-by-layer assembly of nanowires for three-dimensional, multifunctional electronics,” Nano letters, 2007. [39] J. Ahn, H. Kim, K. Lee, S. Jeon, S. Kang, and Y. Sun, “Heterogeneous three-dimensional electronics by use of printed semiconductor nanomaterials,” 2006. [40] H. Craighead, “Nanoelectromechanical systems,” Science, 2000. [41] T. George, “MEMS/NEMS development for space applications at NASA/JPL,” Symposium on Design, Test, 2002. [42] D. Selva and D. Krejci, “A survey and assessment of the capabilities of Cubesats for Earth observation,” Acta Astronautica, 2012. [43] S. Chung and F. Hadaegh, “Swarms of femtosats for synthetic aperture applications,” Proceedings of the Fourth International, 2011. [44] F. Hadaegh and S. Chung, “On development of 100-gram-class spacecraft for swarm applications,” IEEE Systems Journal, 2016. [45] S. Bandyopadhyay, R. Foust, and G. Subramanian, “Review of Formation Flying and Constellation Missions Using Nanosatellites,” Journal of Spacecraft, 2016. [46] A. Labeyrie, “Optics of laser trapped mirrors for large telescopes and hypertelescopes in

135 | P a g e

space,” Optics & …, 2005. [47] J. Benford, “Flight and spin of microwave-driven sails: first experiments,” Pulsed Power Plasma Science, 2001. PPPS-2001. …, 2001. [48] J. Benford, G. Benford, and O. Gornostaeva, “Experimental tests of beam-riding sail dynamics,” FORUM-STAIF 2002, 2002. [49] Schamiloglu, E., C. T. Abdallah, K. A. Miller, D. Georgiev, J. Benford, G. Benford, and G. Singh, “3-D simulations of rigid microwave-propelled sails including spin,” Space Technology and Applications International Forum-2001, vol. 552, no. 1, pp. 559–564, 2001. [50] Z. Manchester and A. Loeb, “Stability of a Light Sail Riding on a Laser Beam,” The Astrophysical Journal Letters, 2017. [51] B. Wie, “Solar sail attitude control and dynamics, part 1,” Journal of Guidance, Control, and Dynamics, 2004. [52] B. Wie, “Solar Sail Attitude Control and Dynamics, Part Two,” Journal of Guidance, Control, and Dynamics, 2004. [53] Y. Tsuda, O. Mori, R. Funase, H. Sawada, and T. Yamamoto, “Flight status of IKAROS deep space solar sail demonstrator,” Acta Astronautica, 2011. [54] A. Borggräfe, J. Heiligers, and M. Ceriotti, “Optical control of solar sails using distributed reflectivity,” Spacecraft Structures, 2014. [55] C. Colombo, C. Lücking, and C. McInnes, “Orbit evolution, maintenance and disposal of SpaceChip swarms through electro-chromic control,” Acta Astronautica, 2013. [56] M. Tajmar, A. Genovese, and W. Steiger, “Indium field emission electric propulsion microthruster experimental characterization,” Journal of propulsion and power, 2004. [57] S. Marcuccio, A. Genovese, and M. Andrenucci, “FEEP microthruster technology status and potential applications,” International Astronautical, 1997. [58] P. Janhunen, “Electric sail for spacecraft propulsion,” Journal of Propulsion and Power, 2004. [59] G. Matloff and L. Johnson, “Applications of the electrodynamic tether to interstellar travel,” 2005. [60] R. Beck, “Galactic magnetic fields,” Scholarpedia, vol. 2, no. 8, p. 2411, 2007. [61] E. Zirnstein, J. Heerikhuisen, and H. Funsten, “Local Interstellar Magnetic Field Determined from the Interstellar Boundary Explorer Ribbon,” The Astrophysical, 2016. [62] L. Burlaga and N. Ness, “Interstellar magnetic fields observed by voyager 1 beyond the heliopause,” The Astrophysical Journal Letters, 2014. [63] T. Grönland, P. Rangsten, M. Nese, and M. Lang, “Miniaturization of components and systems for space using MEMS-technology,” Acta Astronautica, 2007. [64] E. Gill and J. Guo, “MEMS technology for miniaturized space systems: needs, status, and perspectives,” SPIE MOEMS-MEMS, 2012. [65] H. Shea, “MEMS for pico-to micro-satellites,” SPIE MOEMS-MEMS: Micro-and, 2009. [66] R. Osiander, M. Darrin, and J. Champion, “MEMS and microstructures in aerospace applications,” 2005. [67] M. Thompson, M. Li, and D. Horsley, “Low power 3-axis Lorentz force navigation magnetometer,” (MEMS), 2011 IEEE 24th …, 2011. [68] G. Du and X. Chen, “MEMS magnetometer based on magnetorheological elastomer,” Measurement, 2012. [69] J. Reiter and K. Boehringer, “MEMS control moment gyroscope design and wafer-based spacecraft chassis study,” Symposium on, 1999. [70] M. Post, R. Bauer, J. Li, and R. Lee, “Study for femto satellites using micro Control Moment Gyroscope,” 2016 IEEE Aerospace, 2016. [71] T. Brady, “Expanding the spacecraft application base with MEMS gyros,” SPIE MOEMS-MEMS, 2011. [72] C. Liebe and S. Mobasser, “MEMS based sun sensor,” Aerospace Conference, 2001, IEEE, 2001.

136 | P a g e

[73] E. Garcıa, “Development and Verification of the Electro-Optical and Software Modules of the Facet Nano Star Sensor,” 2014. [74] A. Erlank, “Development of CubeStar: a CubeSat-compatible star tracker,” 2013. [75] G. Lammel, S. Schweizer, and S. Schiesser, “Tunable optical filter of porous silicon as key component for a MEMS spectrometer,” Journal of, 2002. [76] E. Wapelhorst, J. Hauschild, and J. Müller, “Complex MEMS: a fully integrated TOF micro mass spectrometer,” Sensors and actuators A: Physical, 2007. [77] J. Hauschild, E. Wapelhorst, and J. Müller, “Mass spectra measured by a fully integrated MEMS mass spectrometer,” International Journal of Mass, 2007. [78] A. Martin, “Project Daedalus: bombardment by interstellar material and its effects on the vehicle.,” Journal of the British Interplanetary Society, 1978. [79] “The interaction of relativistic spacecrafts with the interstellar medium,” The Astrophysical, 2017. [80] I. Crawford, “Project Icarus: A review of local interstellar medium properties of relevance for space missions to the nearest stars,” Acta Astronautica, 2011. [81] E. Stone, A. Cummings, and F. McDonald, “Voyager 1 observes low-energy galactic cosmic rays in a region depleted of heliospheric ions,” 2013. [82] W. Webber and F. McDonald, “25 August 2012 at a distance of 121.7 AU from the Sun, sudden and unprecedented intensity changes were observed in anomalous and galactic cosmic rays,” Geophysical Research Letters, 2013. [83] E. T. Benedikt, “Disintegration Barriers to Extremely High Speed Space Travel,” Advances in the Astronautical Sciences, vol. 6, pp. 571–588, 1961. [84] N. Langton, “The Erosion of Interstellar Drag Screens,” Journal of the British Interplanetary Society, 1973. [85] C. Scharf, “Extrasolar Planets and Astrobiology,” 2009. [86] R. Lange and W. Carroll, “Review of recent advances of radioisotope power systems,” Energy Conversion and Management, 2008. [87] F. Sarvar and D. Whalley, “Thermal interface materials-a review of the state of the art,” 2006 1st Electronic, 2006. [88] M. Biercuk, M. Llaguno, and M. Radosavljevic, “Carbon nanotube composites for thermal management,” Applied physics, 2002. [89] G. Landis, S. Bailey, and E. Clark, “Non-solar photovoltaics for small space missions,” in 38th IEEE Photovoltaic Specialists Conference (PVSC), 2012, pp. 002819–002824. [90] S. Howe, R. O’Brien, and T. Howe, “Compact, Low Specific-Mass Electrical Power Supply for Space Exploration,” International Workshop on Instrumentation for Planetary Missions, vol. 1683, p. 1025, 2012. [91] D. Wilt, D. Chubb, D. Wolford, and P. Magari, “Thermophotovoltaics for space power applications,” : TPV7: Seventh World …, 2007. [92] V. Teofilo, P. Choong, and J. Chang, “Thermophotovoltaic Energy Conversion for Space,” The Journal of Physical Chemistry C, vol. 112, no. 21, pp. 7841–7845, 2008. [93] A. Heller, “Miniature biofuel cells,” Physical Chemistry Chemical Physics, 2004. [94] R. Nastro, “Microbial Fuel Cells in Waste Treatment: Recent Advances,” IJPE, 2014. [95] J. Gutsmiedl, A. Koop, M. J. Losekamm, N. Perakis, and L. Schrenk, “Project Dragonfly: A Feasibility Study of Interstellar Travel Using Laser-Powered Light Sail Propulsion,” to be submitted to Acta Astronautica, 2016. [96] Made in Space, “Archinaut,” 2016. [Online]. Available: http://www.madeinspace.us/projects/archinaut/. [Accessed: 15-Aug-2016]. [97] R. Hoyt, J. Slosad, T. Moser, and J. Cushing, “MakerSat: In-Space Additive Manufacturing of ConstructableTM Long-Baseline Sensors using the TrusselatorTM Technology,” 2016. [98] R. Hoyt, J. Cushing, G. Jimmerson, and J. Luise, “Trusselator: On-orbit fabrication of high- performance composite truss structures,” conference, San Diego …, 2014.

137 | P a g e

[99] R. Hoyt, J. Cushing, J. Slostad, and G. Jimmerson, “SpiderFab: An architecture for self- fabricating space systems,” Am. Inst. Aeronaut., 2013. [100] R. Hoyt, J. Cushing, J. Slostad, and T. Unlimited, “SpiderFabTM: Process for on-‐Orbit construction of kilometer-‐Scale apertures,” Final Report of the NASA, 2013. [101] M. Kaltenbrunner, M. White, and E. Głowacki, “Ultrathin and lightweight organic solar cells with high flexibility,” Nature, 2012. [102] A. Kumar, N. Rosen, R. Devine, and Y. Yang, “Interface design to improve stability of polymer solar cells for potential space applications,” Energy & Environmental, 2011. [103] S. Guo, C. Brandt, T. Andreev, and E. Metwalli, “First step into space: performance and morphological evolution of P3HT: PCBM bulk heterojunction solar cells under AM0 illumination,” applied materials & …, 2014. [104] E. M. Herzig and P. Muller-Buschbaum, “Organic photovoltaic cells for space applications,” Acta Futura, no. 6, pp. 17–24, 2013. [105] T. Taylor, R. C. Anding, D. Halford, and G. L. Matloff, “Space based energy beaming requirements for interstellar laser sailing,” BEAMED ENERGY PROPULSION: First International Symposium on Beamed Energy Propulsion, vol. 664, no. 1, pp. 369–381, 2003. [106] P. Birch, I. Ituen, R. Young, and C. Chatwin, “Long-distance Bessel beam propagation through Kolmogorov turbulence,” Journal of the Optical Society of America A, vol. 32, no. 11, p. 2066, Nov. 2015. [107] D. McGloin and K. Dholakia, “Bessel beams: Diffraction in a new light,” Contemporary Physics, vol. 46, no. 1, pp. 15–28, 2005. [108] S. Basinger and P. G. Swartzlander, “Final Report of NASA Innovative Advanced Concepts ( NIAC ) Phase 1 Task 12-NIAC12B-0038 ORBITING RAINBOWS : OPTICAL MANIPULATION OF AEROSOLS AND THE BEGINNINGS OF FUTURE SPACE,” vol. 14623, no. 585, 2013. [109] W. J. Larson and L. K. Pranke, Human spaceflight: mission analysis and design. McGraw-Hill Companies, 1999.

138 | P a g e

REFLECTIVE CONTROL DEVICES FOR ATTITUDE CONTROL OF SOLAR SAILS

Dakang Ma1,2, Coleman Delude1,2, Tiffany Russell Lockett3, Andrew Heaton3, Keats Wilkie4, Jeremy N. Munday1,2*, 1 Department of Electrical and Computer Engineering, University of Maryland, College Park, MD USA 2 Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD USA 3 NASA Marshall Space Flight Center, Huntsville, AL USA 3 NASA Langley Research Center, Hampton, VA USA

*Corresponding author, [email protected]

Abstract Solar sails offer an opportunity for a cubesat-scale, propellant-free spacecraft technology to enable long-term and long-distance missions not capable with traditional methods. To propel the craft, no mechanically moving parts, thrusters, or propellant are needed. However, attitude control is still performed using traditional methods involving reaction wheels and propellant ejection, which severally limits mission lifetime. For example, the current state of the art solutions implored by the recent Near-Earth Asteroid Scout mission couple the solar sail subsystem with a state of the art propellant ejection gas system. However gas thrusters have a limited supply of propellant, which reduces the lifetime of the mission to less than three years. The solar sail, on the other hand, is able to produce a constant acceleration throughout the duration of its mission, which inherently increases mission lifetime. To replace the traditional gas thruster system for attitude control, we are using propellantless attitude control using an electrically switchable optical film [1]. The technology is based on a polymerdispersed liquid crystal (PDLC), similar to IKAROS; however, my switching between transparent and diffusely reflective (rather than switching between specular and diffuse reflection) upon application of a voltage, a factor of >4 improvement is achieved. This technology removes the need for propellant, which will reduce weight and cost while improving performance and lifetime. The basic concept is shown below in the figure below. This paper is submitted for the day 2 session Sails and Beams.

Figure. Reflective control device. (a) Schematic of a solar sail incorporating polymer dispersed liquid crystal (PDLC) devices along the edge to actively modify the radiation pressure. (b) PDLC device in operation changing between diffusely reflective (left) and transparent (right) states.

Keywords: Solar Sail, Reflectivity Control, Liquid Crystal

139 | P a g e

References [1] Dakang Ma, Joseph Murray and Jeremy N. Munday, “Controllable Propulsion by Light: Steering a Solar Sail via Tunable Radiation Pressure”, Adv. Opt. Mat., 5, 1600668, 2017.

140 | P a g e

EFFECTS OF ENHANCED GRAPHENE REFLECTION ON THE PERFORMANCE OF SUN- LAUNCHED INTERSTELLAR ARKS

Gregory L. Matloff, Physics Dept., New York City College of Technology, CUNY, 300 Jay Street Brooklyn, NY 11201, USA

E-Mail: [email protected]

Graphene, a carbon molecular monolayer, has an essentially zero reflectivity to visible light that can be increased to 0.05 if alkali atoms are intercalated with carbon atoms. Recently published theoretical work considers methods of selectively altering graphene optical properties. This paper considers the effects of increasing graphene fractional reflectivity on the performance of a previously considered Sun-launched interstellar ark. The ark considered has a payload mass of 5×106 kg and a maximum population of 20-50. The hollow-body sail, with a radius of 764 km, is unfurled (or inflated) at the 0.1-AU perihelion of an initially parabolic solar orbit. A multiple-layer structure of graphene and molybdenite is used to increase sail fractional absorption of visible light to 0.4. Fractional reflectivity is varied incrementally between 0.05 and 0.4. Final interstellar cruise velocity, peak acceleration and perihelion temperature are examined as functions of sail reflectivity to sunlight. It is shown that even small increases in reflectivity significantly increases interstellar cruise velocity.

Keywords: Interstellar Ark, Graphene, Interstellar Travel, Photon Sails

1. Introduction: Graphene and its Application to Interstellar Solar Sailing Graphene, a one-atom thick carbon-lattice monolayer, has a thickness of 0.335 nm and its areal mass density is 7.4 X 10-7 kg/m2. Pure graphene has an essentially zero reflectance (R) to visible light. Reflectance can be increased to 0.05 if alkali atoms are intercalated with grapheme. The fractional visible light absorption (A) of a pure graphene monolayer has been measured as approximately 0.023. Other interesting properties of graphene include impermeability to many gases and a very high tensile strength—about 130 GPa [1]. The melting point of graphene is reported to be in excess of 4,000 K [2]. If one creates a two-layer structure consisting of graphene and molybdenite, fractional absorption of visible light can be increased to 0.37. Sandwiching graphene between two appropriate layers may increase fractional absorption of visible light to >0.5 [1]. In Ref. [1], three possible applications of graphene solar-photon sails to interstellar travel are considered. One is a thin-film, high-acceleration probe accelerated by Sunlight after the sail is unfurled at the perihelion of an initially parabolic solar orbit. The second is a robotic interstellar probe. The third is a small interstellar ark with a payload of 5×106 kg. This paper further considers the baseline interstellar-ark scenario in Ref. [1] with fixed fractional absorption of visual spectral- range light and variable reflection. The baseline disc sail in Ref. [1] has a radius of 733 km, a fractional visible-light reflectivity of 0.05 and a fractional visible-light absorption of 0.4. The sail is configured as a hollow-body (inflatable) structure with the payload mounted on the anti-Sun face of the sail. The areal mass

141 | P a g e density of the multi-layer sail is 5×10-6 kg/m2, including hollow-body fill gas. The areal mass thickness -6 2 of the entire spacecraft (σs/c) is 8×10 kg/m . Perihelion distance (Dau) is taken as 0.1 Astronomical Units (AU). The spacecraft departs the solar system at about 922 km/s. Travel time to Alpha

Centauri is about 1,400 years. Peak perihelion acceleration (ACCpeak) is 2.9 g and peak temperature at perihelion (Tperi) is 1021 K. These values are slightly refined in a follow-on paper. Physical properties of the ark are also discussed in that paper and the population of the spacecraft is estimated at 20-50 people [3].

2. Some Analytical Tools One significant parameter in the consideration of Sun-launched interstellar ark performance is the lightness number, η. This is defined as the ratio of solar radiation pressure force on the sail to solar gravitational force on the spacecraft. The Lightness Number can be expressed [1]:

퐴+2푅 휂 = 7.68 × 10−4 ( ) (1) 휎푠/푐

The Lightness Number can next be used to calculate the interstellar cruise velocity of the spacecraft, Vfin. This is expressed using Eq. (3) of Ref. [1]: (퐴+2푅) 푉푓𝑖푛 = 1.167√ km/s, (2) 퐷퐺푀 휎푠/푐 where Dau is the perihelion distance in Astronomical Units (AU).

The solar gravitational acceleration at 1 AU is 6.04×10-4 g. Therefore, peak solar-radiation-pressure acceleration at perihelion can be calculated [1]:

−4 휂 퐴퐶퐶푝푒푟𝑖 = 6.04 × 10 2 g, (3) 퐷퐺푀

To evaluate ark thermal properties at perihelion, it is worth noting that sail fractional transmission of sunlight, T, can be expressed as T = 1- A - R. Emissivity of this non-opaque sail can now be defined [1,4]:

(1−푇)(1−푅) 휀 = (4) 1−푇푅

Emissivity and the grey-body equation can be used with the value of the Solar Constant (1366 W/m2) to estimate sail absolute temperature at perihelion, Tperi. Application of Eq. (7) of Ref. [1] results in:

1/4 퐴 푇푝푒푟𝑖 = 331 ( 2 ) K, (5) 휀퐷퐺푀

As discussed above, it is assumed that the payload is mounted on the anti-Sunward face of the inflated hollow-body sail. Maximum allowable sail stress can be defined using Eq. (8) of Ref. [1]:

11 푆푇푅퐸푆푆 = 휎푝푎푦 퐴퐶퐶푝푒푟𝑖 ≪ 1.30 × 10 Pa, (6) where σpay is the areal mass density of the payload and acceleration is in MKS units. In all cases considered, stress is not an issue because of the very high tensile strength of graphene.

142 | P a g e

3. Results: Effects of Reflection Variation Before considering the effects of reflection variation on interstellar ark performance, it is worth reviewing the baseline case from Ref. [3] and discussing parameters that are fixed for all cases considered in this analysis. This is done below.

3.1 The Baseline Case (R=0.05) and Fixed Parameters In all cases, the sail radius is 764 km. Sail fractional absorption (A) to visible light is 0.4. Fractional reflectivity of visible light is 0.05. The payload mass is fixed at 5×106 kg and the areal mass density of -6 2 -6 the multi-layer sail is 5×10 kg/m . The spacecraft areal mass density is therefore (σs/c) is 7.73×10 kg/m2. At perihelion, the total spacecraft mass is 1.42×107 kg. From Ref. [3], the emissivity of the baseline sail is 0.44; peak perihelion temperature is 1022 K. The spacecraft lightness number (η) is 49.67. The peak acceleration is 3g and the interstellar cruise velocity is 938 km/s. The interstellar transit time to Alpha/Proxima Centauri is about 1375 years.

3.2 Effects of Increasing Reflectivity (R) Possibilities of altering graphene optical properties, including reflection, are discussed in the literature [5]. To consider the effects of increasing sail reflectivity upon ark performance, refer to Eqs. (1)-(5). The spacecraft lightness number (η) varies with (A+2R) from Eq. (1). Applying Eq. (2), interstellar cruise velocity (Vfin) varies with the square root of (A+2R). Peak acceleration at perihelion, from Eq. (3), varies with the lightness number. To calculate thermal properties, it is first necessary to determine the value of emissivity (ε) using Eq. (4). Peak perihelion temperature, from Eq. (5), varies with the fourth root of (A/ε) for the case of constant perihelion distance.

Table 1 summarizes these results for fractional sail visible-light reflectivity varies between 0.05 and 0.4. In all cases, the sail radius, payload mass, sail fractional absorption, payload mass, sail areal mass density and perihelion distance are maintained constant as discussed above. Consideration of the results presented in Table 1 reveals that increased sail visible-light reflectivity increases both interstellar cruise velocity and peak acceleration at perihelion. Increased reflectivity results in slightly lower perihelion temperatures.

Table 1. Effects of Varying Sail Reflectivity (R) on Interstellar Ark Performance.

R η Vfin ACCperi ε Tperi ______0.05 49.67 938 km/s 3.0 g 0.44 1022 K 0.1 59.60 1032 3.6 0.47 1006 0.2 79.47 1192 4.8 0.52 981 0.4 119.20 1454 7.2 0.52 981 ______η = lightness number, Vfin = final velocity, ACCperi = peak acceleration, ε = emissivity, Tperi = peak sail temperature. In all cases, sail visible light absorption=0.4 sail radius = 764 km perihelion distance = 0.1 AU sail mass = 9.16×106 kg payload mass = 5×106 kg ______

143 | P a g e

Conclusions If the occupants of the ark are organic lifeforms similar or identical to humans, it may not be possible to fully take advantage of the higher performance possible with increased sail reflectivity. This is because, as discussed in Ref. [3], the maximum tolerable acceleration by humans during the multi- hour acceleration period is about 3 g. As shown in Table 1, peak acceleration increases more rapidly than interstellar cruise velocity as sail reflectivity is increased. One possibility is to depart from a higher perihelion distance to maintain a 3 g maximum acceleration. A second possibility is to increase payload mass as sail reflectivity is increased. This will decrease lightness number and acceleration as well as the interstellar cruise velocity.

Acknowledgements

Although the author serves as an advisor to Breakthrough Initiative Project Starshot, the scenarios investigated here have no direct relation to the probe and sail concepts under consideration by that project. Discussions with Oleg Berman and Roman Kezerashvili of New York City College of Technology, CUNY and Godfrey Gumbs of Hunter College, CUNY, are greatly appreciated.

References [1] G. L. Matloff, “Graphene: The Ultimate Interstellar Solar Sail Material”, JBIS, 65, 378-381, 2012. [2] K. V. Zakharchenko, A. Fasolino, J. H. Los and M. I. Katsnelson, “Melting of Graphene: From Two to One Dimension”, arXiv:1104.1130v1[cond-mat.mtrl-sci] 6 Apr 2011. [3] G. L. Matloff, “Graphene Solar Photon Sails and Interstellar Arks”, JBIS, 67, 237-248, 2014. [4] W. L. Wolfe, “Handbook of Military Infrared Technology”, Office of Naval Research, Dept. of the Navy, Washington, D. C. (1965), p. 349. [5] O. L. Berman, V. S. Boyko, R. Ya. Kezerashvili, A. A. Kolesnikov and Y. E. Lozovik, “Graphene-Based Photonic Crystal”, Physical Review Letters A, 374, 4784-4786, 2010.

144 | P a g e

GRAM-SCALE NANO-SPACECRAFT ENTRY INTO STAR SYSTEMS

Albert Allen Jackson IV1

1 Lunar and Planetary Institute, Houston, Texas 3600 Bay Area Blvd, Houston, TX 77058 Email: [email protected]

Breakthrough Starshot is a study to consider the concept of ultra-fast Nano-spacecraft probes towards the stellar system Alpha Centuari. These probes leave the solar system at 20% the speed of light. The beginning of the journey and the intermediate interstellar trajectory has been the subject of preliminary studies [1, 2]. Considered here is arrival at destination [3]. In Starshot it is proposed that a bundle of spacecraft be directed towards the target star with the intent that some fraction of the interceptors would make close enough flybys to take physical measurements. If active guidance, navigation and control can be realized for Nano-spacecraft it may be possible to intercept the stellarsphere of one or more stars of the Alpha Centuari system. Of interest here is interaction of an interceptor with the stellarsphere radiation forces and magnetic field of a target star. Of particular consideration is the interaction of a Nano-spacecraft with radiation pressure, Poynting-Robertson drag, Lorentz forces, stellar wind drag and Coulomb drag. Can these forces usefully modify the trajectories of spacecraft at destination? Radiation pressure has been the subject of one study [3]. The dynamics of Nano-spacecraft under the influence of radiation pressure and Poynting Roberton drag is followed by numerical integration of the equations of motion.

Keywords: Nano-ship Trajectories, Stellarsphere Forces, Project Starshot

1. The Spacecraft and Target The vehicle will be taken to be a ‘smart-chip-ship’ (how ‘smart’ is left open). A small-scale starship is modeled with a mass of much less than a kilogram, and a payload of grams. The size, possibly with an attached ‘sail’ is taken as a meter in radius. The craft could be a ‘folded’ package with the configuration deployed at target. It will be taken that the spacecraft can be a member of a cluster of identical vehicles sent in the direction of a target with the aim that at least a subset would encounter a target star or stellar system.

This study operates under the condition that not only is there a statistical survival of a subset of vehicles but also that the individual vehicles are hardened enough to survive the interstellar and stellar thermal and radiation environments, possible even configured to endure the Stellarsphere of the target star.

To make use of known physical conditions in the environment of the target star, it will be taken to be α-Centuari A (Rigil Kentaurus) because it is a GV2 star, thus the magnetic field, luminosity and stellar medium environment can be approximated as being solar-like.

145 | P a g e

At 20% the speed of light the ship arrives at the target with approximately 555 times the escape speed from the galaxy. Taking that there are no dissipation losses on the way the ship arrive with 1 20% the speed of light, or a Lorentz factor γ = 1.02, where 훾 = . 푣2 √(1− ) 푐2

This corresponds to a kinetic energy of about 1013 joules, which is very large for even a 1 gram ship. 2. Trajectory The primary question asked is how can the trajectory of the ship be modified at the target star, when it interacts with the local stellar environment and stellarsphere (heliosphere for the Sun)? This is the question of Heller and Hippke [3], however here the condition of the approach speed is kept at 20% c. It is supposed that a ‘bundle’ of trajectories enter a ‘scattering’ cross section of the target star. It may be that the chip-ship has some GNC (Guidance-Navigation-and-Control) that makes possible some targeting. The vector form of the primary equation of motion becomes [4] (1  )GMr F  (1) gr r3

That is radiation pressure modified Newtonian gravitational force, see section 3 for definitions. The polar equation of motion is well known, p r  (2) 1 e cos( )

Where e is the eccentricity and p is the semi-latus rectum and θ is the azimuthal angle. In this case the incoming orbits will be hyperbolas with velocity at infinity v∞ of 0.2c. An encounter hyperbola can be specified by a single quantity the point of closest approach rp, which determines the impact parameter b, as shown in Figure 1

2GM (1  ) brp 12 (3) rpv

When b is known the eccentricity e can be determined b24v e2 1 ( 4) . G2M 2 (1  ) 2

Take as a test a set of initial conditions where the approach speed is 20% the speed of light and point of closest approach (peri-apsis) is 2 stellar radii , Ra (radius of α-Centauri A) with β = 1032.48 (see section 2). Then the approach impact parameter, b, is 2.05Ra and the eccentricity is 42. The model is essentially Rutherford scattering with a repulsive potential. A couple of results: the time to go from 90 to -90 degrees, the region of strongest reaction, is 142 seconds. The scattering angle is less than 2 degrees, close to being almost a rectilinear orbit.

146 | P a g e

Figure 1: The basic trajectory under study.

Under what condition will the turning angle be increased? The trajectory must lose energy either on the way or at destination. A calculation of how much is shown in Figure 2. It may be possible that one can use the interstellar medium to remove energy before encounter, but that is not clear. Of course not too much energy since that extends the arrival time.

Figure 2. Change in scattering angle with respect to change in energy of the initial orbit.

147 | P a g e

3. Passive Ships

3.1 Definition

The usage of the term ‘passive’ is not meant to imply there may be no modest or minimal GNC aboard to facilitate trajectory control.

3.2 Radiation Forces The main forces in play will be gravitation and radiation pressure. Let the ship characteristic size be a and its area A = πa2, taken as a circular area presented to the direction of motion. If the has a mass = πa2 σ, then the force of gravity at distance r is

휋푎2휎퐺푀 퐹 = − (5) 푔푟 푟2 And the radiation pressure [4] 푆퐴 퐹 = ( )푄 (6) 푟 푐 푝푟 Where 푆 = 퐿/4휋푟2 , a = radius of the ‘sail’, σ = surface density of sail material, G and c gravitational constant, c is the speed of light, M and L are the Mass and Luminosity of the target star. Qpr = 퐹 radiation pressure coefficient. Then the parameter 훽 = 푟 can be written as, 퐹푔 퐹 퐿 푄 훽 = 푟 = ( )( 푝푟). (7) 퐹푔 4휋퐺푀푐 휎 This parameter is a function of only the ship-chip (‘sail’) surface density and Qpr. Taking the ship -4 2 material as Graphene σ = 8.6x10 gm/m . Set Qpr =1, that is the optical properties are black-body in the geometrical optics approximation. (Graphene is an absorber with a Qpr ~1.0). In the following a generic ship will be taken of area 1 square meter and a mass of 10 grams. Using the physical values for Alpha-Centauri A, β=1032.48, a fairly large number. The radiation pressure efficiency coefficient Qpr, depends on wavelength λ, on the refractive index m, shape and spatial structure, and is usually more applicable for microscopic objects. The study here will take this as an engineering problem, that is innovate a surface such that Qpr =1.0. One might speculate on the possibility of a number greater than 1.0. It may also be possible to engineer the surface density to be even smaller. The ratio Qpr/σ could be a crucial factor if it were possible to be manipulated.

If r the distance from the star, r is the radial velocity and v is the velocity of the ship. Fgr and Fpr are respectively the gravitational force and Poynting Robertson effect, the set of equations of motion then are: r F F (8) ) gr pr

(1  )GMr Fgr  3 (9) r

And

GM r rv F  [  ] (10) pr r2 c r c

148 | P a g e

These equations of motion are integrated with the Bulirsch-Stoer numerical integrator [5]. The result of the standard case shows a change of only about 5% in energy, this corresponds to an addition of about 3 degrees in the scattering angle.

Figure 3. Change in encounter angle with the inclusion of radiation pressure and Poynting Robertson drag and a given β.

3.3 Lorentz forces When the ship arrives at the stellar-sphere of Alpha Centuari A it will encounter the system’s magnetic field. The Lorentz force on it as a charged body, of total charge Q is [6] 푭퐿표푟푒푛푡푧 = 푄풗 × 퐁 (11) where v is the system entry speed of 0.2c. Because this velocity is high one can ignore the stellar wind from the star as well as the stars rotation. The magnetic field of the star will be taken as the Parker model [7]: 2 r0 Br =B r0  r

r0 B =B0  cos (12) r

B = 0

Where r and θ are radial distance and azimuth angle with Br0 = Bθ0 = 5nT. This is an extremely simple model but we are after orders of magnitude estimates here. A spacecraft surface can become charged by collisional charging and photoelectric emission (other processes) [6]. We will not make a detailed calculation for the charging process, which may or may not be possible in the situation under consideration. The only other criterion put forward is that there can only be a maximum charge on the spacecraft. The tensile stress on, say, a spherical spacecraft of radius ‘a’

149 | P a g e

Φ 2 푆 = ( ) /4휋 (13) 푎

Where the surface potential Φ is given by,

푍푒 Φ = (14) 푎

Z is maximum number of charges of value e, elementary charge. If one takes the tensile strength of Graphene ~ 1011 Pascals , then about 106 Coulombs can be put on a 10 cm Graphene sphere without breaking it. This is very interesting; the problem is it is not very possible the spacecraft ambient charging processes of collisional ionization and photoelectric emission can put this kind of change on the spacecraft. One might speculate that a very large charge could be put on the spacecraft in an artificial manner, at launch. However a calculation of the charge allowed by field emission would have to be made and a check made of keeping the change for the duration of the flight. One can make a model of a spacecraft as a magnetic dipole with constant magnetic moment μ moving in a magnetic field B, the force on it this is 퐅 = 훍 ∙ 훁퐁. Creation of a strong enough magnetic moment, given a fairly weak environmental field effect seems unlikely or at least a problem for further study. However taking the case of the charged sphere above, spin a charged sphere and there is a magnetic moment m:

푚 = 푄휔푎2 (15)

Where Q is the total charge, a is the radius and ω is the angular speed. Take a Graphene sphere rotating at maximum breakup speed ~104 radians/sec and the charge given above one gets a magnetic moment of ~200,000 A·m2. This is extreme but smaller yet substantial values might be obtained. It seems problematic that large charges and magnetic moments could be sustained for 20 years.

3.4 Induction For a conductor moving through an ambient magnetic field Ba there is a motional emf induced. Take the ambient field to be the azimuthal stellar environmental field then a current ‘loop’ of size a moving in the field, then 푒푚푓 = 푣푎퐵푎 (16)

Which induces a current I

푒푚푓 I = (17) Ω

Where 휴 is the resistance of the loop. The magnetic moment of the loop interacts with the ambient field Ba to produce a force F = IaBa. Taking the loop being made of Graphene which has a high conductivity it is found that because the external B field is weak and the force generated is very small.

Another type of ‘induction’ force is Alfvén Wings. A conductor moving in a magnetic field will produce a charge separation and an electric field. Currents can flow due to conduction in the presence of plasma there can be a coupling to the plasma. These kinds of disturbances are called Alfven waves. The waves carry away energy and cause drag. Unfortunately the entry speed of 20% c will cause a shock in front of the spacecraft muting the Alfven wing drag to point it can’t be used.

150 | P a g e

3.5 Corpuscular Drag A stellar wind will be responsible for corpuscular forces, due to collision and transfer of momentum from the stellersphere protons onto the spacecraft. Their interaction is therefore analogous to radiation forces, depending on the cross section of the space craft. Because of the dilution of the proton number density goes as 1/ r2, the solar wind proton interaction intensity decreases like the radiation pressure for increasing distances. The corpuscular drag can be written as 2 2 퐹푑 = −퐶푑푛푚푝푣 휋푎 (18) In this case n is the number density, mp the mass of the proton, v the speed and a the radius of the spacecraft. This is classical gas drag with drag coefficient Cd, can be a bit complex for stellarsphere space but will be taken to be 2.0 here. At the point of closest approach 2 stellar radii the drag is order of 103 Newtons. However particle drag will be a hazard, heating and erosion will be extreme [2]. Ablation mitigation could be explored however the conditions are extreme.

4. Active Ships

4.1 Definition ‘Active’ means not only a Guidance Navigation and Control system but also a method of power generation; this might be photon power cells. Turning from the study of ‘free’ energy dissipation, two methods of active drag are possible with onboard energy or energy generation, magnetic sails and electric sails.

4.2 Magnetic Sail An artificial magnetosphere has been proposed as an idea for a sail, or a magnetic sail spacecraft [9]. A spacecraft obtains a thrust force based on the interaction between stellar wind particles and an artificial magnetosphere made by electromagnets onboard a spacecraft. Consider an energized magnet moving in a stellar magnetic field. In an encounter with the local wind (or rather the local plasma particle density) a standoff shock of radius Rs emerges. A charged corpuscular drag is induced and can be approximated by 2 2 퐹푑 = 휌푣 휋푅푠 (19) Where ρ = mpn, n = number density and mp the reflected ion mass (taken here to be the mass of a proton). The number density at a distance r from the star can be molded as [7]

푟 2 푛 = 푛 ( 0) (20) 0 푟 6 -3 Taking the solar environment as the model, where r0 is 1 AU, n0 = 7.3x10 m . The stand-off shock has radius 1 2퐵2 6 푅푠 = [ 2] (21) 휇0휌푣 Where μ0 is the permeability of free space. For a loop 1 meter in radius with a current of 100 amps the standoff distance is about 1 meter and the drag about 0.5 Newtons. Unfortunately with a 100 ohm loop of Graphene this requires about a megawatt of power.

4.3 Electric Sail Similar to the Msail, where a magnetic field deflects incoming stellar wind, the Esail [10] uses an electric field to change the trajectories of the stellarsphere protons, to produce drag. The sail consists of extended tethers, arranged in a circular pattern, which are charged with a high positive voltage. The force on the vehicle is a bit complex and is not repeated here. For a ship of size about 1 meter and generating 5 megavolts to the tethers one can obtain a force of approximately 0.5 Newtons. Unfortunately for a 100 ohms system this requires almost a terrawatt!

151 | P a g e

Conclusions The requirements set forward in this study are shown to be difficult to meet. That is if a ship arrives at α-Centuari A it is very difficult to dissipate enough energy from a 20% speed of light trajectory using either passive or active methods. The case of radiation forces merits further study if the optical properties of a sail can be ‘engineered’ to produce useful values for the parameter β. Coulomb drag may be interesting if a way to get a high charge in the spacecraft were possible. Despite the large on board energy generation needed, the magnetic and the electric sails may be worth further study. This is a work in progress.

References [1] P. Lubin, “A Roadmap to Interstellar Flight”, JBIS, 69, pp.40-72, 2016. [2] T. Hoang, A. Lazarian, B. Burkhart, & A. Loeb, “The Interaction of Relativistic Spacecrafts with the Interstellar Medium”, The Astrophysical Journal, Volume 837, Number 1, 2016. [3] R. Heller, M. Hippke, “Deceleration of High-velocity Interstellar Photon Sails into Bound Orbits at α Centauri”, The Astrophysical Journal Letters, Volume 835, Issue 2, article id. L32, 6 pp. (2017) [4] J. A. Burns, P. L. Lamy & S. Soter, "Radiation Forces on Small Particles in the Solar System". Icarus. 40 (1): 1–48, October 1979. [5] W. Press, S. Teukolsky, W. Vetterling & B. Flannery, Numerical Recipes, Cambridge University Press, 1992. [6] R. Feynman, R. Leighton & M Sands, “The Feynman Lectures on Physics”, Three volumes 1964, 1966, Library of Congress Catalog Card No. 63-20717 [7] M. Landgraf, “Modeling the Motion and Distribution of Interstellar Dust inside the Heliosphere”, J. Geophys. Res, 105, A5, 10303-10316, 1 May 2000. [8] S. E. DeForest, “Spacecraft Charging at Synchronous Orbit,” J. Geophys. Res. 77: 3587–3611 (1972). [9] R. M. Zubrin & D. G. Andrews, “Magnetic Sails and Interplanetary Travel”, Journal of Spacecraft and Rockets, vol. 28, issue 2, pp. 197-203, 1991. [10] P. Janhunen, “Electric Sail for Spacecraft Propulsion,” Journal of Propulsion and Power, vol. 20, pp. 763–764, July-August 2004. [11] S. D. Drell, H. M. Foley & M. A. Ruderman, “Drag and Propulsion of Large Satellites in the Ionosphere: An Alfvén propulsion Engine in Space”, Phys. Rev. Lett., 14, 171–175, 1965.

152 | P a g e

RIGHT LIGHT SAIL DYNAMICS AND CONTROL FOR LAUNCH AND ACCELERATION USING CONTROLLED OPTICAL METAMATERIALS

Eric T. Malroy*

NASA Johnson Space Center, 2101 NASA Parkway, Houston TX 77586

March *[email protected] [Abstract Only] AbstractLightweight Spacecraft propelled by laser beams focused on rigid light sails are one approach for the Breakthrough Starshot initiative, which seeks to send probes to Alpha Centauri. One critical challenge is the initial launch and control of the spacecraft as lasers propel it through space, which this paper examines. A large laser phased array system on earth is proposed to power the launch of these small spacecraft, which are jettisoned off an orbiting platform into space. The challenge is to control the attitude of the rectangular flat sail as it is hit by the laser beam as the earth rotates and accelerate it under control in the direction of Alpha Centauri. Photonic metamaterials (including photonic crystals) are one likely option to control the spacecraft moving from orbital velocities to 0.2c under extreme acceleration. For a rectangular sail the metamaterial surfaces would likely be on the corner edges, controlling the optical properties, which would affect the attitude and acceleration. A sensitivity study shows how much optical property variation is needed to control the spacecraft. Although, today there are no metamaterials capable of low absorptivity, prerequisite for these sails, the different metamaterial approaches are examined to see the most promising technologies, thus giving metamaterial researchers the roadmap to develop the needed materials and technologies. Also, a brief discussion is given on other mechanical approaches for control. An algorithm to control the spacecraft is presented, based on the two most promising metamaterial approaches, where an initial launch attitude is assumed. The paper examines the impact of space dust and particles on the spacecraft during acceleration to see if there are control issues. This paper is submitted for the day 2 session Sails and Beams. Keywords: Spacecraft Dynamics, Metamaterials, Light Sail, Project Starshot, Spacecraft Control

References [1] E. Malroy, “Feasibility Study of Interstellar Missions Using Laser Sail Probes Ranging in Size from the Nano to the Macro” Thermal and Fluids Analysis Workshop (TFAWS 2010), JSC-CN-21494, NASA, 2010. [2] P. Lubin, “A Roadmap to Interstellar Flight”, JBIS, 69, pp. 40-72, 2016. [3] B. Fu, E. Sperber, F. Eke, “Solar sail technology—A state of the art review”, Progress in Aerospace Sciences, Vol. 86, pp. 1-19, Oct. 2016. [4] R. Funase, Y. Shirasawa, Y. Mimasu, O. Mori, Y. Tsuda, T. Saiki, J. Kawaguchi, “On-orbit verification of fuel-free attitude control system for spinning solar sail utilizing solar radiation pressure”, Advances in Space Research, Vol. 48, Issue 11, pp. 1740-1746, Dec. 2011. [5] N. Zheludev, “The Road Ahead for Metamaterials”, Applied Physics, Vol. 328, Issue 5978, pp. 582- 583, Apr. 2010.

153 | P a g e

THE PREDICTION OF PARTICLE BOMBARDMENT INTERACTION PHYSICS DUE TO IONS, ELECTRONS AND DUST IN THE ISM AND ON A GRAM-SCALE PROBE

K. F. Long Initiative for Interstellar Studies, The Bone Mill, New Street, Charfield, GL12 8ES, United Kingdom

In this paper we give an assessment of the particle bombardment problem for interstellar spacecraft from dust in the interstellar medium. In particular, we examine the minimum requirements for a set of fusion spacecraft designs under Project Icarus, a successor to the 1970s Project Daedalus study. It is found that whilst protons and electrons may give rise to heating of the spacecraft, the erosion of any shield material is dominated by dust grains. The interstellar dust grains are assumed to have a matter density of 2.57×10-17 gcm-3 and the largest may be as large as 0.1 µm or 5 ng, assuming a typical solid density of 3 gcm-3. Maximum erosion rates are predicted to be of order 3×10-5 g/s for the largest grains. Calculations suggest a shielding mass for Project Icarus of around 1 tons with a thickness of 1 mm, will be sufficient to protect the spacecraft during the cruise phase of the flight. However, a slightly larger shield is recommended to account for impacts occurring during entry into the stellar system prior to planetary encounters occurring, and also to account for high energy ion penetration. Finally, we then apply this analysis technique to the Breakthrough Initiatives Project Starshot Gram-scale probe.

Keywords: Project Daedalus, Project Icarus, particle bombardment, Project Starshot

1. Introduction

Project Icarus [1] is a successor to the 1970s Project Daedalus [2], which was a theoretical effort to design a fusion powered starship capable of conducting a flyby mission to the nearest stars. The main difference is that the Project Icarus vehicle must decelerate fully into the target system. Throughout the journey, the spacecraft will encounter various particle bombardment effects as it moves through the interstellar medium and the impact of these on the design solutions must be understood.

The interstellar medium is comprised on average of gas (~99%) but also of dust (~1%). It is also made up of cosmic rays which are 84% high energy protons, 14% alpha particles and small portions of positrons and antiprotons (<1%). On Earth we are protected from these cosmic rays by the presence of a magnetic field which is able to deflect the charged particles out of harm’s way, except for the most energetic of particles. But on a spacecraft out in deep space these cosmic rays can damage both life and electronic systems and alter the state of electronic circuits.

Any spacecraft needs to mitigate against all of these effects if it is to survive the journey to a nearby star system. To illustrate the energies involved in dust impacts on a spacecraft, for a ng mass, ~10-12 kg, travelling at typically 0.05c (Project Icarus [3-6]) or 0.122c (Project Daedalus [2]) the impact energy will be 112 J (~7.0×1014 MeV) and 648 J (~4.2×1015 MeV) respectively. We have neglected the velocity of the impacting particle itself as well as relativistic effects in this approximation.

154 | P a g e

The gas in the interstellar medium is made up of clouds of materials, surrounded by inter-cloud regions, which is comprised largely of Hydrogen HI and HII regions. The HI regions consist of neutral hydrogen, helium and others. The degree of ionisation is typically small and they emit little visible light with the exception of the spectral lines due to hydrogen. HI regions are mostly an isothermal system with very little changes in temperature, except near the location of an expanding HII region and where the HI region happens to be dense. In this circumstance the undisturbed HI and dense HII regions are separated by a shock front. The dense HI is also separated from the HII regions by an ionisation front. HI regions are typically thin in density except near the galactic centre and they can range in size from 100 pc up to around 1,000 pc. A HII region is a cloud consisting of ionized hydrogen (H+). The degree of ionisation tends to be quite large, and these are dense regions of space. HII regions are usually the location of recent star formation, mostly from short lived blue stars, and so they emit large amounts of ultraviolet light to ionize the surroundings. HII regions tend to be associated with giant molecular clouds such as the Orion nebula which is a stellar nursery. HII regions can range in size from 1 LY up to 100s LY but are not as large as HI regions.

In the Project Daedalus particle bombardment study [7] the authors gave the matter density of gas (mostly hydrogen) in the solar neighbourhood to be around ~1.67×10-21 kgm-3. They also gave the matter density for dust to be ~1.4×10-23 kgm-3 (mean interstellar), ~×10-25 kgm-3 (inter-cloud regions), ~×10-24 kgm-3 (solar neighbourhood). The mean mass of the dust grains was predicted to be around ~10-16 kg.

Evidence for gas and dust grain properties comes from the space missions. This includes HEOS-2 (1972-1974), Pioneer 10 (1972-2003), Pioneer 11 (1973-1995), Voyager 1 and 2 (1977-present), Galileo (1989-2003), Ulysses (1990-2009), Cassini (1997-2007), Helios (1974-1985), Giotto (1985- 1992), Proba 1 and 2 (2001-2016), Rosetta (2004-2016), New Horizons (2006-present). For example, the Galileo mission measured Dust mass range 10-6-10-7 grams, speed 1-70 km/s, and a mean particle mass of 210-12 g. The Ulysses mission measured a mean particle mass of 110-12 g. For the Voyager 1 and 2 missions the dust particle size did not exceed 1 m at 50 AU [12]. Table 1-3 illustrates the expected physics effect on the material surface due to the impact of different types of particles.

Scenario Impact Effects <0.01c Penetration effects insignificant Mild heating >0.01c Penetration effects significant >0.9c Proton collision with nuclei Atomic displacement, plastic deformation, nuclear disintegration Local melting and permanent damage <0.9c Energy dissipation by interaction with electrons, Electron excitation and de-excitation, atomic ionisation and recombination, Radiation emission, absorption and heating Table 1. Proton physics interaction processes

155 | P a g e

Scenario Impact Effects  c Interaction near nuclei results in Pair formation and permanent energy loss and radiation damage emission >0.8c Photons scatter off electrons Some damage (Compton scattering) <0.8c Photon impingement leads to Electron-electron interactions, electron emission (Photoelectric soft x-ray emission effect) (Bremsstrahlung radiation), absorption and heating Table 2. Electron physics interaction processes

Scenario Impact Effects Vsound speed Volume bounded by shock wave Large temperature rise ~1012 K, front, particle slows to sub-sonic material melting and speeds, large Kinetic energy vaporisation, ablative mass loss, deposition into small volume. permanent deformation of material. Table 3. Dust physics interaction processes

Looking at the overall data post Project Daedalus [7], it has been found that dust particles are typically around 1-50 µm at 50 AU. The latest estimates [8] suggest that the matter density is believed to be around ρ=2.57×10-27 gcm-3 and this is similar to modern estimates reported by other authors [9-13]. The dust is expected to have a typical solid density of around 3 gcm-3 and is mostly silicate with large fractions of carbonaceous material. Some of the largest dust grains may be as large as 5 ng. In general, we can split the interstellar dust grains down into three distributions of particles masses. These are given below, along with the estimated number densities (n=ρ/m) from the matter density quoted above.  Typical dust particles: m = 3×10-13 g, n = 8.56×10-15 cm-3.  Mean dust particles: m = 2×10-12 g, n = 1.28×10-15 cm-3.  Largest dust particles: m = 1×10-9 g, n = 2.57×10-18 cm-3. This means that for a 4.3 LY year astronomical target (Proxima Centauri is the target chosen for the Project Icarus study), we can multiply the number density by the number of Light Years to get an estimate for the number of impact events per area per Light Year, or the number of impact events per area throughout the entire mission. This leads to the following estimates: 2 2  Typical dust particles: NLY ~8,100 impacts/cm /LY, Ntot ~34,800 impacts/cm . 2 2  Mean dust particles: NLY ~1,200 impacts/cm /LY, Ntot ~5,200 impacts/cm . 2 2  Largest dust particles: NLY ~2 impacts/cm /LY, Ntot ~10 impacts/cm . We can also calculate the energy of these dust particles and then by multiplying this by the total number of impacts we can find the total energy deposition expected throughout the mission as they impact the spacecraft. This is velocity dependent and so we show the values for both Project Daedalus and Project Icarus, as follows: Project Daedalus (0.122c):- 12 2  Typical dust particles: Ek = 0.2 J ≡ 1.26×10 MeV, Etot = 7.0 kJ/cm . 12 2  Mean dust particles: Ek = 1.3 J ≡ 8.37×10 MeV, Etot = 7.0 kJ/cm . 15 2  Largest dust particles: Ek = 669.8 J ≡ 4.19×10 MeV, Etot = 6.69 kJ/cm . Project Icarus (0.05c):- 11 2  Typical dust particles: Ek = 0.03 J ≡ 2.11×10 MeV, Etot = 1.17 kJ/cm . 12 2  Mean dust particles: Ek = 0.22 J ≡ 1.41×10 MeV, Etot = 1.17 kJ/cm . 14 2  Largest dust particles: Ek = 112.5 J ≡ 7.03×10 MeV, Etot = 1.17 kJ/cm .

156 | P a g e

The above shows that the energy deposition will be a constant for a particular mission velocity. We can see that although the larger mass impacts will be significant to the spacecraft, they will also be very low probable events.

2. Analysis Model The Project Daedalus Reference [7] describes in detail the derivation of equations useful for calculating vehicle temperatures and shielding erosion rates. If we consider only the effects of the protons and electrons then the temperature rise of the material is given by: 휖퐴 휑 1/4 푇 = [ 표 ] (1) 퐴휎퐸푚 Where in this equation Ao is the projected frontal cross-section area, A is the radiating surface area, -8 -2 -4 φ is the flux of energy into the spacecraft, σ is the Stefan-Boltzmann constant (5.67×10 Wm K ), Em is the surface emissivity. The energy flux into the vehicle is given as a function of the relativistic beta value, β, as follows [7]: 휌훽푐3 1 휑 = [ − 1] (2) (1−훽2)1/2 (1−훽2)1/2 The erosion rate is given by [14]: 3 휂퐴표 휌훽푐 1 푚̇ = 2 1/2 [ 2 1/2 − 1] (3) 퐻푠 (1−훽 ) (1−훽 ) Where η is the fraction of the energy transferred to the material that results in permanent changes to the material structure of the spacecraft and in all calculations is assumed to be unity. Others have also derived equations for erosion rates [15], but these results are not discussed here.

It is possible to model many types of materials and the program is coded up for that. However, for these calculations we focussed on Beryllium which is also the shield material adopted for the Project Daedalus study. The assumed physical properties are shown below for Beryllium are atomic number 4, density 1.85 gcm-3, heat of sublimation 35.53×106 Jkgm-1. It is important to note that a careful reading shows that for the Project Daedalus mission, in reference [7], they did not calculate the performance and requirements for the shield material at 0.122c (the final Daedalus cruise velocity) but instead at 0.15c. For the Project Daedalus calculations we also assume a frontal radius of 32 m, 2 2 circular area of 3,217 m , radiating surface area 3,217 m (so Ao=A), surface emissivity of unity. The PARTICLEHIT program also calculates several other performance parameters that were originally calculated by the Project Daedalus team for comparison. The purpose of these parameters is to give 2 metrics for comparing different designs. This includes ṁ/ρAo (m/Yr), m/ρAo (m) and m/Ao (kg/m ).

To assess the impacts of interstellar particles on a spacecraft a code was written in FORTRAN 95, called “PARTICLEHIT”, which allows for the modelling of different frontal area and radiating area geometries, at different speeds and target distances. This speeds up the calculation process significantly. The temperature was calculated using equation (1) and the erosion rates calculated using equation (2). Although the code also calculates the erosion rates using the equation derived by Langston [15] these results will not be shown, considered to give less accurate answers.

Before advancing to model the Project Icarus vehicle, it was firstly necessary to validate the code by comparison to the predicted performance of the Project Daedalus spacecraft discussed in reference [7]. This would give some confidence in the answers obtained.

The calculations are performed assuming a frontal bombardment area of 3,217 m2 and with Ao/A=1.0. We assume an emissivity of unity and a material density of 1.85 gcm-3. The material modelled is Beryllium with atomic number 4. The target is Barnard’s star 5.9 LY distance at 0.122c or 36,575 km/s in a total trip time of 48.36 years.

157 | P a g e

In the Project Daedalus particle bombardment report although the authors did state that “this implies a total mass of beryllium of about 50 tons will be lost” [7], they did not display the predicted shield mass in their Table 7. Instead they provided the calculations for circular radius of 5 m, 10 m, 20 m and 50 m. Taking the data for ρ=10-23 kg/m3 therefore, in order to work out their prediction for a 32 m radius particle shield, it was necessary to derive an interpolation law via the statement of two simultaneous equations as follows: 푚(푡표푛푠) = 훼[푅(푚)]훽 (4) So that 20.96(푡표푛푠) = 훼[20(푚)]훽 (5) 131(푡표푛푠) = 훼[50(푚)]훽 (6) Therefore solving the simultaneous equations leads to α=0.052, β=2 as follows: 푚(푡표푛푠) = 0.052[푅(푚)]2 (7) And the Project Daedalus estimated shield mass comes out as 53.25 tons for a 32 m radius shield. Daedalus Barnard’s Star mission: For the Project Daedalus baseline mission, with a 32 m radius particle shield, and beryllium Shielding Parameters at 0.122c for 48.36 Year mission to 5.9 LY.

2 24 Predicting energy flux 0.064 J/sm , frontal temperature 164.6 K, m/ρAo=1.07×10 m, ṁ/ρAo = 2.21×1022 m/Yr, minimum shield thickness requirement 1.49 mm. The shield mass would be 8.85 tons, and the erosion rates would be 5.8×10-6 kg/s or 8,845.76 kg/Yr.

Daedalus Alpha Centauri mission: For the Project Daedalus design but applied to an Alpha Centauri mission, and beryllium Shielding Parameters at 0.122c for 35.2 Year mission to 4.3 LY. Predicting 2 23 22 energy flux 0.064 J/sm , frontal temperature 164.6 K, m/ρAo=7.80×10 m, ṁ/ρAo = 2.21×10 m/Yr, minimum shield thickness requirement 1.08 mm. The shield mass would be 6.45 tons, and the erosion rates would be 5.8×10-6 kg/s or 6,446.9 kg/Yr.

The results of the calculations are summarised in Table 4.

Parameter Historical Daedalus 1978 Revisited (2017) Revised (2017) (1978) Distance (LY) 6.0 6.0 5.9 Cruise Speed 0.15c 0.122c 0.122c Approx Trip Time (Years) 50.0 49.18 48.36 Energy Flux (J/sm2) -- 0.349 0.064 Temperature at 0.15c (K) 200.0 192.7 192.7 Temperature at 0.122c (K) -- 164.6 164.6 Mass Loss (kg/s) -- 3.16×10-5 5.8×10-6 Mass Loss (kg/Yr) -- 49,004 8,845.76 m/ρAo (m) 1.616×1024 1.09×1024 1.07×2024 ṁ/ρAo (m/Yr) 4.17×1022 2.21×1022 2.21×1022 Shield Mass (tons) 53.25 49.00 8.85 Shield Volume (m3) 29.0 26.49 4.78 Shield thickness (mm) 9.0 8.24 1.49 Table 4. Modelling Project Daedalus. Note that for the ‘revisited’ Daedalus calculations the distance was assumed to be 6 LY. Consistent with the historical, as opposed to 5.9 LY in the ‘revised’ calculations. The average dust density for both the historical and revisited was assumed to be 1.4×10-23 kg/m3, but for the revised it was assumed to be 2.57×10-24 consistent with modern data.

3. Project Icarus Results The code was then applied to various Project Icarus design scenarios over ranges of speed of light fractions and frontal area geometry. It is important to note that the Project Icarus mission has a cruise speed less than half that of the Project Daedalus mission. In addition, the mission requirement

158 | P a g e is for a 100 year duration, as opposed to Project Daedalus which was aiming for 40-50 years and flyby only. Project Icarus fully decelerates into the target system and is to achieve orbital velocity around the target star. The results of various calculations for a Beryllium shield assumption are shown in Tables 5-9 below. The data in the tables aids designers in consideration of design selection choices over varying parameters, which includes frontal area radii and total mission duration.

The 1970s Project Daedalus study had one vehicle design. In Project Icarus, due to the nature of how the project evolved, and the assessment in the lack of maturity with certain critical technologies, no single design has been put forward as a front runner. Instead, the team has opted to pursue several different design paths as an illustration of the likely physics and engineering requirements for a 100 year orbital mission to the nearest stars using fusion propulsion. The key factors that distinguishes the designs is the following: (1) Propulsion ignition system (2) Choice of fuels (3) Mission architecture.

Yet, all of the designs are driven according to the original project requirements [1] and the defined higher level objectives [16]. Each of the designs had a few different people working on them, although there was some cross-over and co-operation between the teams to help each other in critical systems. All of the designs have the same payload mass of 150 tons.

We now give an assessment of the likely minimum shielding requirements for the different starship designs. We also include an analysis of the various interstellar precursor missions known as Starfinder and Pathfinder which were described elsewhere [17]. We also show some analysis for the Icarus Leviathan concept [18]. Table 10 shows the results of these calculations for the different starship design concepts.

2 2 Ro = 16 m, Ao = 804 m Ro = 32 m, Ao = 3,217 m Ro = 64 m, Ao = 12,868 m2 Mass Loss (kg/s) 6.25×10-8 2.50×10-7 9.99×10-7 Mass Loss (kg/Yr) 196.96 787.85 3,151.40 Shield Mass (tons) 0.20 0.79 3.15 Table 5. Beryllium Shielding Parameters at 0.043c for 100.0 Year mission. Predicting energy flux 0.00276 J/sm2, frontal temperature 75.0 K, m/ρAo=9.53×1022 m, ṁ/ρAo = 9.53×1020 m/Yr, minimum shield thickness requirement 0.13 mm.

2 2 Ro = 16 m, Ao = 804 m Ro = 32 m, Ao = 3,217 m Ro = 64 m, Ao = 12,868 m2 Mass Loss (kg/s) 7.16×10-8 2.86×10-7 1.15×10-6 Mass Loss (kg/Yr) 215.76 863.04 3,452.17 Shield Mass (tons) 0.22 0.86 3.45 Table 6. Beryllium Shielding Parameters at 0.045c for 95.5 Year mission. Predicting energy flux 0.00316 J/sm2, frontal temperature 77.6 K, m/ρAo=1.04×1023 m, ṁ/ρAo = 1.09×1021 m/Yr, minimum shield thickness requirement 0.15 mm.

2 2 Ro = 16 m, Ao = 804 m Ro = 32 m, Ao = 3,217 m Ro = 64 m, Ao = 12,868 m2 Mass Loss (kg/s) 9.83×10-8 3.93×10-7 1.57×10-6 Mass Loss (kg/Yr) 266.53 1,066.11 4,264.43 Shield Mass (tons) 0.27 1.07 4.26 Table 7. Beryllium Shielding Parameters at 0.05c for 86.0 Year mission. Predicting energy flux 0.00434 J/sm2, frontal temperature 84.0 K, m/ρAo=1.29×1023 m, ṁ/ρAo = 1.50×1021 m/Yr, minimum shield thickness requirement 0.18 mm.

159 | P a g e

2 2 Ro = 16 m, Ao = 804 m Ro = 32 m, Ao = 3,217 m Ro = 64 m, Ao = 12,868 m2 Mass Loss (kg/s) 1.31×10-7 5.24×10-7 2.09×10-6 Mass Loss (kg/Yr) 322.71 1,290.83 5,163.31 Shield Mass (tons) 0.32 1.29 5.16 Table 8. Beryllium Shielding Parameters at 0.055c for 78.2 Year mission. Predicting energy flux 0.00578 J/sm2, frontal temperature 90.2 K, m/ρAo=1.56×1023 m, ṁ/ρAo = 2.00×1021 m/Yr, minimum shield thickness requirement 0.22 mm.

2 2 Ro = 16 m, Ao = 804 m Ro = 32 m, Ao = 3,217 m Ro = 64 m, Ao = 12,868 m2 Mass Loss (kg/s) 1.70×10-7 6.82×10-7 2.72×10-6 Mass Loss (kg/Yr) 384.32 1,537.27 6,149.1 Shield Mass (tons) 0.38 1.54 6.15 Table 9. Beryllium Shielding Parameters at 0.06c for 71.7 Year mission. Predicting energy flux 0.00751 J/sm2, frontal temperature 96.3 K, m/ρAo=1.86×1023 m, ṁ/ρAo = 2.59×1021 m/Yr, minimum shield thickness requirement 0.26 mm.

Starship Resolution: The spacecraft has a frontal radii of 32 m. Beryllium Shielding Parameters at 0.043c for 100 Year mission to 4.3 LY. Predicting energy flux 0.00276 J/sm2, frontal temperature 75.0 22 20 K, m/ρAo=9.53×10 m, ṁ/ρAo = 9.53×10 m/Yr, minimum shield thickness requirement 0.138 mm. The shield mass would be 0.79 tons, and the erosion rates would be 2.50×10-7 kg/s or 787.85 kg/Yr.

Starship Endeavour: The spacecraft has a frontal radii of 32 m. Beryllium Shielding Parameters at 0.043c for 95.5 Year mission to 4.3 LY. Predicting energy flux 0.00316 J/sm2, frontal temperature 23 21 77.6 K, m/ρAo=1.04×10 m, ṁ/ρAo = 1.09×10 m/Yr, minimum shield thickness requirement 0.15 mm. The shield mass would be 0.86 tons, and the erosion rates would be 2.86×10-7 kg/s or 863.04 kg/Yr. Starship Ghost: The spacecraft has a frontal radii of 54 m. Beryllium Shielding Parameters at 0.043c for 100 Year mission to 4.3 LY. Predicting energy flux 0.00276 J/sm2, frontal temperature 75.0 K, 22 20 m/ρAo=9.53×10 m, ṁ/ρAo = 9.53×10 m/Yr, minimum shield thickness requirement 0.13 mm. The shield mass would be 2.24 tons, and the erosion rates would be 7.11×10-7 kg/s or 2,243.53 kg/Yr.

Starship Zeus: The spacecraft has a frontal radii of 25 m. Beryllium Shielding Parameters at 0.045c for 95.6 Year mission to 4.3 LY. Predicting energy flux 0.00316 J/sm2, frontal temperature 77.6 K, 23 21 m/ρAo=1.04×10 m, ṁ/ρAo = 1.09×10 m/Yr, minimum shield thickness requirement 0.15 mm. The shield mass would be 0.53 tons, and the erosion rates would be 1.75×10-7 kg/s or 526.76 kg/Yr.

Firefly: The spacecraft has a frontal radii of 16 m. Beryllium Shielding Parameters at 0.05c for 86 Year 2 23 mission to 4.3 LY. Predicting energy flux 0.00434 J/sm , frontal temperature 84.0 K, m/ρAo=1.29×10 21 m, ṁ/ρAo = 1.50×10 m/Yr, minimum shield thickness requirement 0.18 mm. The shield mass would be 0.27 tons, and the erosion rates would be 9.83×10-8 kg/s or 266.53 kg/Yr.

Starship Ultra-Dense Deuterium (UDD): The spacecraft has a frontal radii of 16 m. Beryllium Shielding Parameters at 0.05c for 86 Year mission to 4.3 LY. Predicting energy flux 0.00434 J/sm2, frontal 23 21 temperature 84.0 K, m/ρAo=1.29×10 m, ṁ/ρAo = 1.50×10 m/Yr, minimum shield thickness requirement 0.18 mm. The shield mass would be 0.27 tons, and the erosion rates would be 9.83×10-8 kg/s or 266.53 kg/Yr.

Starship Leviathan: The spacecraft has a frontal radii of 32 m. Beryllium Shielding Parameters at 0.063c for 68.25 Year mission to 4.3 LY. Predicting energy flux 0.0087 J/sm2, frontal temperature 23 21 99.9 K, m/ρAo=2.05×10 m, ṁ/ρAo = 3.0×10 m/Yr, minimum shield thickness requirement 0.28

160 | P a g e mm. The shield mass would be 1.69 tons, and the erosion rates would be 7.88×10-7 kg/s or 1,695.67 kg/Yr.

Precursor Mission Starfinder II: The interstellar precursor spacecraft has a frontal radii of 3.2 m. Beryllium Shielding Parameters at 0.01c for 79 Year mission to 0.79 LY or 50,000 AU. Predicting 2 20 19 energy flux 0.0000346 J/sm , frontal temperature 25.1 K, m/ρAo=9.45×10 m, ṁ/ρAo = 1.19×10 m/Yr, minimum shield thickness requirement 0.00131 mm. The shield mass would be 78.12 grams, and the erosion rates would be 3.14×10-11 kg/s or 0.078 kg/Yr.

Precursor Mission Starfinder I: The interstellar precursor spacecraft has a frontal radii of 3.2 m. Beryllium Shielding Parameters at 0.005c for 31.6 Year mission to 0.158 LY or 10,000 AU. Predicting -6 2 19 18 energy flux 4.33×10 J/sm , frontal temperature 14.9 K, m/ρAo=4.73×10 m, ṁ/ρAo = 1.49×10 m/Yr, minimum shield thickness requirement 6.57×10-5 mm. The shield mass would be 3.91 grams, and the erosion rates would be 3.92×10-12 kg/s or 0.00391 kg/Yr.

Precursor Mission Pathfinder: The interstellar precursor spacecraft has a frontal radii of 0.32 m. Beryllium Shielding Parameters at 0.00158c for 10 Year mission to 0.0158 LY or 1,000 AU. Predicting -7 2 17 16 energy flux 1.36×10 J/sm , frontal temperature 6.29 K, m/ρAo=4.73×10 m, ṁ/ρAo = 4.729×10 m/Yr, minimum shield thickness requirement 6.57×10-7 mm. The shield mass would be 3.91×10-4 grams, and the erosion rates would be 1.24×10-15 kg/s or 3.91×10-7 kg/Yr.

Ro (m), Ao Beta, ttot (Years)* Minimum Shield Minimum (m2) mass (kg) Thickness (mm) Daedalus nominal 32 & 3,217 0.122c, 48.4 (49.0) 53,250 9.00 1978 (Barnard’s Star) Daedalus nominal 32 & 3,217 0.122c, 48.4 (49.0) 8,850 1.49 Revised (Barnard’s Star) Daedalus (alpha-Cen) 32 & 3,217 0.122, 35.2 (38.9) 6.45 1.08 Resolution (alpha-Cen) 32 & 3,217 0.043c, 100 (99.52) 790 0.13 Endeavour (alpha-Cen) 32 & 3,217 0.045c, 95.5 (93.79) 860 0.15 Ghost (alpha-Cen) 54 & 9,161 0.043c, 100 (100) 2.24 0.13 Zeus (alpha-Cen) 25 & 1,963 0.045 95.6 (96) 0.53 0.15 Firefly (alpha-Cen) 16 & 804 0.05c, 86 (98.5) 270 0.18 UDD (alpha-Cen) 16 & 804 0.05c, 86 (100) 270 0.18 Leviathan (alpha-Cen) 32 & 3,217 0.063c, 68.2 (100) 1,690 0.28 Icarus Starfinder II 3.2 & 32.17 0.01c, 79 (107.3) 0.078 0.00131 ~1/10 scale (to 50,000 AU) Icarus Starfinder I 3.2 & 32.17 0.005c, 31.6 (49.3) 0.00391 65.7µ ~1/10 scale (to 10,000 AU) Icarus Pathfinder 0.32 & 0.32 0.00158c, 10 (12.5) 39.1µ 0.657µ ~1/100 scale (to 1,000 AU) Table 10. Data for key Project Icarus Vehicle Designs *note that this is the linear transit time from origin to target at the cruise velocity ignoring boost and deceleration phases. However, the actual total mission duration for each design concept is shown in brackets.

161 | P a g e

4. Project Starshot

The Breakthrough Initiatives Project Starshot [10] is an effort to design a gram-scale probe that can be sent to the nearest stars within two decades travelling at ~0.2c. The approximately 3 – 4 m sized sail design would be accelerated at 10,000g by a 100 – 200 GW laser beam system in a matter of minutes. The laser beams would converge on the target as part of a phase array system, irradiating its reflective surface and sending the spacecraft towards its target a few light years distance.

The project builds on earlier work by Robert Forward [24, 25] which proposed to send small spacecraft called Starswisp, to the stars using laser beams instead of direct solar sailing, as a way of getting around the issue of reduced photon intensity with distance from the source. The main difference between the Starwisp and the Starshot concept is that the latter utilising a ground based beaming architecture to facilitate nearer term achievement of the mission.

There are many technical challenges to the fulfilment of this mission, and in this section we demonstrate some calculations for the issue of particle bombardment due to dust, gas and charged particle penetration. In particular, we calculate the likely erosion environment and thereby estimate the amount of shielding material required. The methods and equations are as described for the Project Icarus work in the earlier sections of this paper.

The results for this work are shown in Table 11 and 12 for different materials and different vehicle geometries. Due to the high velocity of the probe, 60,000 km/s, the impacts due to dust erosion will need to be taken into account and for the models examined in this work will result in a frontal area temperature on the spacecraft of ~135.2 K assuming Ao/A ~0.1. If a bombardment shield was to be utilized, we estimate that it would have a mass of order ~0.02 - 0.24 g, depending on the material chosen, which would be. This would be between 2 - 24% and 0.2 - 2.4% of the total mass, assuming a spacecraft mass of 1g or 10g respectively. The inclusion of this shield would obviously affect the payload mass fraction possible for the mission. On the basis of this analysis, a material shielding of order ~1.4 - 3 mm thickness would likely be sufficient to mitigate against any dust impacts. This is a for a cylindrical spacecraft geometry with radii 1 - 10 mm and length 5 - 50 mm. The conclusions relating to the erosion do not take account of the effects due to electrons and ions, which need to be calculated separately as a charged particle transport problem. This analysis also does not take into consideration material ejected from larger objects such as asteroids or comets, although the statistical chance of an encounter is very low unless the mission is directed towards such an object.

162 | P a g e

Table 11. Calculations (R= 1mm model) of Minimum Shielding Requirements for the Starshot Probe.

Table 12. Calculations (R= 10 mm model) of Minimum Shielding Requirements for the Starshot Probe.

5. Charged Particle Penetration Although we have calculated the erosion rate and therefore expected shield requirements due to dust impacts, another consideration is the penetration of energetic charged particles. When a charged particle penetrates matter, it will interact with other charged particles in the target via the Coulomb force. As the particle enters the matter, momentum is transferred via Coulomb interactions and so the particle will slow down, but this interaction time is obviously a function of the particle speed. A faster particle will interact less with other particles that it passes.

During the Project Daedalus particle bombardment study [7], the authors looked briefly at the stopping of interstellar ions, but they only looked at 10 MeV protons, concluding that for beryllium the penetration distance would be around 0.8 mm, suggesting that the estimated particle shield thickness of 9 mm would be approximately 10 times the proton range and so the transmission will be essentially non-existent. This author finds this to be a major assumption in the Project Daedalus study.

Table 11 shows the collision energy of different elements in the interstellar medium, which we assume is dominated by hydrogen, helium and some of the other elements like Carbon and Oxygen. We neglect relativistic effects for this illustration. As can be seen the collision energy increases with the element mass and also with the collision speed.

163 | P a g e

Speed Hydrogen Helium Carbon Oxygen 0.05c 1.17 4.66 13.99 18.63 0.1c 4.69 18.64 55.94 74.52 0.15c 10.56 41.95 125.87 167.68 0.2c 18.78 74.57 223.78 298.09 0.25c 6.99 116.52 349.65 465.77 Table 13. Collision energy (MeV) of impacting elements in Interstellar Medium as a function of speed of light.

Table 13 shows the collisional impact energy due to hydrogen and helium, as the two dominant constitutes of the interstellar medium, making up around ~93% and ~7% respectively. The table also shows the impact energy due to Oxygen and Carbon, representative of the ~0.1% ‘metal’s found in the interstellar medium. As can be seen for the Project Daedalus study, the expected impact energies for hydrogen and helium are in the range ~10-20 MeV. In addition, for the two other representative elements the expected impact energies are in the range ~55-75 MeV. The additional physics expected at these energies, implies that a more detailed analysis of the particle erosion is required. In addition, because of the higher energies, especially from the other elements, the penetration distance would appear to exceed the minimum thickness required purely on the basis of material erosion considerations. It is therefore necessary to estimate the expected stopping distances and therefore the impact on any design decisions for particle bombardment shielding.

The loss of particle energy per unit distance is known as the stopping power S(E) and is given by the kinetic energy Ek of the particle and the distance x that the particles moves through. 푑퐸 푆(퐸) = − (8) 푑푥 In addition to Coulomb interactions there will also be other effects such as quantum mechanics, relativistic velocities, excitation and ionization, radiation losses such as bremsstrahlung (>20 MeV) and even nuclear reactions (>100 MeV). This is all correctly accounted for in the stopping power. A good formulation of this is given by the Bethe-Bloch equation which also takes into account relativistic effects and is given by [19, 20]: 푑퐸 4휋푍2푛 2푚푣2 푆(퐸) = − = 푒 훼 [푙표푔 ( ) − 훽2 − 푙표푔퐼] (9) 푑푥 푚푣2 1−훽2 However for this simple first order analysis we will restrict our assessment to Coulomb interactions only, and this approximation is known as Linear Energy Transferred (LET). The stopping power can then be calculated, by using tools such as detailed in reference [21], as shown in Figures 1, 2 and 3 for a Beryllium particle shield assuming a 10.5 MeV particle impact.

Figure 1. Stopping Power for Electrons

164 | P a g e

Figure 2. Stopping Power for Protons

Figure 3. Stopping Power for Alpha Particles

6. Number of Proton-Induced Nuclear Reactions In the earlier Project Daedalus particle bombardment report [7] the authors also looked at the total number of proton-induced nuclear reactions occurring in the material. We briefly revisit this calculation as a check on the earlier work. As reported in [7] the number of reactions occurring is given by the number density of the target n1 and of the beam of bombarding particles n2, along with the nuclear cross section σ and the relativistic velocity fraction β as follows: 푛휎훽푐 푅 = 푛 푛 휎푣 = 푛 (10) 1 2 1 (1−훽2)1/2 The total number of reactions occurring over the mission lifetime is then given by: 푁푟 = 푅∆푡 (11) Where Δt is the mission duration converted into seconds. The total number of nuclei (m-3) undergoing nuclear reactions is then given by: 푁푟 푁푡표푡 = (12) 푛1 For the Project Daedalus report [7] the authors reported (but assuming 0.15c) the number of reactions occurring throughout the mission to be 3.74×1014 m-3s-1, the total number of reactions over a 40 year mission duration to be 4.72×1023 m-3, and the total number of nuclei undergoing nuclear reactions to be 3.8×10-6 m-3. Using the modern simulation tool developed, and for a 5.9 Light Year mission at 0.122c results in the number of reactions to be 3.0×1014 m-3s-1 and the total number of

165 | P a g e reactions over a 49 year mission duration to be 4.59×1023 m-3, and the total number of nuclei undergoing nuclear reactions to be 3.72×10-6 m-3. These numbers are broadly consistent with the Project Daedalus study.

It is also useful to look at a Project Icarus type mission to 4.3 Light Years and gives a good indication of the likely reaction environment for the Project Icarus probe For the cruise speed range of 0.043- 0.06c with mission trip times that approach a century (Table 10), it is found that the number of reactions occurring throughout the mission to be ~1.5×1014 m-3s-1, the total number of reactions over the mission duration to be ~3.3×1023 m-3, and the total number of nuclei undergoing nuclear reactions to be ~2.7×10-6 m-3.

7. Additional Shielding Methods In the above work we have given an analysis of the expected particle bombardment on the Project Icarus spacecraft but also the expected shielding requirements. However, it is useful to briefly consider alternative shielding concepts which can be utilised for the Project Icarus mission. These are discussed briefly.

Whipple Shields; The type of basic passive particle shields used on modern spacecraft today are known as Whipple Shields or Whipple bumper – named after the person that invented them Fred Whipple. These are used on both the International Space Station and were also used on the Giotto and Stardust mission - a mission to comet wild 2. They are designed to protect the spacecraft from micro-meteroids and orbital debris for velocities in the range 3-18 km/s. They consist of a thin outer bumper placed a distance off the spacecraft wall. This ‘stand-off distance’ effectively increases the thickness of the spacecraft walls. The structure typically has a filling in between the rigid layers made of Kevlar or aluminium oxide fibres. A Whipple shield is designed to shock incoming particles and therefore cause them to disintegrate. The impulse of the impact is dispersed over a large area. The key factors in the design of a Whipple shield includes the type of structure, the material, thickness and the distance between the layers for minimal mass as a trade-off with minimum probability penetration. It is proposed that any vehicle designs for Project Icarus would have advanced Whipple shields positioned at critical locations around the starship, and this especially includes around the payload section. A good overview of calculating Whipple shield designs is given in reference [22].

Debris Shield Cloud; In the Project Daedalus study in addition to a passive particle shield, they also included an innovative Debris ‘Shield cloud’ for particle bombardment protection [23]. This was a cloud of dust that would be flown a few hundred km ahead of the vehicle. Any large dust particles from the interstellar medium would then enter that cloud and be subject to intense heating and vaporisation prior to impact with the main spacecraft. Although the cloud would need to be replenished throughout the planetary and stellar encounter phase of the mission. As the spacecraft approached the target star it was expected that the density and size of particulate matter would increase to high values. The encounter time for the Project Daedalus mission (0.122c) would be of order 100s hours over a distance of 10-100 AU. This was estimated by assuming a debris cloud similar to that of our solar system out to 0.1 LY and would be described by: 푚 1/3 푅푐 = 0.1 ( ) (10) 푚푠 For Project Icarus, the mission target is the Alpha Centauri system. Table 14 shows the estimated debris cloud size and expected encounter time for the three different stars systems. This is an innovative solution, which could be examined for the Project Icarus vehicle, although it is difficult to quantify its effectiveness, and may be unreliable, and would require substantial particle masses.

166 | P a g e

Barnard’s Star Alpha Centauri Beta Centauri Proxima Centauri Mass relative to 0.144 1.1 0.91 0.12 Sun Debris Radius (LY) 0.052 0.103 0.097 0.049 Project Daedalus Encounter Time 314 616 580 295 (days) at 0.122c Project Icarus Encounter Time 766 1,507 1,415 721 (days) at 0.05c Table 14. Estimates of Approximate Encounter times (days) at Stellar Targets

Conclusions In this paper we have reviewed the effects of particle bombardment on an interstellar spacecraft. In terms of material erosion throughout the mission, this is dominated by dust grains in the interstellar medium and on approach to the interstellar system. It is concluded that the Project Daedalus team over-estimated the amount of mass erosion for a nearby interstellar mission and therefore the 50 tons mass 9 mm beryllium particle shield adopted for the design was excessive. The main reason for this was due to the mass-density assumption of dust in the interstellar medium, where the value accepted today is an order of magnitude lower than was adopted in the Project Daedalus analysis. It is to the Project Daedalus credit, that their conservative approach was adopted, to appropriately bound the likely requirements on technology and mission capabilities that had not yet matured.

For the Project Daedalus study the estimated temperature, due to ion and electron impacts on the frontal area, was predicted to be around 200 K, which is close to the main payload, so maintains an equilibrium temperature from the particle heating. However, it is useful to note that this estimate was arrived at by the Project Daedalus team assuming a cruise velocity of 0.15c. For a cruise velocity of 0.122c, the actual Daedalus mission, the temperature drops to 165 K for a Barnard’s Star mission.

For an Alpha Centauri mission, the Project Daedalus temperature is estimated to be 165 K. Examining the various Project Icarus designs, for an Alpha Centauri mission, with cruise speeds in the range 0.043-0.063c, the frontal nose temperature is estimated to in the regime 75-164 K, which is entirely manageable. These temperatures are not considered to be a problem for the mission.

However, in a twist of irony, although erosion due to energetic ions is a minimum issue, for a mission of the Project Daedalus (0.12c) or Project Icarus (~0.05c) type, the penetration of these particles becomes a dominant issue, due to the thinness of the particle shield suggested from the erosion rate calculations. In order to ensure that high energy ions do not penetrate the particle shield, and interact with the payload, the thickness of the shield has to be increased to ensure that it is larger than the average stopping distance of incoming particles that one expects to encounter in interstellar space. This leads to a mass addition on the spacecraft shielding, which is in excess of the minimum mass required for mitigation of particle erosion effects. This might suggest that shielding masses approaching those adopted for Project Daedalus, are not an unreasonable assumption.

Further analysis would need to be performed to investigate this for different material conditions. The various Project Icarus vehicle designs have a cruise velocity in the range 0.043-0.063c and a frontal nose radius in the range 16 – 54 m. On the assumption of a Beryllium particle shield, it is therefore recommended that the minimum shielding mass will be in the range ~0.1 – 1 tons and the shielding thickness will be in the range ~0.1 – 2 mm, both estimates depending on the specific vehicle design and material. Some margin of safety factor would be added to these minimum

167 | P a g e numbers to ensure any uncertainties are correctly captured. To correctly characterise the shielding requirements, a more extensive physics analysis would need to be conducted to take into account the effect of higher energy and higher mass ions, where at large energies additional effects become apparent due to quantum mechanics, relativistic velocity effects, excitation and ionization, bremsstrahlung radiation losses and even nuclear reactions at very high energies (>100 MeV).

Calculations were also performed for the Breakthrough Initiatives Project Starshot Gram-scale probe. The results imply a bombardment shield mass of order ~0.02 - 0.24 g. This would be between 2 - 24% and 0.2 - 2.4% of the total mass, assuming a spacecraft mass of 1g or 10g respectively. On the basis of this analysis, a material shielding of order ~1.4 - 3 mm thickness would likely be sufficient to mitigate against any dust impacts. This is a for a cylindrical spacecraft geometry with radii 1 - 10 mm and length 5 - 50 mm. The conclusions relating to the erosion do not take account of the effects due to electrons and ions.

Acknowledgements The author would like to thank Rob Swinney, Robert Freeland, Richard Osborne, Adam Crowl, and Michel Lamontagne for discussions.

References [1] K. F. Long, M. Fogg, R. Obousy, A. Tziolas, A. Mann, R. Osborne, A. Presby, “Project Icarus: Son of Daedalus – Flying Closer to Another Star”, JBIS, 62, PP.403-414, 2009. [2] A. R. Martin (ed), “Project Daedalus: The Final Report on the BIS Starship Study”, JBIS Supplement, 1978. [3] K. F. Long, R. Osborne, P. Galea, “Project Icarus: Starship Resolution Sub-Team Concept Design Report”, Internal Project Icarus Design Competition Report, October 2013. [4] R. M. Freeland II, “Icarus Firefly: An Unmanned Interstellar Probe Utilizing Z-Pinch Propulsion”, Internal Project Icarus Design Competition Report, October 2013. [5] A. Hein et al., “Project Icarus: TUM Ghost Team Design”, Internal Project Icarus Design Competition Report, October 2013. [6] M. Stanic, “Project Icarus: Ultra-Dense Deuterium Based Vehicle Concept”, Internal Project Icarus Design Competition Report, October 2013. [7] A. Martin, “Project Daedalus: Bombardment by Interstellar Material and its Effects on the Vehicle”, JBIS, S116-S121, 1978. [8] B. T. Draine, “Starchip vs the Interstellar Medium”, Unpublished Note, August 2016. [9] I. A. Crawford, “Project Icarus: A Review of Local Interstellar Medium Properties of Relevance for Space Missions to the Nearest Stars”, Acta Astronautica, 2010. [10] P. Lubin, “A Roadmap to Interstellar Flight”, JBIS, 69, pp.40-72, 2016. [11] J. T. Early, R. A. London, “Dust Grain Damage to Interstellar Laser-Pushed Lightsail”, Journal of Spacecraft & Rocets, 37, 4, July-August 2000. [12] G. A. Landis, “Dust Erosion of Interstellar Propulsion Systems”, AIAA-2000-3339, July 2000. [13] T. Hoang, A. Lazarian, B. Burkhart, A. Loeb, “The Interaction of Relativistic Spacecraft with the Interstellar Medium”, Pre-Print, arXiv, August 2016. [14] E. T. Benedikt, “Disintegration Barriers to Extremely High Speed Space Travel”, Adv in the Astronautical Sci, 6, pp.571-588, 1961. [15] N. H. Langton, “The Erosion of Interstellar Drag Screens”, JBIS, 26, pp.481-484, 1973. [16] P. Galea, higher level objectives document (internal project document)

168 | P a g e

[17] R. Swinney, K. F. Long, A. Hein, P. Galea, A. Mann, A.Crowl, R. Obousy, A. C. Tziolas, “Project Icarus: Exploring the Interstellar Roadmap Using the Icarus Pathfinder and Starfinder Probe Concepts”, JBIS, 65, pp.244-254, 2012. [18] K. F. Long, A. Crowl, A. Tziolas, R. Freeland, “Project Icarus: Nuclear Fusion Space Propulsion & The Icarus Leviathan Concept”, Space Chronicle, JBIS, 65, 2012. [19] S. T. Lai, Fundamentals of Spacecraft Charging: Spacecraft Interactions with Space Plasmas”, Princeton University Press, [20] M. O. Burrel, “The Calculation of Proton Penetration and Dose Rates”, NASA TM X-53063, August 1964. [21] National Institute of Standards and Technology (NIST), U. S Department of Commerce https://www.nist.gov/pml/stopping-power-range-tables-electrons-protons-and-helium-ions [22] E. L. Christiansen, “Performance Equations for Advanced Orbital Debris Shields”, AIAA Space Programs and Technologies Conference, Huntsville, AIAA 92-1462, Al, 24-27 March 1992. [23] A. Bond, “Project Daedalus: Target System Encounter Protection”, JBIS, S123-S125, 1978. [24] R.L.Forward, “Roundtrip Interstellar Travel Using Laser-Pushed Lightsails”, J.Spacecraft and Rockets, 21, pp.187-195, March/April 1984. [25] R.L.Forward, “Starwisp: An Ultra-Light Interstellar Probe”, J.Spacecraft, 22, 3, pp.345-350, May/June 1985.

169 | P a g e

EXPERIMENTAL SIMULATION OF DUST IMPACTS AT STARFLIGHT VELOCITIES

Andrew J. Higgins1* 1 Department of Mechanical Engineering, McGill University, Montréal, Québec, Canada Email: [email protected]

The problem of simulating the interaction of a spacecraft travelling at velocities necessary for starflight with the interplanetary and interstellar medium is considered. Interaction of protons, atoms, and ions at kinetic energies relative to the spacecraft (MeV per nucleon) is essentially a problem of sputtering, for which a wealth of experimental data exists at the velocities of interest. More problematic is the impact of dust grains, macroscopic objects on the order of 10 nm (10-21 kg) to 1 (10-15 kg) and possibly larger, the effects of which are difficult to calculate from first principles, and thus experiments are needed. The maximum velocity of dust grains that can be achieved at present in the laboratory using electrostatic methods is approximately 100 km/s, two orders of magnitude below starflight velocities. The attainment of greater velocities has been previously considered in connection with the concept of impact fusion and was concluded to be technologically very challenging. The reasons for this are explained in terms of field emission, which limits the charge-to-mass ratio on the macroscopic particle being accelerated as well as the voltage potential gradient of the accelerating electrostatic field, resulting in the accelerator needing to be hundreds to thousands of kilometers long for -size grains. Use of circular accelerators (e.g., cyclotrons and synchrotrons) is not practical due to limitations on magnetic field strength making the accelerator thousands of kilometers in size for -sized grains. Electromagnetic launchers (railguns, coilguns, etc.) have not been able to produce velocities greater than conventional gas guns (< 10km/s). The nearest feasible technologies (tandem accelerators, macromolecular accelerators, etc.) to reach the regime of projectile mass and velocity of interest are reviewed. Pulsed laser facilities are found to be the only facilities able to accelerate condensed phase matter to velocities approaching 1000 km/s, but are unlikely to be able to reach greater speeds. They also cannot create well quantified, free-flying projectiles. Instead, it is proposed to use pulse laser facilities to simulate the plasma “fireball” that results from such impacts, rather than try to reproduce the impacts themselves. A number of pulsed laser facilities exists that can provide the energy and power densities to recreate the consequences of an impact (if not an impact itself) in the lab. By performing time-resolved measurements of the effects experienced bymaterial samples at scaled distances from the laser-driven event, the damage to representative spacecraft structures can be accurately assessed.

Keywords: Dust Grains, Impact, High Energy Density

Nomenclature B magnetic field (T) c speed of light d diameter (m) m particle or projectile mass (kg) v velocity (m/s) V voltage potential (V) q charge (C) r radius (m) ratio of wall thickness to shell radius

170 | P a g e

2 2 0 permittivity of free space (C /N m ) 2 0 magnetic permeability of free space (N/A ) p particle or projectile density 2 c surface charge (C/m ) 2 t tensile stress (N/m ) Subscripts FE field emission t tensile ult ultimate strength

1. Introduction Spacecraft traveling at velocities necessary for interstellar travel will encounter interplanetary and interstellar media with potentially devastating consequences [1-7]. The interplanetary and interstellar media encountered consists of both gas (atoms, ions, molecules) and macroscopic particles (dust grains). The response of spacecraft surfaces to the impact of individual atoms, ions, and molecules is essentially a problem of sputtering, a phenomenon that has been extensively studied [8]. Sputtering is the ejection of material from a surface via the impact of atoms or ions due to mechanisms distinct from bulk thermalization of the impact energy, essentially, surface-layer atoms being knocked-off the target material. Sputtering has numerous technological applications, such as thin layer deposition, secondary ion mass spectrometry, and ion implantation, and thus has been widely investigated. Sputtering yield, defined as the number of atoms ejected per incident ion, is usually in the range of 10-3 to 101, generally increasing as the energy of the impacting ion increases. As the ion energies approach 1 MeV2, wherein mechanism of sputtering becomes dominated by interaction with the electron cloud of the target—termed electronic sputtering—the values of yield typically remain less than 102 for metallic targets, although the yield can be orders of magnitude greater (as great as 105) for insulating targets [9]. Using a sputtering yield value of 101 and assuming the Local Interstellar Cloud has an ion density of 1 ion/cm3, then a light year of travel would result in 1020 atoms/cm2 being sputtered off forward-facing spacecraft surfaces, which would only correspond to a thickness on the order of tens of microns of material. While damage to sensitive components (e.g., electronics or optical surfaces) is a valid concern, overall structural degradation of spacecraft structures on the scale of mm thickness due to interaction with the interstellar medium does not appear an insurmountable problem.

More worrisome is the impact of grains, macroscopic objects that can exceed 1 of 0.1 c, a 1- -diameter dust grain (10-15 kg) has approximately 0.5 J of kinetic energy relative to a target, which is equivalent to the energy released by detonation of approximately 0.5 mg of explosives, not a trivial amount. As argued by Schneider [6] -9 kg) were encountered over the duration of the trip, the total kinetic energy of the impactor would be equivalent to half a kilogram of explosives, and even a fraction of this energy couples to the spacecraft structure being impacted, such as a light sail, the vehicle may be compromised. For a classic light sail mission [10-12] wherein the acceleration phase occurs over distances measured in light years (LY), the number of impacts of dust grains expected in interstellar space is essentially the volume swept out by the sail multiplied by the number density of grains. The mass density of dust in the local interstellar medium is 3×10-23 kg/m3 [13]. 3 is assumed, a number density is 3×10-8 grains/m3, yielding 30,000 impacts/cm2 over a light year of travel, giving a mean spacing b Landis [3] and Early and London [4]. Clearly, if the region damaged by the impact exceeds the grain size by a factor of more than 10, there will be no sail left after a LY of travel. Recently, Lubin [14] has suggested performing the acceleration phase of a laser-driven sail over a much shorter distance,

2As discussed later in this paper, energies of MeV per nucleon correspond to velocities of 5% of light speed.

171 | P a g e measured in AU, to avoid the problem of collimating the laser over long distances by exploiting highly reflective sails. This concept has now become the basis for Breakthrough Starshot. The acceleration in this case would occur in the near Earth-orbit region of the solar system, where the mass density of dust is greater (10-20 kg/m3) [13]. The number of impacts expected would be 140 impacts/cm2 per AU if again 1 impact points of approximately 1 mm. Interestingly, this is on the order of the size of the proposed chipsat (or starchip) that would be accelerated by the light sail, meaning the chipsat may be able to avoid impacts during the acceleration phase and then be oriented edge-on for interstellar coasting. The sail (dimensions measured in m) would not be able to avoid impacts during the acceleration process and is thus a significant concern.

The problem of macroscopic objects impacting at velocities in the range of 1000 to 30,000 km/s, i.e., up to 10% light speed, has received only very preliminary theoretical consideration and has never been studied experimentally, for reasons that will be explained in this paper. The closest application that has been considered for macroscopic impactors at these velocities is that of impact fusion, a concept that originated with Harrison [15] and Winterberg [16] and generated some enthusiasm in the 1960s and 1970s. Impact fusion would involve accelerating pellets on the order of a gram to 100 to 1000 km/s, still an order of magnitude below starflight velocities. The impact fusion concept has not been attempted experimentally.

Experience from more prosaic hypervelocity impacts of micrometeoroids and orbital debris (MMOD), while likely of little direct relevance to impacts of dust at starflight velocity, well demonstrates the complex physics that can occur under the extreme conditions generated by impact. The typical double-wall shielding used in orbit today (i.e., Whipple bumper) can results in successive regions of “penetration” or “no penetration” as the velocity of a fixed-sized impactor is increased from 2 to 10 km/s due to tradeoffs in impact-generated pressures and temperatures and material strength. The physics of impacts exceeding just 10 km/s are poorly understood—a regime wherein the impactor and target material are expected to vaporize upon release of the impact- generated shock—due to a lack of constitutive data (equation of state, etc.) and is a direct consequence of our inability to simulate such impact speeds in the laboratory. That different— potentially novel—regimes of impact physics will be encountered as the velocity increases from 10 km/s to 30,000 km/s should be taken as a given.

One such example of possible new phenomenon, originally suggested by Winterberg [17], that might occur as impact velocities begin to exceed 100 km/s (generating pressures exceeding 10 TPa) is the formation of transient, metastable inner shell molecules that, upon decay, would emit copious soft X-rays. This phenomenon was suggested by Bae to be the mechanism responsible for anomalous signals observed at Brookhaven National Laboratory in 1994 examining impact of electrostatically accelerated bio and water particles at ~100 km/s [18]. Further, Bae suggests that since these excited states exist in particles smaller than the wavelength of light emitted, they would decay via the mechanism of Dicke superradiance, which would occur orders of magnitude faster than the usual optical decay. This phenomenon—albeit highly speculative—would significantly alter how the impact-generated plasma would interact with the rest of the spacecraft structure assumed in prior calculations of impact damage.

Thus, it is difficult to conceive at an interstellar mission would be undertaken when it is likely that new physics will be encountered as the spacecraft are impacted by dust grains with problematic or impossible-to-calculate consequences for the survivability of the spacecraft. While more grandiose interstellar mission architectures, such as Project Daedalus, have suggested dust shields that would proceed the spacecraft or active sensing and deflection of dust, the question of what will happen if one grain gets past the shield will always arise. Therefore, the ability to simulate dust grain impacts

172 | P a g e in the laboratory would be of great interest and may well be crucial to the development of interstellar capability. This paper will review the potential for existing or near-future experimental capabilities to address this problem in the laboratory.

2. Accelerator Technologies Detailed overviews of accelerator technologies capable of accelerating macroscopic objects to the 102–103 km/s regime can be found in Manzon [19] and in a more layman-oriented article by Kreisler [20]. A thorough treatment of the problem of acceleration of macroscopic projectiles to the velocity regime necessary to obtain the conditions necessary for thermonuclear fusion (102–103 km/s) can be found in the Proceedings of the Impact Fusion Workshop held at Los Alamos in 1979 [21]. Due to the velocities involved, the only technologies that should be considered are those wherein no contact with the projectile is made, and thus the use of electrostatic or electromagnetic launchers were considered almost exclusively, and this will also be the case in this paper.

2.1 Electrostatic Accelerators Electrostatic accelerators consist of charged particles (either elementary particles or macroscopic pellets) that fall through a voltage potential. The velocity of a particle of mass m accelerated by a V is 푞 푣 = √2 ∆푉 (1) 푚 The particle charge to mass ratio (q/m) is the significant parameter that determines the design and capability of different accelerators. Table 1 lists different types of particles that can be accelerated, V = 1 MV, which is representative of the maximum voltage that can be realized in a single-stage device. Note that a potential of 1 MV is sufficient to accelerate a proton to nearly 5% of light speed, a velocity that was obtained in the earliest particle accelerators built by Van de Graaff and Cockcroft and Walton. Similarly, any fully ionized atom can be accelerated to similar velocities, since the charge-to-mass ratio is half (or a bit less) than that of a proton due to the presence of neutrons in the nucleus. It is for this reason that the study of the impact of atoms and ions at velocities as greatest 107 km/s are encountered in multi-MeV sputtering, as discussed in the Introduction.

The phenomenon ultimately limiting the gradient of the potential field in an electrostatic accelerator is field emission, the profuse streaming of electrons from a surface via quantum tunneling through the potential well that has been distorted by the applied voltage gradient. The onset of significant field emission occurs at a gradient on the order of 109 V/m. Field emission also limits the charge-to- mass ratio of the macroscopic object being accelerated, and larger particles are limited in their charge by the strength of the material, as discussed in the Appendix. The maximum velocity attainable via a 10 MV voltage potential is shown as a dashed line in Figure 1 and forms an upper bound on the velocities of macroscopic projectiles obtained with various single stage accelerator -sized particle representative of an interstellar dust grain, the grain will have a charge to mass limit of q/m = 20 C/kg. If a potential of 109 V/m were applied c (30,000 km/s) would require an accelerator of length 22.5 km, which is impractical.

Cyclotrons and Synchrotrons (e.g., Tevatron, RHIC, and LHC) have accelerated fundamental particles, including the nuclei of heavy (gold and lead) atoms, to very near light speed by successively applying a voltage potential driven by radio frequencies while the nuclei follow a circular track in a static -sized object by similarly employing a circular accelerator is appealing, since the oscillating voltage potential is essentially reused with each trip around the track. The magnetic field strength is limited by the mechanical strength of the magnets and quenching of the superconductors used to create the

173 | P a g e magnetic field. A circular accelerator with a magnetic field comparable to the RHIC or LHC (3 to 8 T) would require a radius measuring r = v/[(q/m) B] ≈ -sized particles with q/m ≈ 20 C/kg traveling at v = 0.2c, which is likely not feasible on earth. Construction of large particle accelerators in space has been proposed, discussed in Varley et al. [22], and several advantages of the concept are discussed therein, but this is likely as significant an undertaking as interstellar travel itself, if not more so. Further, while particle accelerators are a highly developed technique for accelerating elementary particles with known and fixed charge, it is unlikely that the techniques used can be directly translated over to dust grains for which charge is not known a priori and not likely to remain constant during the acceleration process.

Despite these limitations, it is still of interest to examine current state of the art in electrostatic accelerators, as their capabilities might be of interest for experimental simulation of dust impacts at lower velocities and for smaller sized grains. In recent decades, C60 molecules, larger clusters of gold atoms, and biomolecules have been accelerated using the voltage potential generated by electrostatic tandem accelerator facilities [23, 24]. Much of this work has been motivated by mass spectroscopy and secondary ion mass spectrometry of the target material in particular. Molecules +2 +4 and clusters accelerated include C60 and Au400 , but their charge-to-mass ratios, being only partially ionized compared to elementary charged particles, result in velocities of 3000 km/s and 300 km/s, respectively, for at 10 MeV potential accelerator.

Matrix-assisted laser desorption/ionization (MALDI) is a more recent technique applied to mass spectrometry to characterize large biomolecules (e.g., proteins) that benefits from greater ion velocities for greater detection efficiency. To improve this technique for molecules of greater mass, Hsu et al [25]. have recently developed a macromolecular ion accelerator (MIA) that uses voltages applied to plates by fast high voltage switches via a preprogramed waveform generator. This modest device, with a total length of 1 m with an average potential gradient of 1 MV/m, is able to accelerate singly charged immunoglobulins (masses in the 100,000s of atomic mass units or approximately 10-22 kg) to velocities of 35 km/s, and this technique could be extended up to the limit of high voltage switches.

Moving up the mass scale to dust particles in the 10 nm to 1 um size range, Van de Graaff accelerators have seen application to studying impact of interplanetary dust grains for more than 50 years. The original facility built by Friichtenicht in 1962 was able to accelerate 0.1 14 km/s using a 2 MV potential. This original dust accelerator was the basis for a number of active accelerator facilities operating around the world today, including at the University of Kent (Canterbury, UK) [26], University of Colorado (Boulder, USA) [27], and Max Planck Institut für Kernphysik in (Heidelberg, Germany) [28]. These facilities can continuously accelerate dust grains from micron size down to 30 nm size from velocities of 1 to 100 km/s, respectively, at a rate of about one grain per second. The modern facilities have the ability to actively select particles based on velocity, charge, or mass. The maximum velocities obtained are a combination of the charge on the particle (again, field emission limited) and detection limits (i.e., it may be possible that nanometric grains are being accelerated to greater speeds, but cannot be detected). A multistage version of a Friichtenicht-style dust accelerator was proposed by Vedder but did not demonstrate velocities greater than single stage devices [29].

To conclude this discussion, a few concepts—yet to be demonstrated—are mentioned that might have the potential to overcome the limits outlined here. In order to overcome the limitation on the potential gradient of 109 V/m imposed by field emission, Winterberg [30-32] suggested the concept of magnetic insulation, wherein a current is used to create a local magnetic field that would trap and return electrons emitted by field emission to the cathode surface and thereby insulating against breakdown. Harrison [33] suggested the limit on the charge-to-mass ratio of a projectile might be

174 | P a g e increased by using a needle-shaped projectile that, due to the concentration of charge at the tip, would experience massive field emission of electrons, resulting in a highly positively charge projectile. In effect, this field emission projectile idea turns field emission into an advantage rather than a limit. Liu and Lei [34], drawing upon earlier ideas originating from Harrison [35], proposed blowing a continuous stream of ions onto a projectile, generating a local high-strength electric field. None of these concepts—all of which were motivated by fusion research—have been experimentally demonstrated to generate greater projectile velocities.

2.2 Electromagnetic Accelerators The limitations discussed, which suggest a launcher capable of accelerating 1 g to 1000 km/s would be tens of km long, motivated the Los Alamos 1979 Impact Fusion Workshop to consider predominately electromagnetic launchers that utilize the Lorentz force (j × B) to accelerate the projectile. The simplest implementation is the railgun, wherein the projectile comprises the armature for current flowing through the rails that make up the side walls of the launcher. Current flowing up one rail and down the other create the driving magnetic field that exerts a Lorentz force on the current flowing through the projectile. Despite intensive work on rail guns since the 1970s, the maximum velocity of a projectile retaining integrity obtained with a railgun is about 6 km/s, less than conventional light gas guns for the equivalent projectile mass. The use of sliding contact between the projectile and rails would preclude their application for the velocities of interest for this article. Contactless accelerators, such as coil guns, would energize and/or de-energize coil in synchronization with the projectiles, itself a solenoid (either inductive or superconducting). There are a number of embodiments this concept can take, but to date the maximum velocities demonstrated by coilguns is less than 1 km/s. The reasons for these limited velocities are related to the complexities of switching on and off high currents and beyond the scope of this article. The interested reader can find the engineering details of the electromagnetic launchers in the proceeding of the International Symposia on Electromagnetic Launch Technology, most of which are published in the January issue of IEEE Transactions on Magnetics and IEEE Transactions on Plasma Science in odd-numbered years.

2.3 Explosive Accelerators The generation of hypervelocities jets of metal from metal-lined explosive cavities, i.e., a shaped charge, is a well-developed military technology that also sees civilian application, for example, in perforating the casing in gas and oil drilling operations. The mechanism by which these devices operate was explained in a classic paper by Birkhoff, Taylor, and co-workers [36] and extended in a model by Pugh et al [37]. Due to the high pressures that greatly exceed the yield strength of the metal, the collapse of the metal liner can essentially be treated as a flow of liquid toward the centerline that, by conservation of mass and momentum, requires some of the liner be jetted forward. This mechanism is essentially the same as that which results in the generation of a jet when a cavity in water collapses. An interesting feature of the model is that, as the angle of the cavity is made smaller and the phase velocity at which the implosion of the cavity is increased, the velocity of the jet produced can be made arbitrarily great. This motivated Koski et al. [38] to examine the collapse of evacuated metal tubes by imploding toroidal detonations onto them. Jet velocities as great as 100 km/s were observed via streak photography, although the nature of these jets was not determined. Later, Lunc [39] proposed to use a two-stage jet formation process in which an imploding toroidal detonation imploded a tube onto a jet originating from an earlier implosion of the same tube. Again, velocities of 100 km/s were reported. Although the nature of these jets is a mystery, the analysis outlined in Koski and Lunc et al [38, 39]. would suggest these metal jets are likely of the order of 10-3 g, making them the most massive projectiles that have been launch to date by technological means to 100 km/s. These devices are unlikely to be able to be extended beyond 100 km/s and the fact that the projectile is not well quantified makes them less than ideal for impact testing. Explosive accelerators that retain an intact projectile exist and are reviewed in [40], but are

175 | P a g e likely limited to velocities less than 20 km/s. The low cost and the demonstrated ease of scaling shaped charges (scaling as jet mass ~ explosive mass over several orders of magnitude) might still make them attractive for examining impacts of massive projectiles at these velocities.

3. High Energy Density Facilities Drives used for experiments in high energy density physics (not to be confused with high-energy physics) are motivated by interest in inertial confinement fusion, nuclear weapon simulation, fundamental equation of state studies, and experimental astrophysics. These generally fall in two classes: pulsed power and pulsed lasers. These facilities are also capable of accelerating macroscopic objects to velocities approaching, and in some cases exceeding, 100 km/s in very short distances (usually, mm or less). Due to the enormous driving pressures generated, the projectile cannot be allowed to undergo free flight (like the projectiles accelerated by the techniques covered in Section 2) because the projectiles would explosively disassemble or vaporize upon release of the driving pressure. Nonetheless, these facilities are among the most promising for the creation of highly energetic events that are relevant to the simulation of the dust grain impact problem for interstellar flight.

3.1 Pulsed Power The most powerful pulse power facility in existence is the Z-Machine at Sandia National Laboratory, with capacitor banks that store up to 20 MJ of energy that can be released on 100-600 ns timescales, generating currents of 25 MA [41]. The magnetic field generated (1200 GPa) result in magnetic 2 pressures (B 0) as great as 600 GPa. When applied to thin metallic foils, the magnetic pressure can accelerate the foils (typically ≈ 2 cm × 1 cm × 1 mm) to velocities approaching 50 km/s over travel distances of less than 1 cm. As the magnetic field diffuses into the foil being accelerated, it is heated be Joule heating and vaporizes. In addition, the ramp-up of the magnetic field must be sufficiently slow to avoid the formation of a shock within material being accelerated. These two effect sets an ultimate velocity limit on the order of 100 km/s that can be achieved via the application of magnetic pressure [42]. The impact of the metal foil flyers launched by the Z-Machine at velocities of 27 km/s has been used, for example, to shock samples of water to the regime of pressure and temperature encountered at the center of ice giant planets [43].

3.2 Pulsed Lasers The use of very high power pulsed lasers for internal confinement fusion (ICF) has motivated application of these devices to launching thin flyers to velocities exceeding 100 km/s. In ICF, laser ablation of the exterior of a condensed-phase deuterium-tritium pellet (mm-scale) drives a compression pulse or shock into the pellet at speeds on the order of 300 km/s, in a manner similar to rocket propulsion, raising the density by a factor of tenfold, in the hope of achieving fusion conditions. In recent decades, consideration of fast ignition concepts that would use an additional energetic event (e.g., second laser pulse) to ignite the compressed pellet has received significant attention. The use of flyers launched by the laser as the fast ignition source when impacting upon the previously compressed fuel is one such fast ignition concept (note this is separate from impact fusion discussed in the Introduction) [44, 45]. Experiments using the GEKKO XII laser in Japan [44] and the Nike krypton fluoride laser at the Naval Research Laboratory in the US [45] have used laser- driven ablation of polystyrene foils (0.5 900 km/s, respectively. These studies estimated that approximately 90% of the foil mass was lost in ablation, and the density and state of the remaining material was difficult to estimate. Nonetheless, as seen in Figure 1, these tests represent the nearest, in terms of mass and velocity, experiments to -sized dust grains.

176 | P a g e

As discussed by Badziak et al. [46], use of laser-driven plasma ablation has poor efficiency in these experiments and the technique is unlikely to be able to extend launch of foils above 1000 km/s, however, using radiation pressure generated in the laser-driven plasma might allow greater velocities to be achieved. This idea is discussed further by Macchi et al. [47-49], essentially a laser light sail in the lab driven by the radiation created by laser energy deposition. Interestingly, the most recent discussion of this concept mentions it in connection with Breakthrough Starshot, since both concepts rely on radiation pressure to approach relativistic velocities [49].

4. Discussion As accelerators do not appear to be able to achieve the regime of projectile mass and velocity necessary to perform laboratory simulation of dust grain impacts at starflight velocities, it is of interest to explore other types of facilities that could be used to create conditions similar to those encountered in such impacts. In particular, if the correct energy and energy release rate (power) can be realized, then such facilities might be useful for the study of the consequences of such impact on spacecraft structures. The more significant challenge becomes the power density requirement, i.e., the rate of energy density. The energy density deposition time can be estimated for a 1 time across the grain, which at 0.1c is 10-13, or 0.1 ps (100 fs), which is accessible via mode-locking techniques for pulsed lasers and, for even greater energies, via chirped pulse amplification. Thus, rather than use these high-power pulsed laser facilities to launch a projectile (as discussed in Section 4), they could be used to create intense events with the correct power and energy densities as a grain impact, and then representative coupons of spacecraft materials (e.g., sail, etc.) located at various distances could be instrumented to see their time-resolved response. By examining the response seen at different time intervals and different distances, the structural response that would be obtained if the impact fireball was receding at speeds of 0.1c (or less) could be reconstructed.

Conclusions The interstellar medium encountered at velocities necessary for interstellar travel will impact the spacecraft at energies on the order of MeV per nucleon. For elementary particles, due to their large charge-to-mass ratios (i.e., e/Da ~ 1), conventional accelerators operating at MV potentials have been able to reproduce impacts at these energies in the lab for over a century, and thus a wealth of experimental data already exists to address sputtering by interstellar atom and ions. For molecules, atomic clusters, and progressively larger dust grains, the velocity that objects can be accelerated to in the laboratory via electrostatic techniques becomes progressively less as the mass increases, due to the decreasing charge to mass ratio. Charge is limited by field emission and the ultimate strength of the materials involved, and this fundamental limit is not easily overcome; as a result, nanometric to micron-sized dust grains can presently only be accelerated to 100 km/s in the laboratory, or 0.03% lightspeed, but still represent the fastest well-quantified macroscopic objects on Earth. Contactless electromagnetic launchers such as coilguns, utilizing the Lorentz force, have not exceeded 1 km/s. Other technologies, such as explosive accelerators and pulse-power facilities, may be able to contribute by accelerating larger, but poorly quantified, masses (perhaps up to a gram) to velocities exceeding 100 km/s, but likely not greater. Presently, the greatest velocity that can be obtained at near-condensed matter densities is via pulsed laser facilities predominately used for inertial confinement fusion research. Using laser-driven ablation, velocities of almost 1000 km/s (0.3% light speed) have been obtained, although the state of the matter accelerated cannot be precisely quantified and the projectiles cannot be allowed to travel over distances that would permit clean impact experiments to be conducted, independent of the laser energy deposition. Even greater velocities might be attained using radiation-pressure driven acceleration, essentially, laser-driven light sails in the lab, a concept that is presently being explored.

177 | P a g e

Since the prospect for obtaining velocities on the order of 10,000 km/s in the lab is doubtful, it is proposed instead to use pulsed laser facilities to create dense plasmas that can mimic the power and energy densities of impact events without launching actual projectiles. The damage caused by these events on spacecraft and sail can then be studied at scaled distances from the event. By integrating damage accrued over specific time intervals, the motion of the plasma source moving away from the target at high velocity can be simulated in these experiments. A test following this procedure would represent the best terrestrial-based simulation of the impact events likely to be encountered during interstellar flight.

Appendices: Limit on charge to mass ratio of a macroscopic object Appendix A: Field Emission We consider a charged, conductive sphere of radius r and surface charg 푞 푞 = 4휋푟2. The potential outside a sphere is 푉 = , resulting in a potential gradient at the 40푟 surface of the sphere is 푑푉 푞 = − 2 (A1) 푑푟 40푟 푑푉 If the limit of gradient at which the onset of significant field emission is ( ) = 109 V/m, then the 푑푟 FE maximum charge to mass ratio for a solid sphere can be expressed as 푞 3 푑푉 ( ) = 0 ( ) (A2) 푚 sphere 푟 휌 푑푟 FE If the sphere is a shell w t/r, then the charge to mass ratio is 푞  푑푉  푑푉 ( ) = 0 ( ) = 0 ( ) (A3) 푚 shell 푡 휌 푑푟 FE 푟  휌 푑푟 FE Note that the limiting charge-to-mass ratio of a shell of fixed thickness t is independent of sphere 3, representative of an advanced carbon or aluminum/magnesium/lithium material.

Appendix B: Material Strength The other factor limiting charge-to-mass ratio is the strength of the particle material. If the surface of the thin-walled spherical shell has charge q, the tensile stress in the shell due to electrostatic repulsion is 푞2 휎푡 = 3 2 (B1) 32 푡 푟 휋 0 9 For advanced e ult ≈ 10 Pa = 1 GPa. Thus, the charge-to-mass ratio limited by material strength is given by

푞 20ult 1 20ult ( ) = √ 2 = √ (B2) 푚 strength  푟 푡  푟  This relation is also plotted here. For particles of micron size and smaller, field emission sets the limit of the maximum charge-to-mass ratio that can be achieved. Depending on the shell thickness, material strength limits the charge that can be held on a larger spherical shell. The limiting value of q/m determines the velocity that can be obtained in an electrostatic accelerator and the radius through which a particle can be turned in a magnetic field. A more detailed analysis of these considerations can be found in [50].

References [1] E.T. Benedikt, “Disintegration Barriers to Extremely High-Speed Space Travel”, Sixth Annual Meeting of the American Astronautical Society, The MacMillian Company, New York City, 1960, pp. 571-588. [2] C. Powell, “Heating an drag at relativistic speeds”, Journal of the British Interplanetary Society 28 (1975) 546-552.

178 | P a g e

[3] L. Geoffrey, “Dust erosion of interstellar propulsion systems”, 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, American Institute of Aeronautics and Astronautics2000. [4] J.T. Early, R.A. London, “Dust Grain Damage to Interstellar Laser-Pushed Lightsail”, Journal of Spacecraft and Rockets 37(4) (2000) 526-531. [5] I.A. Crawford, A Comment on “The Far Future of Exoplanet Direct Characterization”—The Case for Interstellar Space Probes”, Astrobiology 10(8) (2010) 853-856. [6] J. Schneider, Reply to “A Comment on ‘The Far Future of Exoplanet Direct Characterization’—The Case for Interstellar Space Probes” by I.A. Crawford, Astrobiology 10(8) (2010) 857-858. [7] T. Hoang, A. Lazarian, B. Burkhart, A. Loeb, “The interaction of relativistic spacecrafts with the interstellar medium”, arXiv preprint arXiv:1608.05284 (2016). [8] R. Behrisch, W. Eckstein, “Sputtering by particle bombardment: experiments and computer calculations from threshold to MeV energies”, Springer Science & Business Media2007. [9] W. Assmann, M. Toulemonde, C. Trautmann, “Electronic sputtering with swift heavy ions, Sputtering by Particle Bombardment”, Springer2007, pp. 401-450. [10] R.L. Forward, “Roundtrip interstellar travel using laser-pushed lightsails”, Journal of Spacecraft and Rockets 21(2) (1984) 187-195. [11] G.A. Landis, “Small laser-propelled interstellar probe, Presented at the 46th IAC, Oslo, Norway, October 1995. [12] G.A. Landis, “Optics and materials considerations for a laser-propelled lightsail”, (1989). [13] I. Mann, A. Czechowski, N. Meyer‐Vernet, M. Maksimovic, K. Issautier, N. Meyer‐Vernet, M. Moncuquet, F. Pantellini, “Dust In The Interplanetary Medium—Interactions With The Solar Wind”, AIP Conference Proceedings 1216(1) (2010) 491-496. [14] P. Lubin, “A roadmap to interstellar flight”, JBIS - Journal of the British Interplanetary Society 69(2-3) (2016) 40-72. [15] E.R. Harrison, “Alternative Approach to the Problem of Producing Controlled Thermonuclear Power”, Physical Review Letters 11(12) (1963) 535-537. [16] F. Winterberg, “On the Attainability of Fusion Temperatures under High Densities by Impact Shock Waves of Small Solid Particles Accelerated to Hypervelocities”, Zeitschrift für Naturforschung A, 1964, p. 231. [17] F. Winterberg, “Conjectured Metastable Super-explosives Formed Under High Pressure for Thermonuclear Ignition”, Journal of Fusion Energy 27(4) (2008) 250-255. [18] Y.K. Bae, “Metastable innershell molecular state (MIMS) ”, Physics Letters A 372(29) (2008) 4865-4869. [19] B.M. Manzon, “Acceleration of macroparticles for controlled thermonuclear fusion”, Soviet Physics Uspekhi 24(8) (1981) 662. [20] M.N. Kreisler, “How to Make Things Move Very Fast: The macron accelerator may eventually make energy available for use in a wide range of applications, including controlled thermonuclear fusion”, American Scientist 70(1) (1982) 70-75. [21] “Proceedings of the Impact Fusion Workshop”, in: A.T. Peaslee (Ed.) Los Alamos Scientific Laboratory, 1979. [22] R. Varley, R.G. Hohlfeld, G. Sandri, R. Lovelace, C. Cercignani, Particle accelerators in high earth orbit, Il Nuovo Cimento B (1971-1996) 105(1) (1990) 23-29. [23] P. Attal, S. Della-Negra, D. Gardès, J.D. Larson, Y. Le Beyec, R. Vienet-Legué, B. Waast, “ORION project: acceleration of ion clusters and highly charged biomolecules from 10 MeV to 1 GeV”, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 328(1) (1993) 293-299. [24] Y. Le Beyec, “Cluster impacts at keV and MeV energies: Secondary emission phenomena”, International Journal of Mass Spectrometry and Ion Processes 174(1) (1998) 101-117. [25] Y.-F. Hsu, J.-L. Lin, S.-H. Lai, M.-L. Chu, Y.-S. Wang, C.-H. Chen, “Macromolecular Ion Accelerator”, Analytical Chemistry 84(13) (2012) 5765-5769.

179 | P a g e

[26] M.J. Burchell, M.J. Cole, J.A.M. McDonnell, J.C. Zarnecki, “Hypervelocity impact studies using the 2 MV Van de Graaff accelerator and two-stage light gas gun of the University of Kent at Canterbury”, Measurement Science and Technology 10(1) (1999) 41-50. [27] A. Shu, A. Collette, K. Drake, E. Grün, M. Horányi, S. Kempf, A. Mocker, T. Munsat, P. Northway, R. Srama, Z. Sternovsky, E. Thomas, “3 MV hypervelocity dust accelerator at the Colorado Center for Lunar Dust and Atmospheric Studies”, Review of Scientific Instruments 83(7) (2012) 075108. [28] A. Mocker, S. Bugiel, S. Auer, G. Baust, A. Colette, K. Drake, K. Fiege, E. Grün, F. Heckmann, S. Helfert, J. Hillier, S. Kempf, G. Matt, T. Mellert, T. Munsat, K. Otto, F. Postberg, H.-P. Röser, A. Shu, Z. Sternovsky, R. Srama, “A 2 MV Van de Graaff accelerator as a tool for planetary and impact physics research”, Review of Scientific Instruments 82(9) (2011) 095111. [29] J.F. Vedder, “Microparticle accelerator of unique design”, Review of Scientific Instruments 49(1) (1978) 1-7. [30] F. Winterberg, “Magnetically Insulated Transformer for Attaining Ultrahigh Voltages”, Review of Scientific Instruments 41(12) (1970) 1756-1763. [31] F. Winterberg, “On the Concept of Magnetic Insulation”, Review of Scientific Instruments 43(5) (1972) 814-815. [32] F. Winterberg, “Attainment of Gigavolt Potentials by Magnetic Insulation”, Nature 246(5431) (1973) 299-300. [33] E.R. Harrison, “Impact fusion and the field emission projectile”, Nature 291(5815) (1981) 472- 473. [34] J. Liu, Y. Lei, “Acceleration of Macroscopic Particle to Hypervelocity by High-Intensity Beams”, IEEE Transactions on Plasma Science 37(10) (2009) 1993-1997. [35] E.R. Harrison, “The problem of producing energetic macrons (macroscopic particles)”, Plasma Physics 9(2) (1967) 183. [36] G. Birkhoff, D.P. MacDougall, E.M. Pugh, S.G. Taylor, “Explosives with Lined Cavities”, Journal of Applied Physics 19(6) (1948) 563-582. [37] E.M. Pugh, R.J. Eichelberger, N. Rostoker, “Theory of Jet Formation by Charges with Lined Conical Cavities”, Journal of Applied Physics 23(5) (1952) 532-536. [38] W.S. Koski, F.A. Lucy, R.G. Shreffler, F.J. Willig, “Fast Jets from Collapsing Cylinders”, Journal of Applied Physics 23(12) (1952) 1300-1305. [39] M. Lunc, N. H., S. D., “Accelerator for Jets Formed by Shaped Charges”, Bulletin de l'Académie Polonaise des Sciences XII(5) (1964) 295-297. [40] A.J. Higgins, J. Loiseau, J. Huneault, “The Application of Energetic Materials to Hypervelocity Launchers”, International Journal of Energetic Materials and Chemical Propulsion submitted (2017). [41] R.W. Lemke, M.D. Knudson, J.P. Davis, “Magnetically driven hyper-velocity launch capability at the Sandia Z accelerator”, International Journal of Impact Engineering 38(6) (2011) 480-485. [42] R. W. Lemke, M. D. Knudson, K. R. Cochrane, M. P. Desjarlais & J. R. Asay, “On the scaling of the magnetically accelerated flyer plate technique to currents greater than 20 MA”, Journal of Physics: Conference Series 500(15) (2014) 152009. [43] M.D. Knudson, M.P. Desjarlais, R.W. Lemke, T.R. Mattsson, M. French, N. Nettelmann, R. Redmer, “Probing the Interiors of the Ice Giants: Shock Compression of Water to 700 GPa and 3.8 g/cm3”, Physical Review Letters 108(9) (2012) 091102. [44] H. Azechi, T. Sakaiya, T. Watari, M. Karasik, H. Saito, K. Ohtani, K. Takeda, H. Hosoda, H. Shiraga, M. Nakai, K. Shigemori, S. Fujioka, M. Murakami, H. Nagatomo, T. Johzaki, J. Gardner, D.G. Colombant, J.W. Bates, A.L. Velikovich, Y. Aglitskiy, J. Weaver, S. Obenschain, S. Eliezer, R. Kodama, T. Norimatsu, H. Fujita, K. Mima, H. Kan, “Experimental Evidence of Impact Ignition: 100-Fold Increase of Neutron Yield by Impactor Collision”, Physical Review Letters 102(23) (2009) 235002.

180 | P a g e

[45] M. Karasik, J.L. Weaver, Y. Aglitskiy, T. Watari, Y. Arikawa, T. Sakaiya, J. Oh, A.L. Velikovich, S.T. Zalesak, J.W. Bates, S.P. Obenschain, A.J. Schmitt, M. Murakami, H. Azechi, “Acceleration to high velocities and heating by impact using Nike KrF laser”, Physics of Plasmas 17(5) (2010) 056317. [46] J. Badziak, S. Jabłoński, T. Pisarczyk, P. Rączka, E. Krousky, R. Liska, M. Kucharik, T. Chodukowski, Z. Kalinowska, P. Parys, M. Rosiński, S. Borodziuk, J. Ullschmied, “Highly efficient accelerator of dense matter using laser-induced cavity pressure acceleration”, Physics of Plasmas 19(5) (2012) 053105. [47] A. Macchi, S. Veghini, F. Pegoraro, “Light Sail'' Acceleration Reexamined”, Physical Review Letters 103(8) (2009) 085003. [48] A. Macchi, S. Veghini, T. V. Liseykina & F. Pegoraro, “Radiation pressure acceleration of ultrathin foils”, New Journal of Physics 12(4) (2010) 045013. [49] A Macchi, C. Livi & A. Sgattoni, “Radiation pressure acceleration: perspectives and limits”, Journal of Instrumentation 12(04) (2017) C04016. [50] Z. Wang, J.L. Kline, “Electrostatic method to accelerate nanoshells to extreme hypervelocity”, Applied Physics Letters 83(8) (2003) 1662-1664.

Table 5 Properties of particles that can be accelerated by an electrostatic field Particle Mass Charge q/m Velocity via Gryoradius 1 MV Potential v/c = 0.1, B = 1 T (kg) (C) (C/kg) (e/Da) v (m/s) v/c Proton 1.67×10-27 1.60×10-19 9.58×107 1.0 1.38×107 0.046 0.31 m Au nucleus 3.27×10-25 1.27×10-19 3.87×107 0.4 8.80×106 0.029 0.77 m C60+2 1.20×10-24 3.20×10-19 2.68×105 0.0027 7.32×105 0.0024 1.1 m +4 -22 -19 3 -5 4 -4 Au400 1.31×10 6.41×10 4.90×10 5×10 9.90×10 3.3×10 6.1 km Biomolecules 2.5×10-22 1.60×10-19 640 2.6×10-6 36×103 1×10-4 47 km (immunoglobulins, 6.4×10-22 250 2.6×10-6 22×103 7×10-5 120 km etc.) Dust grain 3) d = 10 nm 1.3×10-21 2.7×10-18 2000 2×10-5 65×103 2×10-4 15 km d 1.3×10-15 2.7×10-14 20 2×10-7 6.5×103 2×10-5 1500 km d 1.3×10 -9 2.7×10-10 0.2 2×10-9 0.65×103 2×10-6 150,000 km

181 | P a g e

Figure 1: Overview of accelerator technologies and their capability in terms of particle mass and velocity. 3 with charge- to-mass ratio limited by field emission at the surface critical gradient of 109 V/m and accelerated through a 10 MV potential.

182 | P a g e

Figure 2: Charge to mass ratio (C/kg) for spherical particles as a function of size. Field emission due to the voltage gradient at the particle surface sets a limit for smaller particles. Larger particles made of thin-walled shells are limited by material strength.

183 | P a g e

Session 3: Breakthrough Propulsion

The following is a report from the Breakthrough Propulsion session. The Chairman for this session was Dr Harold ‘Sonny’ White. The purpose of this session was to bring together papers which discussed any concepts which involves any breakthrough propulsion concepts, an area of technology development that seeks to explore and develop a deeper understanding of the nature of space-time, gravitation, inertial frame, quantum vacuum, and other fundamental physical phenomena with the overall objective of developing advanced propulsion applications and systems that will revolutionize space exploration. Specific problems identified for possible focus were to include:

(1) Proposed methods for mining energy from the Quantum Vacuum (2) The generation and control of large negative energy densities, deprivation of space- time metrics to reduce negative energy requirements, and/or higher dimensional physics models (3) Emergent gravity / emergent quantum mechanics models, pilot wave theory, or other new approaches to reconciling Quantum Mechanics and General Relativity which leads to new space-time transport solutions (4) Space drive concepts that generate force by interactions with the vacuum / space- time (5) Experimental approaches / findings related to the exploration of breakthrough propulsion concepts.

:

184 | P a g e

PILOT WAVE MODEL FOR IMPULSIVE THRUST FROM RF TEST DEVICE MEASURED IN VACUUM

Harold White, James Lawrence, Andre Sylvester, Jerry Vera, Andrew Chap, Jeff George NASA Johnson Space Center, 2101 NASA Parkway, MC EP4, Houston, TX 77058 primary author e-mail: [email protected]

A physics model is developed in detail and its place in the taxonomy of ideas about the nature of the quantum vacuum is discussed. The experimental results from the recently completed vacuum test campaign evaluating the impulsive thrust performance of a tapered RF test article excited in the TM212 mode at 1,937 megahertz (MHz) are summarized. The empirical data from this campaign is compared to the predictions from the physics model tools. A discussion is provided to further elaborate on the possible implications of the proposed model if it is physically valid. Based on the correlation of analysis prediction with experimental data collected, it is proposed that the observed anomalous thrust forces are real, not due to experimental error, and are due to a new type of interaction with quantum vacuum fluctuations.

Keywords: Pilot Wave, Quantum Vacuum, Dynamic Vacuum

1. Introduction This paper will focus on the development of the guiding physics model that is conjectured to be at the heart of thrust production of a form of electric propulsion known as a Quantum Vacuum Plasma Thruster (Q-thruster). A Q-thruster is an electric thruster that uses electric and magnetic fields to push vacuum fluctuations/quantum particles in one direction, while the q-thruster recoils in the other direction of this wake in the quantum vacuum to conserve momentum. Figure 1 shows a 100 watt laboratory test article. A terrestrial analog to help communicate this concept is to think of a submarine in the sea. The submarine does not utilize onboard sea water as propellant to be expelled from the back of the boat to generate thrust, rather it utilizes its propeller to push the surrounding sea water in one direction, while the submarine recoils to conserve momentum. In this situation, the submarine takes advantage of the fact that it is imbedded in its propellant medium. In an analogous manner, the q-thruster may be an embodiment of Arthur C. Clarke’s quantum drive described in his book “The Songs of a Distant Earth” in that the thruster utilizes the electromagnetic fields as a vacuum turbine that sucks in and spits out space time to generate thrust. As a measure of controlling expectations, it should be noted that the current thrust to power levels measured in the lab (0.001 N/kW) are an order of magnitude below a state of the art Hall thruster. At this level, without the advent significantly higher power levels, the thruster technology will only be useful in an orbit maintenance role.

185 | P a g e

(a) integrated test article (b) test article mounted on torsion pendulum Figure 1: Q-thruster laboratory prototype used to complete the recent vacuum campaign

2. Pilot Wave Background Prior to discussing some of the proposed physics at work in the tapered RF test articles, it will be useful to provide some brief background on the supporting physics lines of thought. In short, the supporting physics model used to derive a force based on operating conditions in the test article can be categorized as a non-local, hidden-variable theory, or pilot-wave theory for short.

Pilot wave theories are a family of realist interpretations of quantum mechanics that conjecture that the statistical nature of the formalism of quantum mechanics is due to an ignorance of an underlying more fundamental real dynamics, and that microscopic particles follow real trajectories over time just like larger classical bodies do. The first pilot wave theory was proposed by de Broglie in 1923 [1] where he proposed that a particle interacted with an accompanying guiding wave field, or pilot wave, and this interaction is responsible for guiding the particle along its trajectory orthogonal to the surfaces of constant phase. In 1926, Madelung [2] published a hydrodynamic model of quantum mechanics by recasting the linear Schrödinger equation into hydrodynamic form where the Planck constant ℏ is analogous to a surface tension σ in shallow-water hydrodynamics and vacuum fluctuations are the reason for quantum mechanics. In 1952, Bohm [3,4] published a pilot wave theory where the guiding wave is equivalent to the solution of the Schrödinger equation and a particle's velocity is equivalent to the quantum velocity of probability. Soon after, the Bohmian mechanics line of thinking was extended by others to incorporate the effects of a stochastic subquantum realm, and de Broglie augmented his initial pilot wave theory with this approach in 1964[5] adopting the parlance “hidden thermodynamics”. A family of models categorized as vacuum-based pilot wave theories or Stochastic Electrodynamics (SED)[6] further explore this idea in that the zero-point field, electromagnetic vacuum fluctuations, represent a natural source of stochasticity in the subquantum realm and provides classical explanations for the origin of the Planck constant, Casimir effect, ground state of hydrogen, and much more.

It should be noted that the pilot wave domain experienced an early setback when von Neumann [7] published an impossibility proof against the idea of any hidden-variable theory. This and other subsequent impossibility proofs were later discredited by Bell 30 years later in 1966 [8], and Bell goes on to say in the preface of his 1987 book [9] that the pilot wave eliminates the shifty boundary between wavy quantum states on the one hand, and Bohr's classical terms on the other. Said simply, there is a real quantum dynamics underlying the probabilistic nature of quantum mechanics.

While the idea of a pilot wave or realist interpretation of quantum mechanics is not the dominant view of physics today (which favors the Copenhagen Interpretation), it has seen a strong resurgence of interest over the last decade based on some experimental work pioneered by Couder and Fort

186 | P a g e

[10] with walking droplets. Couder and Fort discovered that bouncing a millimeter sized droplet on a vibrating shallow fluid bath (of Silicone oil) at a frequency just below the Faraday frequency (~60Hz in this case) created a scenario where the bouncing droplet created a wave pattern on the shallow bath that also seemed to guide the droplet along its way. To Couder and Fort, this seemed analogous to the pilot wave concept with the droplet serving as the particle and the wave pattern on the shallow bath of Silicone oil representing the pilot wave. In tests performed by Couder and others, this macroscopic classical system was shown to exhibit characteristics thought to be restricted to the quantum realm. To date, this hydrodynamic pilot wave analog system has been able to duplicate the double slit experiment findings, tunneling, quantized orbits, and numerous other quantum phenomenon. Bush from MIT has put together two thorough review papers chronicling the experimental work being done in this domain by numerous universities [11,12].

In addition to these quantum analogs, there may be direct experimental evidence supportive of the pilot wave approach - specifically Bohmian trajectories are conjectured to have been observed by two separate experiments working with photons [13,14]. Reconsidering the double slit experiment with the pilot wave view, the photon goes through one slit, and the pilot wave goes through both slits. The resultant trajectory that photons follow are continuous real trajectories that are affected by the pilot wave's probabilistic interference pattern with itself as it undergoes constructive and destructive interference due to the presence of the slits. The photon follows an undulating path that follows the regions of constructive interference in the quantum potential. The flux variations of these preferred paths in the pilot wave medium at a detector plane result in the familiar double slit interference pattern associated with the double slit experiment.

3. Q-Thruster Model Background In the approach used in the Q-thruster supporting physics models, the Zero Point Field (ZPF) plays the role of the guiding wave in a similar manner to the vacuum based pilot wave theories. To be specific, the vacuum fluctuations (virtual fermions and virtual photons) serve as the dynamic medium that guides a real particle on its way. Two recent papers explored the scientific ramifications of this ZPF-based background medium. The first paper [15] considered the quantum vacuum at the cosmological scale in which a thought experiment applied to the Friedmann equation yielded an equation that related the gravitational constant to the quantity of vacuum energy in the universe. This implies that gravity may be viewed as an emergent phenomenon - a long wavelength consequence of the quantum vacuum. This viewpoint was scaled down to the atomic level to predict the density of the quantum vacuum in the presence of ordinary matter. This approach yielded a predicted value for the Bohr radius with a direct dependency on cosmological dark energy (see Equation 1). The corollary from this work pertinent to the q-thruster models is that the quantum vacuum is a dynamic medium and can potentially be modeled at the microscopic scale primarily as an electron-positron plasma.

(1)

The quantum vacuum around the hydrogen nucleus was considered in much more detail in the second paper [16]. Here, the energy density of the quantum vacuum was shown to theoretically have a 1/r4 dependency moving away from the hydrogen nucleus (or proton). This 1/r4 dependency was correlated to the Casimir force suggesting that the energy density in the quantum vacuum is

187 | P a g e dependent on geometric constraints and energy densities in electric/magnetic fields. This paper created a quasi-classical model of the hydrogen atom in the COMSOL Multiphysics software (COMSOL is not an acronym) that modeled the vacuum around the proton as an electron-positron plasma. Analysis results showed that the n=1 to 7 energy levels of the hydrogen atom could be viewed as longitudinal resonant wave modes (acoustic resonances) in the quantum vacuum. Figure 2 depicts some of the COMSOL results co-plotted alongside the corresponding probability density based on currently accepted physics for the denoted orbital. In each pane, the left side of the axis of rotation is the probability density for the corresponding state, and the right side of the axis shows the results from the COMSOL analysis. Comparing the COMSOL results with the probability densities, one can hypothesize that the probability density is analogous to a normalized pressure tensor for the corresponding acoustic resonance mode. This suggests that the idea of treating the quantum vacuum as a medium capable of supporting oscillations may be valid. If a medium is capable of supporting oscillations, this means that the internal constituents are capable of interacting and exchanging momentum. Further, the strong dependency on geometry highlighted in this paper is used with the photon number density inside the thruster to derive a local effective energy density of the quantum vacuum.

(a) 2p orbital (b) 3d orbital (c) 4f orbital Figure 2: Comparison of COMSOL results with probability densities: the COMSOL results are on the right, and the corresponding probability density plots are shown to the left with the nodal surfaces.

Before proceeding, a few more sentences need to be dedicated to the topic of virtual particles and real particles in the context of this (early stage) dynamic vacuum pilot wave theory. In the consideration of the vacuum around the hydrogen atom in the papers just discussed, the vacuum is treated as an ever-present dynamic medium, said simply a “vacuum fluid”. This medium can vary both spatially and temporally without the need to “boil off” electron-positron pairs from the virtual state to a real state, and this medium is capable of supporting oscillations through internal interactions including momentum exchange, and communicating these interactions to real or non- quantum particles. Perturbation of the density of this dynamic vacuum does not, for example, require exceeding the Schwinger limit for real pair production. Further, as a precedent of a dynamic vacuum, it should also be noted that a recent monograph published by Wang, Zhu, and Unruh [17] derives a Lorentz invariant spatially and temporally dynamic cosmological vacuum model to explain the fine-tuned cosmological constant value and the currently observed accelerating universe.

4. Vacuum Campaign Summary It has been previously reported that RF resonant cavities have generated measureable thrust on a low thrust torsion pendulum [18,19] in spite of the apparent lack of a propellant or other medium with which to exchange momentum. It was recently shown [20] that a dielectrically loaded tapered RF test article excited in the TM212 mode (see Figure 3) at 1,937 MHz is capable of consistently generating force at a thrust to power level of 1.2 ± 0.1 mN/kW with the force directed to the narrow end under vacuum conditions. This recent test campaign consisted of a forward thrust element that included performing testing at ambient pressure and subsequent power scans at 40, 60, and 80

188 | P a g e watts at vacuum. The test campaign included a reverse thrust element that mirrored the forward thrust element. The test campaign included a null thrust effort of three tests performed at vacuum at 80 watts to try and identify any mundane sources of impulsive thrust. None were identified. Thrust data from forward, reverse, and null suggests that the system consistently performed at 1.2 ± 0.1 mN/kW, which is very close to the average impulsive performance measured in air. Table 1 provides a summary of the results from the forward thrust runs and Table 2 provides a summary of the results from the reverse thrust runs.

Figure 3: TM212 RF mode field lines in dielectric loaded cavity with red arrows represent electric field and blue arrows represent magnetic field; panel.

Table 1: Forward Thrust Results in Vacuum Conditions

Table 2: Reverse Thrust Results in Vacuum Conditions

Although this test campaign was not focused on optimizing performance and was more of an exercise in existence proof, it is still useful to put the observed thrust to power figure of 1.2 mN/kW in context (this was also done in the introduction). The current state of the art thrust-to-power ratio for a Hall thruster is on the order of 60 mN/kW. This is a one and a half order of magnitude higher than the test article evaluated during the course of this vacuum campaign, however, for missions with very large delta-v requirements, having a propellant consumption rate of zero could offset the higher power requirements. The 1.2 mN/kW performance parameter is approximately three orders

189 | P a g e of magnitude higher than other forms of “zero-propellant” propulsion such as light sails, laser propulsion, and photon rockets having thrust to power levels in the 3.33-6.67 µN/kW (or 0.0033- 0.0067 mN/kW) range. The current view of physics would explain this force as experimental error. It is proposed here that the tapered RF test article pushes off of quantum vacuum fluctuations. The thruster generates a volumetric body force and moves in one direction while a wake is established in the quantum vacuum that moves in the other direction.

5. Vacuum Plasma Physics The dominant viewpoint of the quantum vacuum, or vacuum state, is that one cannot push off of it without violating the Laws of Conservation of Energy and Conservation of Momentum. What if, however, the vacuum has the capability to support particle-vacuum or particle-particle interactions that allow lower-energy ground states? It is known from experimental observation that the vacuum can exhibit characteristics that can best be described as a degraded vacuum in the form of the Casimir force [21-25]. The idea of a dynamic and natural vacuum was recently explored in significant detail [16] as applied to the hydrogen atom where the quantum vacuum was treated as a medium able to support longitudinal wave modes and consisting of primarily relativistic electron-positron ephemeral pairs (virtual pairs). If the vacuum is indeed mutable and degradable, then it might be possible to do/extract work on/from the vacuum, and thereby be possible to push off of the quantum vacuum while preserving the Laws of Conservation of Energy and Conservation of Momentum. The essence of the analytic physics models that underlie and guide the development/assessment of a test article design is that the vacuum is a dynamic medium that can be modeled as an electron-positron plasma and has an energy density dependent on geometric constraints and energy densities in electric/magnetic fields.

The theory behind the generation of force from the tapered RF test article works on the premise of pushing off of the quantum vacuum. The thruster generates a volumetric body force moving in one direction, while a wake is established in the quantum vacuum moving in the other direction. The test article is pumped with microwaves at the resonant frequency, and the high energy microwaves within the cavity increase the number density of the virtual electron-positron pairs (see calculation of  v in Table 4). The particles are accelerated by the electric and magnetic fields in the cavity. Due to the shape of the tapered cone and the presence of the dielectric disc, the final mode shape and strength of the time varying electric and magnetic fields coupled with the nonlinear variation in vacuum density yields a slightly asymmetric flux of vacuum fluctuations along the central axis of the thruster and a predicted force directed from the large end to the small end. This force is calculated using a numerical analysis tool that utilizes a Particle-In-Cell (PIC) plasma simulation technique. The forces on individual particles are determined using Equation 2:

(2)

   In Equation 2, the following definition is used: xij  xi  x j . The first bracketed term represents the electric field force exerted by the cavity; the second bracketed term represents the magnetic force

190 | P a g e exerted by the cavity; the third bracketed term represents the electric force from other particles; and the fourth bracketed term represents the magnetic force from other particles. Particles in the simulation are moved using the leap-frog method with the velocity updated using the Boris method[26]. Table 3 shows the sequence of equations of the particle mover portion of the custom simulation tool (position at step t  nt and velocity at time t  (n 1/ 2)t are known).

Table 3: Particle Mover Simulation Steps

The code discretizes the thruster geometry into cells and branches with each cell having an associated electric and magnetic field assigned to it from the COMSOL solution that varies with time:       ECOMSOL  Ereal cos(t)  Eimag sin(t) and BCOMSOL  Breal cos(t)  Bimag sin(t) . All particles within that cell experience that field. The cell boundaries and branch boundaries need not be identical. Branches are volumetric body elements analogous to cells, but a branch focus is to track and update particles within that volume for a particular time step using the appropriate cell forcing function (electric and magnetic fields). Inter-particle forces are calculated within each branch, and forces from particles in other branches are approximated with center-of-mass data.

The perturbed density in the quantum vacuum,  v , is calculated for each cell and is a function of the characteristic length established as a result of photon packing from the energy density of the electric and magnetic fields within that cell at that time step of the simulation run. This potential connection to characteristic length was identified in the work performed modeling the hydrogen atom [16]. Some indirectly supportive work done by Urban [27] suggested that photon interaction with the quantum vacuum through a series of transient captures with continuously appearing and disappearing charged fermion pairs (each ephemeral fermion pair “is assumed to be the product of the fusion of two virtual photons of the vacuum”) is responsible for establishing the speed of light (in vacuum). The possible connection is that real photons are affected by the vacuum, and it could be posited that the vacuum can also be affected by real photons. Table 4 shows the sequence of steps used in the code to calculate a density value for the quantum vacuum within a given cell.

Table 4: Vacuum Perturbation Calculation Method

191 | P a g e

There are two primary force calculation methods used by the code. One method performs a volumetric integral of the force density over the thruster volume as a result of the induced pressure    2 gradient: F  fdVol   v dVol . The second method performs a volumetric integral of the   v V V    force density as a result of the induced acceleration: F  fdVol   a dVol . In both cases,   v V V the velocity and acceleration terms are dependent on the particle pair dynamics and the integration is performed on the thruster model over several hundred RF cycles to establish steady state conditions. With the current design, dielectric loading, RF resonance mode, and frequency, the first method predicts forces about half the value of the second method. The second method is what is used to compare to the empirical data collected during the experimental campaign. The “wake” in the quantum vacuum from the operation of the thruster is not well collimated. Figure 4 shows some of the analysis results from the simulation approach just described. It depicts the non-collimated wake for the tapered test article being excited in the TM212 mode. The left pane shows a side view of the tapered test article wake. The thruster boundary is roughly visible evidenced by the increase in particle density at the center of the plume. The right pane shows the view of the thruster looking from the large end towards the small end. The TM212 node structure is slightly defined by the cross- like shape in the center of the cavity face.

(a) Orthographic Projection from side (b) Trimetric Projection from aft Figure 4: Visualization of Non-Collimated Plume from Thruster (TM212 mode shown)

Figure 5 presents a collection of all the empirically collected data from the vacuum campaign [20]. The averaging of the forward and reverse thrust data is presented in the form of larger circles. The error bars about the average data points represent a 2σ error. The error bars about the individual data points represents the force measurement uncertainty of ± 6 µN. A linear curve was fitted to the data and is shown with the corresponding fitted equation. The blue line at the bottom of the figure shows the results from the dynamic vacuum plasma simulation tool.

192 | P a g e

Figure 5: Graph of Forward and Reverse Thrust Vacuum Testing: predicted thrust performance from the vacuum plasma physics model derived in this paper is shown as a dash-dot blue line on the graph.

6. Discussion One question that typically comes up when considering the images in Figure 4 is what exactly is being modeled in the simulation? The screen shots in Figure 4 present a balanced mixture of positively and negatively charged relativistic fermions that have a relativistic mass equivalent to ~15x the rest mass of the electron. This was the required scaling [16] to produce accurate hydrogen atom energy levels in a model of the quantum vacuum as an acoustically excited medium. On a related note, in an effort by Urban [27] to show that photon interaction with the quantum vacuum (a series of transient captures and emissions with continuously appearing and disappearing fermion pairs) may be the origin of the speed of light, his analysis showed that the ephemeral fermions of the vacuum need have a relativistic mass value of ~30x the rest mass of the electron. Due to the Heisenberg Uncertainly Principle, the lifetimes of vacuum fluctuations are quite short. However, if the vacuum can be posited to be a dynamic medium that can be shown to be degradable, and has the capability to support particle-vacuum or particle-particle interactions that allow lower-energy ground states, then the following (sub quantum dynamics) scenario might occur in this medium:

1. a charged fermion fluctuation pair (dubbed pair A) is created from the fusion of two virtual photons. 2. the positively charged fermion of the fluctuation pair A annihilates with a negative fermion from a different but nearby pair dubbed pair B. 3. the resultant pair of virtual photons created from this positive A fermion annihilating with negative B fermion have a slightly different energy and momentum from the virtual photons that created pair A. If these virtual photons annihilate (either with each other or with other virtual photons) and create a new pair of charged fermions (dubbed pair C), the new pair of fermions will be imbued with the “memory” of the energy and momentum from the A-B annihilation pair. If there is any external field present, then any changes to the energy and momentum of the A-B pair, no matter how small, will be encoded in the dynamic vacuum medium in the form of these virtual photons and survive to the creation of this C-pair of fermions.

193 | P a g e

A related thought experiment was provided by White, et. al. [16] that likened the interaction of the quantum vacuum fluctuations with the real electron in the hydrogen ground state to a room full of paired square dancers, and one unpaired dancer. In this analogy, the room full of paired square dancers progress through the dance moves smoothly as called by the caller, and they occasionally change partners when instructed. The rule is established that when a trade call is issued, the free dancer will couple to the nearest available dance partner of the opposite gender, and the previously paired dancer that misses out is now the free dancer until the next trade call is issued. As the evening progresses, nearly every dance partner of the gender that had the extra dancer has had a period where they were the “unique” solitary dancer. In an analogous way, perhaps the “real” electron is also “unique”. In one instance, the “real” electron collides with a positron vacuum fluctuation elevating the now un-paired electron vacuum fluctuation to the “real” state. This real electron continues in its real state for a brief period until it too collides with a positron vacuum fluctuation, elevating the next un-paired electron vacuum fluctuation to the “real” state. In this way, the vacuum is capable of exchanging momentum directly between virtual particles and between non-quantum objects and the quantum vacuum. It should be noted that the concept of vacuum fluctuation separation having macroscopic phonon behavior resulting in hydrodynamic characteristics of the vacuum medium was first developed and discussed by Stevenson [28] to explore the “hydrodynamics of the vacuum” motivated by the study of the behavior of a Bose- Einstein condensate.

One may ask how a wake is created - if the walls of the test article volume are conductive, then how are the photons/fields/virtual pairs inside the cavity having any substantial effect in creating a wake outside the cavity? What does the wake “look” like to an external observer? Consider back to the treatment of the quantum vacuum as a medium capable of supporting oscillatory modes mediated by vacuum fluctuations [16]. If the vacuum is a ubiquitous continuum that permeates all of space and has temporal and spatial variations down to and through the atomic level, it would not “stop” at the walls of the cavity, and any hydrodynamic pressure gradients in the dynamic vacuum resulting from the imposed external fields would cross the “boundary” of the test article cavity. Even if the vacuum is perturbed inside the cavity in a way to make the thruster more capable of pushing off of the vacuum and generating usable force, the vacuum wake collapses to its unperturbed and weakly interacting state (a fluid shock if you will) as it leaves the thruster volume, making detection of the wake difficult with a traditional “dumb” sensor like a passive ballistic pendulum target. One might detect the wake with another test article to re-couple with the quantum vacuum and better see any anisotropic conditions present as a result of an upstream test article's wake.

Conclusions Realist interpretations of QM such as the pilot wave theory first proposed by De Broglie [1] and later further developed by De Broglie [5] and Bohm [3, 4], have recently seen a resurgence in interest, in part due to experimental work on classical analogs to particle-wave duality by Couder and Fort [10]. Initial dismissal of these ideas due to Neumann's proof of the impossibility of hidden variable theories of QM [7] were challenged 30 years later by Bell's proof that nonlocal hidden variable theories are permissible [8]. Together, these earlier works motivated recent efforts [15, 16] to explore the treatment of the quantum vacuum as a medium capable of momentum exchange. If the vacuum is indeed mutable and degradable as was explored, then it might be possible to do/extract work on/from the vacuum, and thereby be possible to push off of the quantum vacuum while preserving the Laws of Conservation of Energy and Conservation of Momentum. Based on the model developed in this manuscript and the correlation of analysis prediction with collected experimental data, it is proposed that the observed thrust forces are real, not due to experimental error, and are due to a new type of interaction with quantum vacuum fluctuations.

194 | P a g e

Acknowledgements The primary author would like to thank the Eagleworks team for support and hearty discussions about the concepts and testing discussed and explored in this paper. The team would like to extend a special thanks to Andrew Chap for detailed and rigorous work to validate and optimize the plasma analysis tools. The team would like to thank one of its recently retired members (Paul March) for all of his contributions in the lab to collect the low thrust performance data referenced in this paper. The team would like to thank the National Aeronautics and Space Administration for organizational and institutional support in the exploration and analysis of the physics in this paper.

References [1] L. de Broglie, “Interpretation of quantum mechanics by the double solution theory”, Ann. Fond. Louis Broglie, Vol. 12, No. 4, 1987, pp. 1-23. [2] E. Madelung, “Quantentheorie in hydrodynamischer Form”, Z. Phys., Vol. 40, Issue 3, 1927, pp. 322-326. doi:10.1007/BF01400372 [3] D. Bohm, “A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables. I”, Phys. Rev., Vol. 85, Issue 2, 1952, pp.166-179. doi:10.1103/PhysRev.85.166 [4] D. Bohm, “A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables. II”, Phys. Rev., Vol. 85, Issue 2, 1952, pp.180-193. doi:10.1103/PhysRev.85.180 [5] L. de Broglie, “La thermodynamique <> des particules”, Annales de l'I.H.P. Physique théorique, Vol. 1, No. 1, 1964, pp.1-19. [6] T. H. Boyer, “Any classical description of nature requires classical electromagnetic zero-point radiation”, Am. J. Phys., Vol. 79, No. 11, 2011, pp. 1163-1167. doi:10.1119/1.3630939 [7] J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Springer, Berlin (1932). [8] J. S. Bell, “On the Problem of Hidden Variables in Quantum Mechanics”, Rev. Mod. Phys., Vol. 38, Issue 3, 1966, pp.447-452. doi:10.1103/RevModPhys.38.447 [9] J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge Univ. Press, Cambridge, UK (1987). [10] Y. Couder an E. Fort, “Single-Particle Diffraction and Interference at a Macroscopic Scale”, Phys. Rev. Lett., Vol. 97, Issue 15, 2006, pp.154101. doi:10.1103/PhysRevLett.97.154101 [11] J. W. M. Bush, “The new wave of pilot-wave theory”, Physics Today, Vol. 68, 2015, pp. 47-53. doi:10.1063/PT.3.2882 [12] J. W. M. Bush, “Pilot-wave hydrodynamics”, Ann. Rev. Fluid Mech., Vol. 47, 2015, pp. 269-292. doi:10.1146/annurev-fluid-010814-014506 [13] S. Kocsis et. al., “Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer”, Science, Vol. 332, Issue 6034, 2011, pp.1170-1173. doi:10.1126/science.1202218 [14] D. H. Mahler et. al., “Experimental nonlocal and surreal Bohmian trajectories”, Science Advances, Vol. 2, Issue 2, 2016, e1501466. doi:10.1126/science.1501466 [15] H. White, “A Discussion on Characteristics of the Quantum Vacuum”, Physics Essays, Vol. 28, No. 4, 2015. [16] H. White, J. Vera, P. Bailey, P. March, T. Lawrence, A. Sylvester and D. Brady, “Dynamics of the Vacuum and Casimir Analogs to the Hydrogen Atom”, Journal of Modern Physics, Vol. 6, 2015, pp.1308-1320. doi: 10.4236/jmp.2015.69136 [17] Q. Wang, Z. Zhu, W. G. Unruh, “How the huge energy of quantum vacuum gravitates to drive the slow accelerating expansion of the Universe”, Phys. Rev. D, 95, 2017. doi:10.1103/PhysRevD.95.103504 [18] D. Brady, H. White, P. March, J. Lawrence and F. Davies, “Anomalous Thrust Production from an RF Test Device Measured on a Low-Thrust Torsion Pendulum”, 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA, Jul. 2014. doi:10.2514/6.2014-4029 [19] M. Tajmar and G. Fiedler, “Direct Thrust Measurements of an EMDrive and Evaluation of Possible Side-Effects”, 51st AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA, Jul. 2015. doi:10.2514/6.2015-4083

195 | P a g e

[20] H. White, P. March, T. Lawrence, J. Vera, A. Sylvester, D. Brady and P. Bailey, “Measurement of Impulsive Thrust from a Closed Radio Frequency Cavity in Vacuum”, Journal of Propulsion and Power, Vol. 33, No. 4 (2017), pp. 830-841. https://doi.org/10.2514/1.B36120 [21] H. B. G. Casimir, “On the attraction between two perfectly conducting plates”, Proceedings of the Royal Netherlands Academy of Arts and Sciences, Vol. 51, 1948, pp.793-795. [22] S. K. Lamoreaux, “Demonstration of the Casimir Force in the 0.6 to 6 µm Range”, Phys. Rev. Lett., Vol. 78, No. 1, 1997, pp. 5-8. doi:10.1103/PhysRevLett.78.5 [23] P. W. Milonni, R. J. Cook and M. E. Goggin, “Radiation pressure from the vacuum: Physical interpretation of the Casimir force”, Phys. Rev. A, Vol. 38, No. 3, 1988, pp. 1621-1623. doi:10.1103/PhysRevA.38.1621 [24] K. A. Milton, “The Casimir effect: Physical manifestations of zero point energy”, arXiv:hep- th/9901011 [hep-th], 1999. [25] F. Chen, U. Mohideen, G. L. Klimchitskaya and V. M. Mostepanenko, “Demonstration of the Lateral Casimir Force”, Phys. Rev. Lett., Vol. 88, No. 10, 2002, pp. 101801. doi:10.1103/PhysRevLett.88.101801 [26] C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation, Taylor and Francis, Boca Raton, FL (1976). [27] M. Urban et. al., “The quantum vacuum as the origin of the speed of light”, Eur. Phys. J. D, Vol. 67, 2013. doi:10.1140/epjd/e2013-30578-7 [28] P. Stevenson, “Hydrodynamics of the Vacuum”, International Journal of Modern Physics A, Vol. 21, No. 13n14, 2006, pp.2877-2903. doi:10.1142/S0217751X06028527

196 | P a g e

THE MACH EFFECT GRAVITY ASSIST DRIVE

H. Fearn1*, J. J. A. Rodal2 and J. F. Woodward1 1 Physics Department, California State University Fullerton, Fullerton CA 92834. 2 Rodal Consulting, Research Triangle Park, North Carolina.

*Corresponding author, [email protected]

This paper begins with a brief review of what a Mach Effect Gravity Assist (MEGA) drive is and how it works as a propellant-less propulsion device. A typical experimental set up and results for the resonant frequency operation and a chirped frequency response are shown. We continue by highlighting problems we have found in testing the properties of the lead zirconate titanate (PZT) material and the design of the end masses in the stack. The paper concludes by suggesting possible solutions to optimize the thrust of these devices. Keywords: Mach effect, propellant-less propulsion, space-drive

1. Introduction What follows is a description of the MEGA drive component parts. At the core is a stack of lead- zirconate-titanate (PZT) 19 mm diameter by 2 mm thick plates. Silver electrodes are deposited on the flat surfaces of the plates. PZT is a ferroelectric material with a dielectric constant typically of more than 1000 that, because of the asymmetry of the crystalline structure of the material, can be polarized by the application of electric fields. If mechanical stresses are applied to polarized PZT, generally, an electric field is induced in the material and electric charge appears on the surfaces of the material. The inverse of this process is to apply an electric field to the material (by charging adjacent electrodes) and produce a mechanical deformation of the material. The resulting piezoelectric strain is a linear function of the applied electric field. ``Poled'' PZT has many electromechanical applications, audio transducers and micro-linear actuators being typical uses. The MEGA drive has a PZT stack made of 8 plates. Four pairs of plates, typically about 17 mm long when the electrodes and a strain gauge are included. The strain gauge consists of 2 unpowered PZT discs, which are only 0.3 mm thick. The piezoelectric stack is compressed by two end masses; an aluminum mass of 28.2mm diameter and about 4 mm thick and a cylindrical brass mass of the same diameter and 16mm long (or 19mm). Both masses are machined flat with a circular indent for the PZT stack, which is about 0.25mm deep. This indent is just enough to help align the stack while the device is put together, which is its sole purpose. The brass mass is at the supported end and is attached to the aluminum mass by six 2-56 stainless steel socket head cap screws (torqued to 4.0 in- lbf) as shown in Fig. 1. These screws have heat shrink tubing around them, for electrical insulation. There is a thin rubber pad between the brass mass and the mounting bracket. The purpose of this padding, cut away so that it only surrounds the mounting 4-40 cap screws, is to minimize transmission of high frequency oscillations of the brass to the mounting bracket. The device is placed inside a sealed Faraday cage, which is mounted on the end of a balance beam able to twist in the horizontal direction. The deflection of the beam is measured with a Philtec optical sensor. The stack is subjected to ~200 Volts (amplitude) using 30-40 kHz frequency sine waves. The PZT is also electrostrictive, which produces a force due to the volumetric expansion of the stack at twice the frequency of the applied sine wave – that is, at the frequency of the mass fluctuation produced by the piezoelectric response- that combined with the mass fluctuation produces a net time-averaged force on the device.

197 | P a g e

Figure 1. A MEGA device photograph. Taken by Charles Platt. The 6 Bolts have heat shrink wrapped around them to prevent electrical shorts.

The MEGA drives operates by producing a small fluctuation in the PZT mass, which is undergoing energy fluctuations. This is used to produce a steady thrust, which we measure during the experiment. We push on the PZT (whose mass is fluctuating) when it is more massive and pull back when it is less massive, this produces a steady linear acceleration, which is detectable in the laboratory. (You can equally well think of this the other way; push when less massive, pull back when more massive for motion in the opposite direction.) These devices can change direction with different input frequency, they do not need a rotation by 180 degrees. This steady force could be used to produce a propulsive force on a massive object without having to expel propellant from the object. This would be highly desirable from a space rocket point of view, which then would not have to carry a massive payload of expendable fuel. The mass fluctuation formula was derived by JFW many years ago and is in a recent book [1], it has also been re-derived for HF [2] using the advanced wave gravitational theory of Hoyle and Narlikar. Tests of Mach effect thrusters (or as they have recently been renamed, MEGA drives) in three labs other than ours, have produced thrust signatures like those we have obtained. These tests were performed by, Nembo Buldrini at FOTEC (Austria), George Hathaway in Toronto, and Martin Tajmar at Dresden Technical University. All these experiments have been conducted by experts, with good where here facilities at their disposal. These results have been shared at a recent workshop in Estes Park, Colorado, in September 2016. The proceedings of the Estes Park Advanced Propulsion Workshop is freely available online at the Space Studies Institute website [2]. This paper will show the latest experimental results and explain recent systematic testing, being performed in the laboratory, at CSU Fullerton, since January 2017.

198 | P a g e

Figure 2. Torsion balance beam used at CSUF physics department. The Faraday cage is on the right. The coils below the cage are for calibration only and usually turned off. The brass masses on the top left are a counterweight for the Faraday cage. The Philtec optical sensor mount bracket and stepper motor are seen on the lower left. Just to the right of the black stepper motor is a magnetic damper. The power supply is fed into wires, threaded inside the rectangular aluminum beam arm, via galinstan contacts to prevent the weight of the power leads from torquing the beam to one side or the other when the power is applied. The galinstan contacts are centered above the C-flex flexural bearings of the balance beam. The device is mounted on the vertical side of the Faraday cage, so it makes no difference whether the Faraday cage is oriented in one direction or inverted.

2. Basic Theory of the Mega Drive Operation The basic theory for the MEGA drive has been given by JFW in many papers and in a recent book [1]. The theory and experimental details can also be found in the Estes Park proceedings [2]. The idea is that Mach’s principle as stated by Wheeler in [3,4] and in [5] is correct, inertia here is due to mass & energy from the distant matter in the universe. An extended body, undergoing acceleration (due to force1), with internal energy changes, can interact with the distant matter in the universe, instantaneously creating a mass fluctuation. This mass fluctuation can be used to generate thrust, if a second oscillating force is present, in sync with the oscillating mass. You may push light and pull heavy for motion in one direction (or vice versa, for the opposite direction push heavy & pull back light). The center of mass (COM) of a system with oscillating mass can be shown to accelerate [6]. The calculation is very simple and can be reproduced here in a few lines.

Consider the mass spring arrangement in Figure 3 below. The masses m1 and m2 are coupled by a spring with spring constant k. The system of two masses and spring are free to move in space and not attached to anything. We measure the distance of the two masses from a fixed wall at x=0. For example the distance of mass m1 to the fixed wall is x1. The un-extended (or relaxed) length of the spring is L. Using the two masses as constant, we can write down two equations as follows;

(1)

adding these equations gives,

199 | P a g e

(2)

The COM of this mass-spring arrangement is given by

æ m1x1 + m2 x2 ö xcom = ç ÷ . (3) è m1 + m2 ø

The acceleration of the COM, for masses taken to be constant, is therefore

(4)

Figure 3. Simple two masses connected by a spring model.

However, if we allow the masses to change dmj/dt ≠0, where j=1,2,then starting from Eq. (3) and differentiating,

(5)

Using =0 from Eq. (2), the total mechanical momentum p is given by,

(6)

Momentum is not conserved, that is , unless . The unidirectional acceleration of the COM does not violate momentum conservation since momentum is not generally conserved (locally) in the case of oscillating masses. You need to consider the momentum of the entire universe, in order for the total momentum to be to conserved.

Let

200 | P a g e

(7)

Subtracting the equations in Eq. (1) above gives,

(8)

Introducing the reduced mass m ,

æ m1m2 ö m = ç ÷ è m1 + m2 ø (9) 1 æ 1 1 ö = ç + ÷ m è m1 m2 ø

Thus from Eq. (8) we get,

(10)

Using m0 in Eq. (9) for the rest masses m01and m02 .

(11)

where masses m01 , m02 and phases f1, f2 are constant. The mass change dm is considered very small. Similar equations to Eq.(11) hold also for m2 and its derivatives with respect to time. We take 1/2 for the reduced mass μ = μ0 (when the masses do not change) and ω=ω0 = (k/μ0 ) . The solution for u(t) is found as follows:

(12)

where the last equation above, comes from substituting the results for u(t) and its derivatives into

Eq. (10) using constant masses. This gives us the expression for u0. The time dependent u(t) solution can be written, taking F (as defined in Eq. (11) ) instead of F0 in the last expression of Eq.(12) above,

æ F ö cos(wt) u(t) = 0 ç 2 2 ÷ . (13) è w0 -w ø m0

201 | P a g e

Now using,

(14) we can write

æ m02 ö x1(t) = ç ÷ u(t) è m01 + m02 ø (15) æ m01 ö x2 (t) = -ç ÷ u(t) è m01 + m02 ø substituting these expressions into the equation for the COM acceleration Eq.(5), or alternatively in Eq. (6) we find,

(16)

where terms in dm2 have been dropped, as being negligible. It can be shown that the COM acceleration, which has no sine or cosine oscillations in it, can be written as

1 æ w 2F ö édm dm ù a = 0 1 cosf - 2 cosf com ç 2 2 ÷ ê 1 2 ú (17) 2(m01 + m02 )è w 0 -w ø ë m01 m02 û which agrees with Ref. [6] except here we have a factor half. It appears that a steady linear acceleration of the COM, not just an oscillation, is possible when the masses are allowed to change and the masses are unequal. If the masses m1 and m2 were the same and changed in time by the same amount, there would be no linear COM acceleration possible. In reality we need to also consider damping. For the detailed theory of the MEGA device, we refer the interested reader to [1,2] and papers therein. The mass fluctuation can be derived directly from the gravitational absorber theory of Hoyle and Narlikar [7]. This fully Machian theory does not require a steady state universe. Simply omit the creation C-field and it is an expansion theory. The mass fluctuation appears in the Hoyle Narlikar field equation as the trace of the energy momentum tensor, see Fearn in [2]. The trace of the energy λ stress tensor (T=Tλ ) comes into the derivation of the curvature by a slight modification of the field equations, shown in the gravitation text by Carroll p281 using a signature (+---) , or Weinberg p155,

8pG 1 l Rmn = - 4 (Tmn - Tl gmn ), (18) c 2

where we have put the speed of light c back into the expression. Here we shall merely state that the mass fluctuation expected in the device, given by a gravitational interaction with the distant matter in the universe, is δm0 and is given by, 2 1 é 1 ¶P æ 1 ö P2 ù (19) dm = ê - ú 0 4pG r c2 ¶t èç r c2 ø÷ V ëê 0 0 ûú where P is the instantaneous power delivered to the capacitor, ρ0 is the density of the PZT, c is the

202 | P a g e velocity of light and V the volume of the PZT stack dielectric. Note that the assumption that all of the power delivered to the capacitors ends up as a proper energy density fluctuation is an optimistic, indeed, perhaps wildly optimistic, assumption. In a very simplified picture, one can imagine the brass end mass varying only slightly due to heating, and the PZT and thinner aluminum end mass (thought of as one mass) having most of the variation of mass. The mass fluctuations would be very different and the masses are also unequal. The mass of the 16mm length brass is ~ 77g, the 4mm length Aluminum end mass is ~7.3g and the PZT stack has a mass of 48.6g. So combined the PZT and aluminum would be only 48.6g. The change in the brass mass would be minimal almost zero. One can at least see in this toy model, how the device can have an acceleration (not just an oscillation) of the COM from Eq. (17). In general, a real system would need to include damping. This model has no damping, but it would be straight forward to include as a dashpot say between the two masses together with the spring, see [2]. It is possible now to give an order of magnitude estimation of the force from the device. We will take the force to be approximated by from Eq. (6) , where the extension of the stack with six, 2-56 stainless steel bolts, is Δx ~ 5μm and the resonant frequency of operation is ~36 kHz, so the period of oscillation is Dt ~2.75 x 10-5 seconds. So m/s. Using the first term in Eq. (18) the value of dm~6.27 x 10-6 kg. Using Power, P = I V, current I = 0.5 A,V=200 volts, 3 3 -1 2 density PZT, r = 7.9 ´103 kg/m and G = 6.674 ´10-11 m kg s . We find the force F »1.09mN . The order of magnitude of this force is correct. The model of the device, as two unequal masses which can vary in time (coupled by a spring and dashpot), including detailed numerical calculations of the force produced, has been given in by José Rodal [2]. This model too was deemed to simplistic and has since been modified to a full differential equation of a viscous elastic material with damping and entropy.

3. Experimental Setup Initially a new device is first tested on a vector network analyzer (VNA) to determine its natural resonance frequencies. As an example, in figure 4. is shown the result of running white noise at 5 volts through our demonstration device on the VNA (Stanford Research 780 model). This particular device showed a resonant frequency around 36 kHz, slightly higher than the lowest impedance dip on the plot which was at 32.384 kHz.

203 | P a g e

Figure 4. The upper diagram shows the frequencies of the Impedance dips and peaks. The lower picture is screenshot of the SR780 vector network analyzer screen. The upper window is the white noise, the lower window shows the impedance dips.

After measuring for the capacitance of the device and running it on the VNA the test device is placed into the Faraday cage. The whole balance beam is placed inside a vacuum chamber. The soft vacuum pressures we run at are around 5-10 mTorr. A typical run consists of taking ambient noise data for about 15 seconds, followed by a 3 second voltage pulse, on the resonant mechanical frequency of the device. This is followed by a frequency sweep (of about 10-30 kHz) through the resonant frequency for about 8 seconds and then a second on resonant pulse (for 3 seconds) and finally by more ambient noise for 15 or more seconds. The frequency sweep is a way of tracking the resonance frequency of the device. We find that when the device heats up the resonance frequency can change. We should see a large response to the voltage pulse at the resonant frequency (or very close to it). Since the sweep has the resonance at the center (and we usually sweep high to low frequency) if the large response occurs early (or late) in the sweep we can tell that the resonance has shifted higher (or lower) in frequency in relation to the center (resonance) frequency we were running at. For steady operation under optimal conditions, a resonance tracking circuit employing a feedback would be desirable. We also routinely run the device in one orientation and then rotate the entire Faraday cage by 180 degrees and run the same experiment again. By rotating the Faraday cage, we have essentially reversed the direction of the device. Data is taken in one orientation and averaged, then we subtract off an average of runs done in the opposite direction, thereby eliminating any non-reversing thrust signatures. In effect, this eliminated any common mode noise. As an example, here is a single pulse averaged over a dozen runs given by two different groups. See figure 5. The data from Woodward was taken with a voltage of 200V amplitude. The data by Buldrini was taken using 200V peak-to- peak, so half the voltage Woodward was using. The force is known to vary (via experiment and theory) as voltage to the fourth power, which explains the discrepancy in the size of the forces seen. The force shown by Woodward is about 2μN which is ~13 times larger than Buldrini’s result. However, double the voltage gives 24 =16 times larger force. So that works out about right. Of course the devices used were not exactly identical. The resonant AC voltage pulse at the resonant frequency gives a transient switch-on spike, then a steady force, then a switch-off spike in the opposite direction to the switch-on spike. See figure 6

204 | P a g e and look back at figure 5 for comparison with experiment. Note that the switch off spike (in this particular orientation) adds to the steady force to give a larger force momentarily.

Figure 5. Test results by two groups Woodward (left) and Buldrini (right), showing a single on resonance pulse and data averaged over a dozen runs. Woodward was using twice the voltage (V) that Buldrini was using. The force scales as V4. For data on the left by Woodward, the jagged line is force, the darker (slightly lower) square pulse line is applied voltage (lasting 11 seconds) and the lighter square pulse is the strain gauge inside the stack. Photos taken from Buldrini [2].

It would be of interest to utilize the switch-off transient as a propulsive force and eliminate the switch-on transient, which is in the opposite direction. Then by using a rapid succession of these switch-off transients we might propel a craft along in space more efficiently than by using the steady thrust as he power duty cycle could be kept small.

Figure 6. Diagram showing the main features of the force trace during the voltage pulse at the resonance frequency. Sometimes the horizontal dotted lines can be tilted, this is caused by thermal drift in the data. Diagram by Buldrini, [2].

4. Results Since the force has been shown to go with the rate of change of power P, and dP/dt has opposite signs for the on and off transients, the thrust transients have opposite signs too. If the magnitudes of the thrust impulses are the same, or nearly the same, the off transient will cancel the on transient and the net thrust over one cycle will be small or zero. If everything were simple and linear, it might well be the case that the on and off impulses were equal and opposite. But the devices tested here are not simple and linear, so there is a real prospect that one of the transients can be suppressed, leaving the other transient unbalanced. The simplest way to accomplish this is to turn on or off either the on or off transient slowly, leaving the other transient prompt. Since these devices run on

205 | P a g e an electro-mechanical resonance of the device, there is a simple way to affect slow turn-on or turn- off. Say we want to turn the device on slowly (and off promptly). We simply energize the device with a voltage signal several kHz away from the resonant frequency. Then, using the control voltage of the voltage controlled oscillator, we bring the operating frequency onto resonance slowly. Code was written to affect this procedure. The result is shown in Figure 7. The quality of the thrust resolution is good enough to show an at first negative, and then positive going thrust as the frequency is brought down to resonance (by raising the oscillator control voltage). The switching transient that follows the power being switched off is obvious and cannot be due to power considerations as the power is off.

Figure 7. Chirped 8 second pulses. The pulses start at a frequency above the resonant frequency of the device and then slowly the pulse is tuned onto the resonant frequency. The lower line shows an inverted frequency change, the frequency actually starts high and gets tuned quadratically lower during the pulse. The square-like pulses represent the voltage amplitude applied to the device. The jagged line with the peaks in the force trace. This data was recorded using a Picoscope, model 4244.

When the Faraday cage is rotated by 180 degrees, the device is then forced in the opposite direction. The resulting force trace can be seen in figure 8.

Figure 8. Chirped 8 second pulses. The pulses start at a frequency above the resonant frequency of the device and then slowly the pulse is tuned onto the resonant frequency. This jagged curve shows the force in the opposite direction as compared with figure 7. This force plot has a slight downward slope due to thermal drift. These plots are reproduced from the paper by JWF in the Estes Workshop [2].

206 | P a g e

It has also been observed that the direction of the force can change depending only on the frequency of the input voltage to the device. This was noticed, during a run of chirped pulses where the frequency was changed inbetween pulses of the applied voltage. Figure 9. shows a set of chirped pulses which started off by using a slightly higher than resonance frequency, the voltage oscillator input frequency was set at 36.7 kHz. The sweep starts high then is swept down to the voltage oscillator input frequency. The actual resonance of the device was 36.3kHz, so between pulses the voltage oscillator frequency was lowered to 35.8 kHz so that the entire resonance is swept through. It appears that very close to the resonant frequency is another frequecy where the device would move in the opposite direction. It is reasonable to think that one could tune the device to move either in one direction or the opposite without having to rotate the device by 180 degrees. This would be a convenience for a space-drive, since it entails essentially no moving parts. (No gimbal required, as for ion drives and hence less weight.)

Figure 9. Force plot versus time showing a reversal in the direction due to frequency change. 5. Problems and Solutions The PZT being used regularly at CSUF by JWF is purchased form Steiner Martins and is called SM- 111 material. It has some nice properties which can be found online [8], on the steminc.com 10 2 webpages. The material has reportedly a Young’s modulus (stiffness) of E=Y33= 7.3 x10 N/m , 3 -12 density of 7.6 g/cm , the piezoelectric constant d33= 320 x10 m/V, a Curie temperature of 320 degree Celcius, a dissipation tan δ =0.4, and the mechanical quality factor, Qm=1800. Well actually, we measured the Qm and found it to be closer to 80 when the discs are glued together into a stack and Dr. Martin Tajmar also measured the Q at his facility in Dresden TU and found a Qm ~ 60 for the stack. So we decided to have a closer look at these sintered discs to see what the problem might be and why the quality factor seemed so low. One SM-111 disc was mounted to a small 3/8 inch diameter aluminum cylinder and then placed inside an electron microscope. We obtained the following images. See Figure 10. There appear to be a great deal of voids present in this sintered powered material. This could account for the low quality factor measured. For comparison we decided to purchase some sintered discs from a different vendor, APC international [9] and also look at these under an electron microscope. Some PZT discs, material APC- 844, (19mm diameter and 2mm thick) were purchased and examined under the electron microscope. The APC material also has some desirable properties, the reported Qm was 1500. The electron microscope photographs are shown in figure 11.

207 | P a g e

Figure 10. Electron microscope images of a 19mm diameter disc of SM-111. No etching was done, the only preparation was a simple wipe with an alocohol swab. The disc had a silver coating used as an electrode. This was considered sufficient and no further conductive coating was needed. On the left the photograph shows a scale of 50 microns. On the right the scale is 10 microns. The dark spots are voids in the material.

208 | P a g e

Figure 11. Electron microscope images of a 19mm diameter disc of APC-844. No etching was done, the only preparation was a simple wipe with an alocohol swab. The disc had a silver coating used as an electrode. This was considered sufficient and no further conductive coating was needed. On the left the photograph shows a scale of 50 microns. On the right the scale is 10 microns. The dark spots are voids in the material. Note that there are considerably fewer voids than in the photographs in Fig.10. The slight glow is caused by electron discharge, the silver coating may not have had a good ground to the small aluminum mounting bracket in this case.

The APC 844 has very similar properties to SM-111. Curie temperature is also 320 degree C, -12 dissipation given by tan δ =0.4 , piezoelectric constant d33= 300 x10 m/V, Young’s modulus Y33=6.3 x1010 N/m2 and density of 7.7 g/cm3. It appears that the sintering of the APC material is superior to the SM discs. The failure of conductive cracks in thermally depoled PZT-4 ceramics have been studied by Zhang et al [10]. We also would like to try crystal discs rather than sintered. We are currently waiting for our first shipment of crystal PIN-PMN-PT, (TRSX4B), from TRS technologies. There are multiple paths forward regarding the quality of materials. Using a different manufacturer is one and moving up to crystal discs is another. Both options will be tested. The reason for wanting the high quality factor is because the force produced by the device has been shown in a model to scale with the Qm factor. To make the point, we include two plots by JJAR using his model to predict the force at various Qm values. See figure 12 and 13 which use different damping models. Also note that both models predict a change of direction in the force close to the resonant frequency, which we showed experimentally in figure 9.

209 | P a g e

Figure 12. Plot of frequency in Hz verse force in micro Newtons for various Qm values.

These plots were using a Kelvin-Voigt damping model.

Figure 13. Plot of frequency in Hz verse force in micro Newtons for various Qm values.

These plots were using a Maxwell visco-elastic damping model.

210 | P a g e

It also came to out attention, that if we are to try expensive crystals we would want to make sure that our mounting brackets are capable of evenly distributing the pressure, from the bolts, over the surface of the crystal so as not to crack them. So far we have been using flat surface brass and aluminum end masses. We decided to test the pressure distribution using Fuji-film, a pressure sensitive film [11]. The stress σ can be calculated as follows,

Nt s = = 793.77t (19) Am f dbolt where N is the n umber of 2-56 bolts (N=6) , τ is the torque on the bolts (in-lbf), A is the area of the 2 PZT ( which is 0.4395 in ), μf =0.2 the coefficient of friction between stainless steel and brass, and bolt diameter dbolt =0.086 in (for 2-56 ANSI screws). Hence we can form a table of values for the stress given a certain torque on the bolts. See Table 1.

Table 1. Stress for a given torque Torque τ in (in-lbf) Stress σ (psi) 3 2381 4 3175 5 3969 6 4762

The Fujifilm pre-scale comes in different pressure ratings, it was determined that medium (MS rating 1,400-7,100psi) would be best for our application. The high (HS) film has a rating of (7,100-18,500 psi). The results of our test are shown in figure 12. The distribution of pressure was far from even. We instead got a contact ring around the edge where the 6 bolts were located. The test shows we certainly have room for improvement. The outside pressure was measured to be quite high ~ 7,300 psi. A way forward would be to profile the brass and aluminum end caps in a domed shape to more evenly distribute the pressure from the bolts. We might also try using Kapton film as a gasket between the PZT stack and the end masses.

211 | P a g e

Figure 14. The test rig on the left and the actual film used in the center. The medium sensitive pressure film was seen to be the best fit (the high sensitive pressure film was discarded). On the right is a “color” version of the medium film, with a detailed cross section given of the pressures.

In order to correct for this highly asymmetric pressure distribution we utilized contact mechanics and found the correct dome profile (h) for the end masses in contact with the disc crystals should be,

é x2 ù h = ℓn ê 1- 2 ú (20) ëê R ûú which is plotted in figure 15. The dome height was estimated to be 0.8 thousandths of an inch. The profile is calculated from contact mechanics of a rigid flat punch on an elastic half space, see for example [11]. This is known as a Boussinesq problem [12,13]. In the text [11], equation (2.66) is when the x>a, where a=R is the radius of the disc. So (x/a)2 -1 would become 1 – (x/a)2 for when x

212 | P a g e

Figure 15. This is the profile of the end masses, both brass and aluminum. Both are in contact with the PZT stack. We tested this profile using only the machined brass side and found that the Fujifilm gave a much more even distribution of pressure and the pressure (at 4 in-lbfs torque on the bolts) was reduced to 3057 psi.

To calculate the thickness of the gasket between the stack and the end masses, we should first analyze the indentation of a flat axisymmetric punch on an elastic half plane. Using again σ as the average contact stress, F= σ πR2 as the contact force, E≅2 x 106 lbf/in2 as the modulus of elasticity (smaller due to porosity of the SM-111), ν=0.3 as the Poisson ratio, R=0.3740in (8.5mm) as the radius of contact area and Δ as the deflection (in inches). Then

F D = = 0.0008 (21) æ E ö 2Rç 2 ÷ è1-n ø which explains our choice of the dome height.

213 | P a g e

Conclusions We have presented new experimental work done and testing currently in progress at the CSUF lab. We have shown that chirped pulses can be used for a space-drive, otherwise known as a propellant- less propulsion drive. Our PZT stacks are certainly not optimized yet. There is need to invest some time deciding which PZT materials to use and how to machine the end masses. There is the possibility of also using Kapton film gaskets, to more evenly distribute pressure from the bolts. The use of brass and aluminum for the end masses may also not be optimal. We have a cooling issue and using copper or silver as electrodes in the stacks may assist with heat dissipation. Operation at higher frequencies also holds out promise of improved behavior. Further suggestions for bolt materials have been made by JJAR in [2]. We are in the process of optimizing the MEGA drive at this time. Furthermore, the absorber theory (using advanced and retarded waves) first outlined by Richard Feynman for classical electromagnetism, and later for quantum electrodynamics (QED) by P. Davies and J. Narlikar has been applied to gravitation by Hoyle and Narlikar [7]. The gravitational theory so derived is fully Machian and reduces to Einstein’s theory of general relativity in the limit of a smooth fluid and a conformal transformation. The use of advanced and retarded waves in gravitational theory does not automatically imply a static universe model. In a foreword to “Feynman’s lectures on gravitation” [15], John Preskill and Kip Thorne write on Mach’s idea, “Mach’s idea- that inertia arises from the interactions of a body with distant bodies- bears a vague resemblance to the interpretation of electrodynamics proposed by Feynman and Wheeler when Feynman was in graduate school [WhFe 45, ref. [16], WhFe 49 , ref. [17]]; that the radiation reaction force on an accelerated charge arises from interactions with distant charges, rather than with the local electromagnetic field. So perhaps it should not be surprising that in §5.3 and §5.4 Feynman seems sympathetic to Mach’s views. He gropes for a quantum mechanical formulation of Mach’s principle in §5.4 and revisits it in a cosmological context in §13.4. Feynman’s reluctance in §9.4 and §15.3 to accept the idea of curvature without a matter source also smacks of Mach.”

With Hoyle Narlikar theory, Feynman would have found a duplicate of his own absorber theory, but now for gravitation. No curvature without matter is allowed in the Hoyle Narlikar theory and the gravitational constant G is defined as positive in the theory (attractive), rather than put in by hand as positive as Einstein did. The theory has been criticized since the equation of motion is no longer a geodesic. However, this is not a problem, since only non-spinning particles (also tending toward a point particle) do in fact follow geodesics. It was shown by Papapetrou in 1951 that real particles, with finite extent and spin, do not follow exact geodesic paths, there are extra terms present, [18- 20]. It has been suggested that with the MEGA device we are getting “free” energy in the form of kinetic energy since we get out more energy than we put in. This is not the case, the energy comes from the gravitational field. A simplified explanation follows:- According to Eötvös, if we excite a body of mass m, (our MEGA 2 device for example) by excitation energy E0, it gets heavier by (E0/c )g then its mass becomes m 2 +(E0/c ). Let us first raise the body to height hg above ground level and then excite it, the body 2 contains energy, E0 +(E0/c +m)ghg more than the unexcited device at ground level. Bringing this 2 device back to ground level gives us (E0/c )ghg in “free gravitational energy”. The gravitational energy has lost a little energy, which has been given to the body as heat, internal energy or kinetic energy in the MEGA drive case. This idea can account for gravitational red shift (as the photon climbs out of the gravitational well of a star) or blue shift if the photon falls into the star. The kinetic energy of our device comes from the gravitational potential of the universe (which is enormous, roughly equal to c2), the energy we put in, is instrumental in tapping into this universal potential energy, not in supplying it. With the MEGA drive we are not physically lifting the device, we are allowing a time dependent mass change, a small δm decrease, which essentially “lifts” the device out of its gravitational well just a little (consider this due to the piezoelectric effect at frequency ω), then a

214 | P a g e second force due to electrostriction at frequency 2ω gives a small push in the direction of the cylindrical axis of the device as the mass change goes back to normal and then positive δm. We only want to push when the mass is lighter, not when it is heavier hence the requirement for a force at 2 frequency 2ω. You can imagine a small gain in energy from the gravitational field of (E0/c + δm)ghg where the δm change, coming directly from the Hoyle Narlikar field equations, is larger than the 2 (E0/c ) term. The direction of motion is determined from the “push” along the axis of the device. That is the source of our kinetic energy. If R is the radius of the earth then a device of mass m is at “height” mgR. A device with a slightly lower mass, but the same energy, would be raised a little (m-δm)(R+hg)g=mgR which implies hg=Rδm/(m-δm). This is a simplified explanation. More details to follow in a longer paper.

Acknowledgements We thank NASA innovative advanced concepts division for a phase 1B grant number NNX17AJ78G which assisted with this research. We thank Paul March, Bruce Long and Marshal Eubanks for helpful discussions. HF thanks Steve Karl (CSUF technical staff) for assistance obtaining the electron microscope photographs and Jon Woodland (CSUF master machinist) for his careful machining of the dome structure on the brass end mass.

References [1] J. F. Woodward, “Making Starships and Stargates, The science of Interstellar Transport and Absurdly Benign Wormholes”, Springer Press, New York, December 2013. [2] H. Fearn & L. L. Williams editors, “Proceedings of the Estes Park Advanced Propulsion Workshop”, Estes Park CO , September 19-22 (2016). Free download is available at the Space Studies Institute (SSI.org) http://www.ssi.org [3] I. A. Ciufolini & J. A. Wheeler, “Gravitation and Inertia”, Princeton Series in Physics, Princeton University Press, New Jersey (1995). [4] C. H. Misner, K. S. Thorne & J. A. Wheeler, “Gravitation”, W. H. Freeman and Company, San Francisco 1973. [5] J. B. Barbour & H. Pfister editors, “Mach’s Principle: From Newton’s Bucket to Quantum Gravity”, Birkäuser , Berlin (1995). [6] K. Wanser, “Center of mass acceleration of an isolated system of two particles with time variable masses interacting with each other via Newton’s third law internal forces: Mach effect thrust 1”, Journal of Space Exploration 2, (2) pp121-130 (2013). [7] F. Hoyle and J. V. Narlikar, “Action at a distance in physics and cosmology”, W. H. Freeman & Company San Francisco (1974). See also, Hoyle, F. and Narlikar, J.V. (1964) Proceedings of the Royal Society of London A, 282, 191. http://dx.doi.org/10.1098/rspa.1964.0227 and Hoyle, F. and Narlikar, J.V. (1966) Proceedings of the Royal Society of London A, 294, 138. http://dx.doi.org/10.1098/rspa.1966.0199 [8] Steiner and Martins piezoelectrics CO. https://www.steminc.com/ material properties https://www.steminc.com/PZT/en/piezo-materials-properties [9] APC International Ltd, , Piezoelectrics Ceramics & Piezo components, https://www.americanpiezo.com/ the material properties can be found here; https://www.americanpiezo.com/apc-materials/physical- piezoelectric-properties.html [10] Tong-Yi Zhang et al., “Failure behavior and failure criterion of conductive cracks (deep notches) in thermally depoled PZT-4 ceramics”, Acta Materialia , 51, pp4881-4895 (2003). [11] Fujifilm Prescale. Pressure Metrics LLC, www.pressuremetrics.com Medium (MS) film. [12] K. L. Johnson, “Contact Mechanics”, Cambridge University Press, 1985. (See Rigid punch pp35- 38. Also Eq. (2.24b) using Log[s-x] for x ≤ a where a is the radius of the disc.)

215 | P a g e

[13] Ian N. Sneddon, “The relaxation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile”, Int. J. Engineering Sci. 3, pp47-57 (1965). [14] J. R. Barber, “Indentation of an elastic half-space by a cooled flat punch”, http://qjmam.oxfordjournals.org/ Radcliffe science library. [15] R. P. Feynman , F. Morinigo and W. Wagner, “Feynman Lectures on Gravitation”, Frontiers in Physics series, (1995). [16] J. A. Wheeler and R. P. Feynman, “Interaction with the Absorber as the Mechanism of Radiation”, Reviews of Modern Physics, 17, 157-181 (1945). http://dx.doi.org/10.1103/RevModPhys.17.157 [17] R. P. Feynman and J. A. Wheeler, “Classical Electrodynamics in terms of Direct Particle Interaction”, Reviews of Modern Physics, 21, 425-433 (1949). http://dx.doi.org/10.1103/RevModPhys.21.425 [18] A. Papapetrou, “Spinning Test-Particles in General Relativity. I”, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Vol. 209, No. 1097, pp248-258 (1951) [19] E. Corinaldesi and A. Papatrou, “Spinning Test Particles in General Relativity II”, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 209, No. 1097 pp. 259-268 (1951) [20] G. W. Dixon, “Dynamics of Extended Bodies in General Relativity. III. Equations of Motion ”, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 277, No. 1264 (Aug. 29, 1974), pp. 59-119

216 | P a g e

ENTANGLEMENT AND CHAMELEON ACCELERATION

Glen A. Robertson GAResearch, LLC, Madison, AL 35757 Corresponding author, [email protected]

New Frontiers in Space Propulsion Science is a growing science, but has been progressing slowly over the last half century partly due to the difference between Einstein Physics and Quantum Physics, and more so to the incapability of propulsion engineers to understand both. To help resolve these differences, a modified form of Chameleon Cosmology, referred to in this paper as Chameleon Acceleration, was developed in an attempt to bring non-classical propulsion concepts into focus for engineers. However, Chameleon Acceleration still lacked a real connection between Einstein Physics and Quantum Physics even though the base model of Chameleon Cosmology crosses both. To further this along, this paper draws entanglement into Chameleon Cosmology and Chameleon Acceleration through the work of Leonard Susskind, who lays the foundation that entanglement is the bridge between Einstein Physics and Quantum Physics. Follow this, a rendition of Chameleon Acceleration is discussed. Keywords: interstellar travel, space propulsion, Chameleon acceleration

1. Introduction Since indulging in the aspects of Space Propulsion Science, I have had a hard time seeing how Einstein Relativity (ER) and its sub-theories could ever lead to the engineering of a real space drive. From my prospective, ER can only tell one that space drives are possible within the understanding of the Universe (i.e., things on a big scale) with little focus back to us mundane humans (i.e., things on a smaller scale). In recent years, there has been a focus to bring the large scale of Newtonian gravity (where today’s propulsion lives) down to the smaller scale of quantum gravity (where future propulsion theories are arising). However, little (if any) engineering progress has been made.

A big step toward bridging ER to the quantum nature of things may have been done by Leonard Susskind. In his paper, “Copenhagen vs Everett, Teleportation, and ER=EPR,” Susskind [1] provides a means to connect Quantum mechanics to Einstein Relativity and its sub-theories through a kind of non-locality called Einstein-Podolsky-Rosen (EPR) entanglement. “EPR does not violate causality, but it is, nevertheless, a form of non-locality. It is most clearly seen if one imagines trying to simulate quantum mechanics on a system of classical computers. By assuming the computers are distributed throughout space and represent local degrees of freedom. The whole conglomeration is required to behave as if there were quantum systems inside the computers; systems that local observers can “observe" by pushing buttons and reading outputs. The computers will of course have to interact with each other, as they also would if we were simulating classical physics. But simulating classical physics only requires the computers to interact with their local neighbors.” Susskind [1] Susskind’s idea of entanglement may one day represent a neat way to bridge Newtonian gravity to quantum gravity through ER. However, when dealing with space drive theories, it may be better to indulge in the concept of coupled entanglement, for as stated above “simulating classical physics only requires the computers (i.e., space drive) to interact with their local neighbors (i.e., external environment).” Therefore, only theories that provide a measure of coupling to the local external environment should be considered for developing into space drive theories.

217 | P a g e

This does not mean that old theories should be thrown out. For example, space drive concepts dealing with the quantum theory known as zero-point energy (ZPE) may better be presented with the ZPE propulsion theory including coupled entanglement by adding a coupling factor into the ZPE propulsion equations. That is, the coupling factor represents the amount of coupling a ZPE propulsion system has to the enormous amount of ZPE energy in the Universe by only considering the coupled entanglement amount in the neighboring or local external environment about the ZPE propulsion system. In other words, ZPE propulsion theories and other space drive theories have not consider entanglement to the local environment, whereby they represent a coupling factor = 1 (i.e., complete entanglement to the local ZPE environment) when it may be much-much smaller (i.e., << 1). That is, by using the concept of coupled entanglement, disagreements between ER and quantum theory could be solved by applying coupling factors in ER, related to the degree of coupled entanglement to the local environment, to solve both mathematical and experimental discrepancies with quantum physics.

Although, using the concept of coupled entanglement to the local environment may bring about many modified or new theories and models, there is one new model develop from a new theory called Chameleon Cosmology [2, 3] that represents a starting point. This new model will be hereafter referred to as Chameleon Acceleration and is a correlation of references [4-9]. Chameleon Acceleration generally presents a new acceleration model aimed at providing new directions in Space Propulsion Science.

2. Entanglement: Chameleon Cosmology and Chameleon Acceleration Chameleon Cosmology [2, 3] was developed from a Lagrangian where matter fields couple to a metric related to an Einstein-frame metric by conformal transformation, and represents an approach that ties the energy in the Universe to its density environment. The changes in the density environment across the Universe provides numerous neighboring or local entanglement systems, each being in a coupled entanglement to its surrounding neighborhood of other density environment systems. Chameleon Cosmology represents a small subtractive change to the gravitational force on an object related to the local density environment, having coupling factors that are introduced as dimensionless constants. These coupling factors provide a means for considering the amount of coupled entanglement across local density environments.

The change to gravity under Chameleon Cosmology [2, 3] is mediated by a thin-shell mechanism that is represented by a thin-shell thickness that exist about all objects. Given that a density environment is an object whether composed of solid matter, a gas, a liquid, a plasma, mass equivalent energy in empty space, etc., or a combination, then the thin-shell is a subsystem between local density environments throughout the universe. And given that, “The universe is filed with subsystems, any one of which can play the role of observer. There is no place in the laws of quantum mechanics for wave function collapse; the only thing that happens is that the overall wave function evolves unitarily and becomes more and more entangled. The universe is an immensely complicated network of entangled subsystems, and only in some approximation can we single out a particular subsystem as the OBSERVER.” Susskind [1] the thin-shell in Chameleon Cosmology is an OBSERVER and effectively represents a localized subsystem governed by quantum mechanics to provide a quantum entanglement process, called the thin-shell mechanism, between an object’s internal density environment and its external density environment. Such that, the observer, i.e., the thin-shell reacts using a quantum entanglement process to increase or decrease the thin-shell’s thickness when changes occur in either the object’s internal or external density environments to maintain entanglement.

218 | P a g e

It is noted that the thin-shell mechanism in Chameleon Cosmology has already been brought into the realm of quantum physics by its relationship to the Casimir force [10], where the thin-shell between to plates (objects) effectively acts like the bridge that draws the spatially distant points (densities of the plates) close to one another. In other words, once the two approaching plates have attained a specific close distance, the two-object density environment, having independent thin-shells, changes to a one object density environment, having a single thin-shell. Whereby to conserve energy in the single thin-shell about both plates, the plates are driven together to form a single object with a single density environment.

In reference to Susskind [1], the thin-shell mechanism in Chameleon Cosmology effectively acts like the bridge between “folded space” in order to draw spatially distant points (density environments) close to one another and is basically the short black line in Susskind’s figure 2 and the two density environments are the two red dots. “The two red dots are maximally entangled particles and I indicate their entanglement by linking them by a short black line. The black link has some structure; for example, it distinguishes between the various maximally entangled Bell states.” Susskind [1]  The Bell states are a concept in quantum information science and represent the simplest examples of entanglement. An EPR pair is a pair of qubits (or quantum bits) which are in a Bell state together, that is, entangled with each other. Unlike classical phenomena such as the nuclear, electromagnetic, and gravitational fields, entanglement is invariant under distance of separation and is not subject to relativistic limitations such as the speed of light (though the no-communication theorem prevents this behavior being used to transmit information faster than light, which would violate causality). (From Wikipedia) General Relativity also has its non-local features. In particular, there are solutions to Einstein's equations in which a pair of arbitrarily distant black holes are connected by a wormhole or Einstein- Rosen bridge (ERB). The thin-shell in Chameleon Acceleration [4-10] effectively acts like a wormhole or Einstein-Rosen bridge (ERB) (see reference [6]) connecting density environments and is basically the ERB in Susskind’s figure 3 [1] and the “folded spaces” are density environments. “At first sight, it would seem that ERBs can be used to superluminally transmit signals. But this is not so; the wormhole solutions of general relativity are “non-traversible.” (Non- traversibility means that two observers just outside the black holes cannot communicate through the ERB. Non-traversibility does allow them to jump in and meet in the ERB.) The similarity between figures 2 and 3 is quite intentional. The punchline of the ER=EPR joke is that in some sense the phenomena of Einstein-Rosen bridges and Einstein-Podolsky-Rosen entanglement are really the same: ER=EPR.” Susskind [1] In the context of thin-shells in Chameleon Cosmology as observers, the above means that two thin- shells about two density environments at large distances (i.e., non-local density environments) cannot transmit information about changes in their density environment instantaneously to one another, but two thin-shells that meet adjacently (i.e., local density environments) can as the separation between their thin-shells begin to merge as is the case with the Casimir effect, previously mentioned.

In the context of Chameleon Acceleration, Newton’s cradle is a good example, in which a first moving ball collides with four others to stop while only the fifth ball is accelerated. That is, the momentum in the thin-shell of the first moving ball is transferred through the adjacent/merged thin- shells of each ball to be passed to the fifth ball, which is accelerated by virtue of the group of five ball’s entanglement to the first and fifth ball’s thin-shell. Whereby, the fifth ball’s thin-shell is accelerated and effectively drags the fifth ball with it.

Susskind further states:

219 | P a g e

“This is a remarkable claim whose impact has yet to be appreciated. There are two views of what it means, one modest and one more ambitious. The ambitious view is that some future conception of quantum geometry will even allow us to think of two entangled spins – a Bell pair – as being connected by a Planckian wormhole. The modest view first of all says that black holes connected by ERBs are entangled and also the converse; entangled black holes are connected by ERBs. But there is more to it than that. The idea can be stated in terms of entanglement being a “fungible resource.” Entanglement is a resource because it is useful for carrying out certain communication tasks such as teleportation. It is fungible because like energy, which comes in different forms – electrical, mechanical, chemical, etc. – entanglement also comes in many forms which can be transformed into one another. Energy is conserved but entanglement is not, except under special circumstances. If two systems are distantly separated so that they can't interact, then the entanglement between them is conserved under independent local unitary transformations. Thus, if Alice and Bob, who are far from one another, are each in control of two halves of an entangled system, the unitary manipulations they do on their own shares cannot change the entanglement entropy. If Alice's system interacts with a nearby environment, the entanglement with Bob's system can be transferred to the environment, but as long as the environment stays on Alice's side and does not interact with Bob's system, the entanglement will be conserved.” Susskind [1] From the viewpoint of Chameleon Cosmology, let Alice's system be the thin-shell about an object and let Bob's system be the external density environment to the object. Then let the environment in Alice's system be the object’s internal density environment, whereby changes to the object’s internal density environment stays on Alice's side, whereby entanglement and energy between the object’s internal and external density environments are conserved.

From the viewpoint of Susskind, the thin-shell acts as a mediator (i.e., ERB) to conserve energy and as a mediator (i.e., EPR) to conserve entanglement between density environments. This basically entails that all objects whether stationary (as in Chameleon Cosmology) or moving (as in Chameleon Acceleration) reside within the fundamental constitutes of the “so called exotic energy” (i.e., the energy of the thin-shell) needed in specific solutions of general relativity. For example, as an object moves, the thin-shell thickness (exotic energy) changes around the object, first in similarity to “Warp Drive” models and overtime in similarity to “Wormhole” models. Whereby, an object produces exotic energy in similarity to “Warp Drive” models to move at any speed, and never has to cross an event horizon in similarity to “Wormhole” models as the event horizons forms in the aft and forward wakes of the thin-shell contraction and expansion (see reference [6]).

This viewpoint infers that only a means to change an object’s internal density environment is needed for developing new Space Drives. The references [4-9] has already established the foundation for this, outside the concept of entanglement, and the remaining sections are presented as a rendition of these references with periodic reference to entanglement.

3. Chameleon Cosmology: Planck Normalization and Gravity Given that the thin-shell mechanism in Chameleon Cosmology is a quantum entanglement process between an object and its density environments mediated by a thin-shell about the object, then there must be a strong relationship between the thin-shell thickness and the Planck scale, but as a cosmology model a universe presence should be maintained. This is easily seen in the thin-shell equation given per references [4-9] as

1 3 1 3 M 2 2M 4 42  8 mm   RR E Pl  2 pp, (1) cc      cR c  00 3 8 l p  m c  8  

220 | P a g e

3 where the subscript c infers any type of object, c 34mR c c is the object’s density with mass mc and radius Rc , and 0 is the external atmospheric density, which represents the surrounding

8 local universe density environment. The reduce Planck mass MmPl p 8 ( mp 2.176 10 kg )

2 41 and the factor MlEp8 to give ME 1 . 37 10 m to coincide with the energy scale associated with dark energy causing cosmic acceleration, see the comment below equation (11) in reference [3], where  1.m 19  1052 2 is the cosmological constant to give a universe present and 35 lmp 1.616 10 is the Planck length.

The strong Planck scale relationship is then made by defining the following parts of equation (1) as follows:

 2 Rc RRcc - a Plank length lp normalization of the object’s radius Rc with respect to a llpp

cosmological constant  normalization of the object’s radius Rc , where the cosmological constant bridges the object’s radius to ER and the Planck length bridges the object’s radius to Quantum physics, which infers the object’s entanglement across the large universe scale and the small Planck scale.

mc - a Planck mass mp normalization of the object’s mass mc , which infers the thin-shell’s mp entanglement to the object’s internal density environment at the Planck scale.

00m 31  3 - a Planck mass mp normalization of the object’s external atmospheric mp m p4 R c

environment mass m0 with respect to a length factor  Rc , the object’s radius, where the Planck mass normalization infers the thin-shell’s entanglement to the object’s external atmospheric density environment, and where the length factor infers the thin-shell entanglement to both local density environments, i.e., the object’s internal and external density environments. 3.1 Planck Scale Normalization of Gravity Planck mass normalization is then a means to evaluate the Human scale to the Planck scale. As example, the effect of quantum gravity is thought to present itself at the Planck scale. As will later be shown (see equation (20)), the Human Factor of the acceleration of gravity gc is connected to forces related to an object’s thin-shell. Therefore, an object’s acceleration of gravity must be a Planck acceleration a p normalization proportional to the objects thin-shell, given as

4 13 gMc 2 2 Pl   MRE    c c ; (2) aRpc  0  using equation (1), where the Planck acceleration

l p a p  2 (3) t p

221 | P a g e and  is a geometric factor for corrections between the scale geometries, t p is the Planck time, and where the universe and local external environment effects are nulled from the thin-shell

2413 thickness by the product MME2 Pl 0  , as neither of which are known to have any great effect on an object’s acceleration of gravity.

Since the Human factor of gravitational acceleration gc is being normalized by the Planck acceleration ap , then the Human scale product ccR needs to be normalized to the Planck scale as well, i.e., so let

gR   c c c , (4)    alp p  p  where the Planck density

mp  p  3 , (5) lp or by rewriting equation (4), the acceleration of gravity is given by

a gRp . (6) c c c  ppl It is shown that the gravitational constant

l33   l  l 1  a G p    p  p    p , (7) 22      mp t p   m p  t p  l p   p l p whereby combining equations (6) and (7) yields

gc G c R c . (8) To convert the cubic geometry of the Planck density to the spherical geometry of the mass’s 3 density c 34mR c c , let  43, which yields equation (8) as

Gmc gc  2 , (9) Rc which is an object’s acceleration of gravity, such that equations (2-9) demonstrate that the acceleration of gravity is a Planck scale normalization.

4. Chameleon Cosmology in a Mini-Universe

In Chameleon Cosmology, the thin-shell thickness Rc is static as the object’s density c , radius Rc

, and the external atmospheric density 0 are taken to be constant. From a static thin-shell thickness point of view and in a mini universe containing a single object, equation (1) can be rewritten as

13 2 4 M E 2M Pl Ri , (10) R  ii 0i

222 | P a g e where i  0,1,2,3,... is the incremental places outward from the object. Then let the incremental densities be given as

3 mi i  3 , (11) 4 Ri and let the incremental distances be given as

Ric R ixmin (12) where xmin is the minimum change length to the incremental distance, noting that at i  0 , RR0  c k , and where the incremental mass m m c2 , the object’s mass m plus the sum of ic k c i0 equivalent mass of the energy  in the incremental thin-shells. k

Equations (10 – 12) then tells us that at every distance ixmin from the object in this mini universe, a thin-shell thickness Ri can be defined that remains homogeneous about the object. Therefore, from equations (9) with ci , the object’s acceleration of gravity remains homogeneous about the object at every incremental change ixmin in the radius, as is known.

Then given that the mini universe started out with an initial radius R equal to the object’s initial Uint radius R with initial mass m , where over time the object lost mass by conversion to energy in cint cint the thin-shells and by virtue of the concentric thin-shells throughout the entire mini universe, the object is in entanglement to the mini Universe. That is, any change in the object’s density is reflexed across every concentric thin-shells throughout the entire mini universe in order to maintain the initial mass equivalent energy to that of the initial object’s mass . This is not to say that change occurs across the thin-shells in the mini universe instantaneously.

At the Planck scale, the minimum change length xlmin  p , the Planck length, and the minimum time that change can be applied is t p , the Planck time. Therefore, the fastest speed of change that can be propagation across the thin-shells is lpp t c , the speed of light. This sets the fastest acceleration of

2 change across the thin-shells at the Planck acceleration ap l p t p c t p .  It is noted that it is the Planck scale that sets the universe speed limit to the speed of light. Therefore, one would think that to go faster than the speed of light ones needs to first establish a different scale. Then normalize to that scale and establish the scale parameters at that scale that allow for faster than light. Such scales can be referred to as dimensions. I.E., the speed of light sets the maximum speed of the Human scale, only because the Planck dimension is the normalization scale humans (i.e., Einstein) have currently chosen to use.

5. Entanglement and Chameleon Acceleration In our universe, there are many objects present, which require the geometry of the concentric thin- shells throughout the entire universe to be a bit inhomogeneous or be redefined in like to the Casimir effect between to plates as previously mentioned. Further, example is a galaxy, wherein locally each piece (stars, planets, and etc.) in it has a homogeneous thin-shell out to a point where

223 | P a g e the thin-shell interactions become a bit inhomogeneous, but remain entangled to allow the galaxy to have a homogeneous thin-shell.

Given that inhomogeneous thin-shells are allowed in our universe, then inhomogeneous entanglement must also exist. Therefore, when an object moves, the entanglement of the thin-shell between the object and its external environment is allowed to be inhomogeneous about the object. That is, in response to the movement of an object, a change occurs in the homogeneous entanglement about the object to cause change to the thin-shell thickness in the plane of movement. Then by virtue of equation (1), a change in the thin-shell thickness must produce a change in either the object’s density, the external density or both. A change in an object’s density environment is warranted by the fact that the observer of the entanglement is the object’s thin- shell, which must change with movement of the object to maintain the entanglement and conserve energy.

When an object’s motion is caused by the object, the universe and local external environment

2413 effects, given by MME2 Pl 0  in equation (1), must be nulled, similarly to what was done for gravity in equation (2). Nulling this product leaves only the product ccR , the objects density environment, and therefore infers that the objects density environment must change to cause change to the thin-shell thickness, or vice versa, a change to an object’s thin-shell infers a change to the objects density environment.

Given that observable changes to an object’s density environment from movement is not known to happen. The position is taken that the object’s density environment is defined by a density field  c that changes with movement, but is at a scale too small to be seen by humans, e.g., the Planck scale. Therefore, the outer perimeter of the density field was chosen to be the outer perimeter of the thin- shell; containing the object’s density, which establishes the object’s acceleration of gravity per equations (2-9), and the energy density in the thin-shell, which changes under non-gravity accelerations. Whereby, changes to the geometry of an object’s density field is most entirely a result of changes to the thin-shell. Therefore, the expression “changes in the thin-shell” or some similarity infers changes to an object’s density field geometry.

5.1 Acceleration Chameleon-Force Given that non-gravity accelerations produce a non-homogeneous thin-shell about an object, a simple Planck normalization process cannot be done. The proper analysis for non-gravity accelerations has been done under references [4-9] even though the model was developed without respect to entanglement. The following is a rendition from references [4-9] with some small changes for clarity and is referred to here as Chameleon Acceleration. I.E., the reference Chameleon Acceleration refers to non-gravity accelerations.

Under Chameleon Acceleration, a non-gravitational force or Acceleration Chameleon-force F that  a gives rise to a non-gravity acceleration or Chameleon-acceleration a on any object of mass m , is  c c given in form to the Chameleon Cosmology equation (20) in reference [2] as  Famma   acca c , (13) M Pl

224 | P a g e where  is the acceleration a coupling factor of the object’s thin-shell, and the acceleration a   scalar field gradient a is the change in the sum of the scalar field gradient of the thin-shell change due to the object’s acceleration. The acceleration coupling factor is given from references [4-9] as

12 13 M 2 2M 4 E Pl , (14)    a  apR  l R  0 a a a where  is referred to as the motion coupling factor,  is the object’s acceleration density field a a and R is the spherical radius approximation of the object’s acceleration density field  . The a a factors and R will be discussed later under the section 5.2. The acceleration coupling factor a of equation (14) then infers that the object’s thin-shell entanglement is to both the object’s accelerated density field and the external density 0 .

 The motion coupling factor is hard to define without knowing the object’s acceleration. Therefore, a different method was developed that removes the need to know the acceleration coupling factor . This method is discussed in section 6.

For simplicity, it is taken that the object is moving in a linear direction in a gravitational field from a large object of mass M and radius RM , such that, the change in the sum of the acceleration scalar field gradient a about the object is directly related to the change in the object’s thin-shell R R thicknesses  c left (opposition to the motion) and  c right (in the direction of motion). Whereby, the changes to the thin-shell perpendicular to the motion and therefore the gradients thereof are zero.

The left and right change to the acceleration scalar field gradient in the direction of motion is given from the Chameleon Cosmology equation (19) in reference [2] as  RR    1 ccleftMMˆˆ  1  3  left a    3;       left 44MRRMRR22 Pl  c M  Pl  c  c (15)  RR    1 ccrightMMˆˆ  1  3  right a   3.      right 44MRRMRR22 Pl  c M  Pl  c  c  It is noted that there may be multiple nearby gravitational sources to include the object’s. Here only the dominate local nearby gravitational field of the large object of mass M is taken into account in this paper. In other analysis’s, the multiple nearby gravitational fields may need to be accounted for by performing a vector sum of the accelerations of gravity on the object to 2 estimate the ratio MRM . In the far universe away from large objects, the dominate local nearby gravitational field is that of the object. I.E., as an object moves through the universe, the gravitational field on the object will change, but is never zero. This fact may account for spacecraft flight anomalies outside our solar system. Equation (15) yields the acceleration scalar field gradient as

225 | P a g e

 RR    31 ccright left M  ˆ a   a    a  =       right left 4 MRRR2 Pl  c c  c  , (16) 31 R M    a   ˆ 4 MRR2 Pl a  c  where R is an estimation of the object’s thin-shell thickness change in the direction of motion, a given by

R RRcc   a  right left ’ (17) RRR a cc and where the object’s thin-shell thickness change is given in similarity to equation (1) as

13 2 4 M E 2M Pl R . (18) a R cc0

12 As is done in ref. [2, 3], MPl m p 8  c 8  G   8  G , which sets the factors c 1 to give the Acceleration Chameleon-force units of newtons, which allows equation (16) to be rewritten as

RR GM   ccˆˆ a 66MPl   M Pl   g M  . (19) RRR 2   cc c  

2 where gMm GM R the estimated magnitude of the local gravity field, which can be used to perform the vector sum of the acceleration of gravities (mentioned earlier) when there are multiple nearby gravitational sources.

Combining equation (19) back with equation (13) gives the Acceleration Chameleon-force as

RR    Fa66aa m gˆˆ    W  m , (20)  aaaRR c M   c c c aa    where Wc m c g M is the estimated local gravitational weight of the object. Equation (20) then asserts that the Acceleration Chameleon-force is entangled to the object’s acceleration density field  and the external density  through the coupling factors  . a 0 a

5.2 Acceleration Density Field Cases An object’s acceleration density field  is due to accelerations within the outer perimeter of the a thin-shell about the object, where the outer perimeter of the thin-shell changes due to acceleration of the object’s mass as a whole or of particulates in the object when the sum total of the particulate accelerations does not sum to zero. That is, an object has a thin-shell by fact that there exist particulate accelerations in the object with sums not equal to zero in the opposite direction of gravity, but is uniform in all directions from the center of the object so as not to cause any motion to the object. Whereby, an object’s acceleration density field is approximately equal the object’s density only when the object is not moving or when the sum total of the particulate accelerations in the object does not change the object’s normally uniform thin-shell to cause motion. (Noting that

226 | P a g e the term particulate is generic and can be any matter composing the object that is free to move under applied forces without destroying the object.)

Three cases of object mass accelerations are identified in this paper, but others exist. It is hoped that these three cases will help to understand other cases. Each of the three mass acceleration cases infers a different acceleration density field  as follows. a Case 1.

For an object of total mass mc and density c , having accelerated particulates k of mass mmkc with particulate acceleration aa0 in the direction of motion, i.e., the total mass of the object k c is accelerated as a whole, i.e., the object’s acceleration a a a , such that, the density of the k c accelerated particulates in the object is the object’s density c (e.g., a ballistic object, such as a baseball in motion), the acceleration density field  and the estimated acceleration spherical radius a R is given as a

1 aa 3 mc 33    c    c  RR  1   c . (21) aag4 R3 g MM a   Case 2.

For an object of total mass mc and density c , having accelerated particulates of mass mmkc with particulate acceleration aa0 in the direction of motion, where the Chameleon- k c acceleration aa the acceleration of the object, such that the accelerated particulates in the c object has a density kc , the acceleration density field and the estimated acceleration spherical radius is given as

1  ak 3 m c33  a k  m k  c    k  RR 1    c , (22) aag4 R3  g m M a   M  c

3 where the accelerated particulate’s density k 34mR k c . Case 3.

For an object of mass m with a Chameleon-acceleration a  0 , that is a result of exhausted mass c c m m m having an exhaust mass acceleration a a a , the acceleration of the object, k ex c ex c there are two density fields to consider. The change in the density field of the object, due to the loss of the exhausted mass mex through an initial exit radius or throat radius RT , is given by 3 mm  c ex c 3 (23) 4 RT and the addition of a new acceleration density field  due to the acceleration and expansion of a the exhausted mass , given by

227 | P a g e

amex3 ex    ex  , (24) a ex gR4 3 M ex where R is the estimated spherical radius at maximum expansion  R of the exhausted mass m ex T ex , which occurs at the aft extent of the object’s thin-shell as the exhausted mass leaves the acceleration density field  of the object. The exhaust mass density is given by a

3 FT ex  2 , (25) 4 AvT ex

2 where FT is the force on the exhausted mass at the throat over throat area ARTT  and vex is the exit velocity of the exhausted mass .

The two density fields  and  are treated as two adjoining, but separated density fields. c ex

6. Chameleon-Acceleration As An Accelerated Mass Phasing Using equation (20) to determine the Chameleon Acceleration on an object can be quite complex, e.g., see reference [8]. To simplify the Acceleration Chameleon-force equation, it was shown in 2 reference [8] that the thin-shell thickness Rc G l p R c , where G is the coupling factor to the local gravitation sources, which is calculated by combining with the gravitational source form of equation (1) to give

12 13 M 2 2M 4 E Pl G   (26)  R l R  G G p G 0 and represents an entanglement to both the density G of the local gravitation source and the external density 0 .

Then let the acceleration thin-shell thickness change

R 2 l R ; (27) aaGp noting that an object’s acceleration does not change the coupling to the local gravitation source.

Now let the coupling factor product

2    , (28) a G  3 where  is an arbitrary factor that will divide out later, and let

1 a 13  c   , (29) 6 gM where  is referred to as the object’s phase factor, to be discussed later in the section 6.1.

Now noting that equation (28) yields

228 | P a g e

13  1  13 (30)  2  a G  and equation (29) yields

13  g  6 M , (31)  a c which when combined yields

a 1 c   13  . (32) 2 6  gM  a G  Then noting that by combining equation (27) with equation (20) yields the Acceleration Chameleon- force as  lp Fa62  m gˆ m , (33)  aa GR c M c c a which yields

a l c  62 p , (34) gRa G M a and when combined with equation (32) yields  l R R . (35) p aa13 24  a G  Now combining equation (35) back with equation (27) yields the acceleration thin-shell thickness as

13  2 RR G . (36) aa 2 a  Given that the coupling factors  of equation (26) and  of equation (14) have similar form, G a 22 the ratio G a in equation (36) nulls the universe and local external environment effects by 13 the product MM242  . However, since the change in the thin-shell thickness R is a E Pl 0  a factor of the local external environment, it is asserted that the phase factor  is also. This will be discussed in the next section.

6.1 Phase Factor

The phase factor  is defined for any object having accelerated particulates k as

time rate of change of the density field dt    , (37) time rate of change of the accelerated mass dtk where the factor  was added to account for the local external environment.

229 | P a g e

The time changes are generally defined as

R R dta ; dt c , (38)  vvk a k where v is the velocity at which the acceleration density field  is changing and v is the a a k average velocity of the accelerated particulates k in the object.

Now given that the universe is an object, accelerations of objects within the universe change the universe’s density field, per equation (22) of case 2 in section 5.2 – that is all objects in the universe are entangled to the universe’s density field. Therefore, the time change factors dt and dtk must be normalized to the universe’s density field; so, let

Universe normalization of dt dtk  m U , (39) Universe normalization of dt dt  U which yields the phase factor of equation (37) as

dt dtk   U . (40) dt dt U k

6.2 Chameleon Acceleration Now combining equations (28) with equation (33) yields the Chameleon-acceleration as

3   1 ˆ a  6lgpM  , (41) c  R a which when combined with equation (29) yields the Chameleon-acceleration as

12    3 a  6 g ˆ , (42)  c M 1 lp  R a eliminating the coupling factors and presented a new acceleration equation for non-gravity accelerations.

6.2.1 Chameleon Acceleration Cases The Chameleon-acceleration of equation (42) was found to be of different form for each of the three acceleration density field cases discussed in the section 5.2 and there are likely to be others. The Chameleon-acceleration forms for the three cases in the section 5.2 are as follows, and reviewed in reverse order to allow a better understanding of the phase factor change between each case.

Case 3: Equation (42) for case 3 in section 5.2, where an object has particulate accelerations with mass ejection, was found to take the form

230 | P a g e

12    3 a  6 g ˆ , (43)  c M 11 lpl  RR T e x where the change in the object’s field density  and the acceleration density field  is c ex represented by the factors R and R . T ex

For an object with internal particulate mass mmk ex being accelerated and exhausted from the object’s acceleration density field, it was found that the time changes

dt dt , (44) UUk which results from the fact that the force on the exhausted mass mex is equivalent to the force on the thrusting object, whereby the net acceleration effects on the universe’s density field is near zero. I.E., the universe sees them as equal object going in opposite direction to give a net change to the universe’s density field of zero; requiring no normalization to the universe’s density field.

The time rate of change of the accelerated mass mmk ex is given by

Rmaccexhausted mass flow rate ex dtk    . (45) vacc exhausted mass m ex Then using equations (40) and (45) with dt dt , the density field case 3 phase factor is given by UUk

dt RRvm   exacc  ex ex . (46) 3 dt v R v m k exacc ex ex A density field case 3 example is done in appendix A1.

Case 2: Equation (42) was found to hold for equation (22) of case 2 in section 5.2, where an object has particulate accelerations with no mass ejection, only when the accelerated particulates k are captured. This however leads to the exhaustion of particulates to accelerate in the direction of motion (FWD), much like a rocket motor using up its propellant. However, if one allows the internal accelerated mass to relax back (BWD) into the object for future re-acceleration, then equation (42) takes the form

1 2 1 2 RR    a  633FWD ggˆˆ 6  BWD  . (47)  c FWDll  M  BWD  M pp     It is noted that the phases , may be equal and the radial factors RR, may be FWD BWD FWD BWD equal, resulting in a net acceleration on the object of zero. This is more than likely the reason why the case 2 type of Chameleon-acceleration has not been readily utilized, but this is not always the case and will lead to new acceleration devices.

231 | P a g e

The case 2 phase factor was found (from calculation and testing) to be given as

 1 dt dt  k , (48) 2  M2 d R M d dt   M R dt  k E k c Ek  k E c k where dk is the distance that the internal particulates k move in the object and the factors  , k are geometric factors due to changes in the universe and local scales. The universe energy scale constant M E provides a universe normalization of the distance factors dRkc, .

Equation (48) then implies that the universe time normalizations, for an object with internal particulate accelerations with no mass ejection, are

1 dt M d dt; dt dt . (49) UU E k  k k kMR E c A density field case 2 example is done in appendix A2.

Case 1: Equation (42) was found to hold for equation (21) of case 1 in section 5.2, where the object is ballistic (i.e., a projectile – baseball, cannonball, or etc.) with no internal particulate accelerations and no mass ejection. For a ballistic object, one would assume that the phase factor of equation (48) would apply. However, the object’s accelerated mass mmkc the mass of the entire object, whereby the factor dk is undefinable. So, we let

   , (50) kMd E k where from equation (47) the universe time normalizations are

 1 dt dt; dt dt ; (51) UUkk k kMR E i to give the density field case 1 phase factor from equation (48) as

1 1  ; (52) MREk noting that the factor  must be defined for the object under study.

A density field case 1 example is done in appendix A3.

7. Conservation of Energy In physics, the law of conservation of energy states that the total energy of an isolated system remains constant, that is, it is conserved over time. Energy can neither be created nor destroyed; rather, it transforms from one form to another. For instance, chemical energy can be converted to kinetic energy in the explosion of a stick of dynamite. A consequence of the law of conservation of

232 | P a g e energy is that a perpetual motion machine of the first kind cannot exist. That is to say, no system without an external energy supply can deliver an unlimited amount of energy to its surroundings.

Another way to express conservation of energy is

11tt ii . (53) where 1 is the total energy in one system delivered to a second system i over time t1 and iit is the sum of the energies i per times ti received by the second system.

Under Chameleon Acceleration, kinetic energy  c imparted to an object (e.g. baseball hit by bat) is converted to a field energy  in the thin-shell over a time dt . Also, kinetic energy k from accelerated mass mk in the object (e.g., propellant flow in a nozzle) can also be converted to a field energy  in the thin-shell over a time dt . Noting that in some cases mmkc , where ck . Whereby for energy to be conserved between the accelerated mass k and the acceleration density field  , a

kdt k   dt   loss dt loss (54) where loss is the energy lost in conversion over time dtloss .

If none or very little energy is lost, i.e., kkdt  dt , then

 dt k   , (55)  dtk which is part of the phase factor  of equation (37), whereby implying that conservation of energy is taken into account in Chameleon Acceleration. That is, energy is conserved between the accelerated mass mk of an object and the resulting change to the object’s thin-shell. And given that the object and the object’s thin-shell are separate systems, the object can transfer a limited amount of energy to its thin-shell without violating conservation of energy; noting that energy is neither lost nor gained within the accelerated density field, unless energy is radiated out of the thin-shell as a loss or into the thin-shell from an external source as a gain.

8. Conservation of Momentum in Quantum Mechanics

The energy  in the thin-shell of an object of mass mc is taken to be governed by quantum mechanics with the energy conversion occurring at the speed of light, whereby the change in momentum in the acceleration density field is a relativistic momentum. That is, the object’s thin- shell thickness changes and therefore the object’s density field changes in a quantum mechanical relativistic manner, even though the object is moving slower than the speed of light.

In quantum mechanics, for both massive and massless objects, relativistic momentum p is related to a phase constant  , which carries units of m-1, by

p   . (56)

The momentum carried by the object’s acceleration thin-shell R must be equal to the a momentum carried by the object, so in term of Chameleon Acceleration

233 | P a g e

p  m v  m a dt , (57) cc c c k where vc is the velocity imparted to the object over the accelerated particulate time dtk . Then with

lp m p c l p m p a p t p , the phase

11m a  dt    ma dt ck  c    , (58) ck c      mp  a p  t p  l p  is shown to be a Planck scale normalization with respect to the Planck length, whereby the momentum in the thin-shell

a dt  p  mc c k (59) c    atpp   is the object’s mass times a Planck scale normalization with respect to the speed of light. That is, although the acceleration density field  can change at the speed of light, the velocity of the object a is

a dt  v   c k c ; (60) c    atpp   a Planck scale normalization with respect to the speed of light.

9. Engineering Light Speed Equation (60) tells us that an object’s velocity is the speed of light when

a dt a t c . (61) c k p p Such that, equations (42) and equation (61) establishes the parameters toward engineering light speed space drive concepts.

For example, for a spacecraft of estimated spherical radius Rc and density c having a space drive with the non-mass exhausting systems of case 2 (section 5.2 and 6.21), to develop the space drive acceleration mechanism requires only knowing the accelerated particulate mass mk , travel distance dk and time of travel dtk (FWD >> BWD). From these parameters, the phase factor  and estimated acceleration radius R can be determined. The only problem is in establishing the correct a space drive concept to deliver these parameters so that the FWD Chameleon-acceleration a c dt with a BWD Chameleon-acceleration near zero. c k

Although, hopefully other forms of the Chameleon-acceleration equation (42) my lead to different space drive concepts not having the BWD Chameleon-acceleration limitation.

234 | P a g e

Conclusions Chameleon Cosmology and Chameleon Acceleration are discussed in terms of coupled entanglement, which establishes the thin-shell about objects as an observer acting to changes in the density field of an object to conserve energy, momentum, and entanglement between the object and the universe at the local density environment of the universe.

A compilation of several papers toward the development of Chameleon Acceleration with added entanglement connections and with additional results from recent calculation and experiments is also presented. The recent results give a clearer picture of the phase factor used in the Chameleon Acceleration model toward the understanding of past, current and future space drive concepts.

It is noted that the equations for Chameleon-acceleration presented in this paper seem complete, it is suspected that different types of accelerated particulates may require different normalization factors. As such the phase factor would change and would greatly affect the calculated Acceleration Chameleon-force. For example, particulates closer to the Planck scale may require an inverse normalization to the Planck mass or Planck length, both of which could reduce the phase by many orders of magnitudes.

References 1. L. Susskind, “Copenhagen vs Everett, Teleportation, and ER=EPR,” arXiv:1604.02589 v2 [hep-th], 23 Apr. 2016. 2. J. Khoury and A. Weltman, “Chameleon Cosmology,” arXiv: 0309411v2 [astro-ph], 1 Dec. 2003 and Phys. Rev. D, 69, (2004), p. 044026. 3. J. Khoury and A. Weltman, “Chameleon Fields: Awaiting Surprises for Tests of Gravity in Space” arXiv: 0309300v3 [astro-ph], 9 Sept. 2004 and Phys. Rev. Lett., 93, (2004), p. 171104. 4. G. A. Robertson, “Experimental Applications of Chameleon Cosmology,” in: Proceedings of the Estes Park Advanced Propulsion Workshop, Eds. H. Fearn and L. Williams (Space Studies Institute Press, Mojave, CA, 2017), pp. 183 – 196; and in: Scheduled Technical Proceedings of the Estes Park Advanced Propulsion Workshop 2016, Eds. H. Fearn and L. Williams, Konfluence Press, Manitou Springs, Colorado, 2017, pp. 239 – 259. 5. G. A. Robertson, “Propulsion Physics under the Changing Density Field Model,” JANNAF, 2012 and presented at the Advanced Space Propulsion Workshop 2012. 6. G. A. Robertson and M. J. Pinheiro, “Vortex Formation in the Wake of Dark Matter Propulsion,” Physics Procedia, Volume 20, Elsevier Science, 2011. 7. G. A. Robertson, “The Chameleon Solid Rocket Propulsion Model,” in these proceedings of Space, Propulsion & Energy Sciences International Forum (SPESIF-10), edited by Glen A. Robertson, AIP Conference Proceedings, CP1208, Melville, New York, (2010). 8. G. A. Robertson, “Engineering Dynamics of a Scalar Universe, Part II: Time-Varying Density Model & Propulsion,” Lecture Series paper in these proceedings of Space, Propulsion & Energy Sciences International Forum (SPESIF-09), edited by Glen A. Robertson, AIP Conference Proceedings, CP1103, Melville, New York, (2009). 9. G. A. Robertson, “Engineering Dynamics of a Scalar Universe, Part I: Theory & Static Density Models,” Lecture Series paper in these proceeding of Space, Propulsion & Energy Sciences International Forum, edited by Glen A. Robertson, AIP Conference Proceedings, CP1103, Melville, New York, (2009). 10. A. Almasi, P. Brax, D. Iannuzzi and R. I. P. Sedmik, “Force sensor for chameleon and Casimir force experiments with parallel-plate configuration,” arXiv:1505.01763v1 [physics.ins-det], 7 May 2015.

235 | P a g e

Appendix: Examples A1. Rocket Motor

For a rocket motor, the thrust can be given by T mr  m ex a  m BO a , where mr is the initial mass of the rocket, mex is the exhausted mass from the rocket, mBO m r m ex is the rocket’s mass at propellant burnout, and a is the rocket’s acceleration at propellant burnout. However, the case 3 Chameleon-acceleration equation (43) can also be used.

For example, the data from example 2-1 in the book “Rocket Propulsion Elements” by Sutton and Ross (1976) converted to metric units as follows:

mex  31.75 kg m10.58 kg s

vex  2355.49 m s TN2.49 104 (Thrust of rocket at propellant burn out)

WNBO  578.74 (Rocket weight at propellant burn out)

2 and for the earth, the acceleration of gravity g  9.81 m s , so the burnout mass of the rocket is mBO W BO g 59 kg to give the rocket’s acceleration a T mBO 422 m s .

The Sutton and Ross example appears to be a Sidewinder, AMRAM or Similar Small Missile, where it is surmised that the radii

r0.0128 m R Throat T r0.0508 m  R  0.0508 2  0.0718 m nozzle ex where rThroat is the estimated throat radius and rnozzle is the estimated nozzle exit radius, the factor of 2 is needed to account for the exhausted mass leaving the density field of the rocket, which is beyond the nozzle exit.

Using equation (46) gives the rocket’s phase factor as R ex m 5 r  1.02  10 . vmex ex

35 Then given the parameters above and the Planck length lmp 1.6 10 , equation (43) gives the rocket r acceleration as

12    3 a6 g 421.9 m s r  . 11 l  p RR T ex which is the same as given by .  It is noted that the Chameleon-acceleration calculated above for the rocket was sensitive to the 4th or 5th decimal place in both radii, which indicates that throat and nozzle erosion can

236 | P a g e

greatly effect a rocket’s acceleration, which is the case for rockets and is not obvious using

the rocket form T mBO a .

A2. Pulsed Actuator

The fact that in the rocket motor example, the exhausted mass mex attains an acceleration density field due to it being accelerated indicates that any object having linear mass accelerations within it must have a change in it density field, whereby a change in an object’s density field infers a Chameleon-acceleration be imparted to the object. Noting that reversal of the linear mass accelerations will subtract and can give a null result.

To verify this, we consider a magnetically attracted armature of mass mmk arm moving a distance ddk arm in an actuator () act having an electromagnetic of mass mem for a total actuator mass mact m em m arm . The armature is a part of the actuator system and cannot leave it. Therefore, the armatures acceleration must impart a Chameleon-acceleration a to the actuator system in the act direction of the armature movement.

As example, an actuator, having a radius Rmact  0.0191 , a magnetic armature of mass marm  0.1093 kg and electromagnet of mass mem  0.1167 kg for a total actuator mass mact  0.226 kg , was tested. The armature moved a distance dmarm  0.0013 over time 22 dtarm  0.0025 s to give the armature acceleration aarm d arm dt arm 208 m s .

Given that the forward and backward movement of the armature gives identical results to effectively null-out the Chameleon-force, only the forward Chameleon-acceleration is calculated.

The forward direction spherical estimated acceleration radius is given from equation (22) as

13 am   R1 arm arm R  0.0085 m . FWD    act gm act  and the forward direction phase factor using equation (48) with  k  8   is calculated as

1 5 FWD  2   1.24  10  8 ME d arm R act to give the forward direction Chameleon-acceleration from equation (47) with  1.0256 as

12 R a6 32act g 404.34 m s FWD actl N p for a net forward direction Acceleration Chameleon-force given as

F m  m a  91.38 N 20.54 lbs FWD  act arm    , where the values and were adjusted to match the Acceleration Chameleon- force from the actuator test. Noting that these values are within normal reasoning. The actuator used in these test is of the form described in US patent publication 2012/0175974 dated July 12, 2012 by the author. This actuator has an armature with two movable outer pole pieces firmly attached by a non-magnetic shaft through the center of a two-pole permanent

237 | P a g e electromagnet to alternating attract the outer pole pieces. The actuator was firmly attached to a load cell and free to move on a sliding surface. The two-pole permanent electromagnet has two coils to independently control which outer pole piece to attract.

Fig. 1 shows the force traces from the load cell measurements taken during the test of the actuator. The solid line represents one direction of the armature caused by one outer pole attraction, and the dotted line represents the second direction of the armature movement caused by attraction of the second outer pole. The movement of the armature produces both a thrust T due to part of the armature mass moving away from the electromagnet and an Acceleration Chameleon-force (CF) F opposite to the direction of thrust in the direction of the armature movement. At the end of armature movement, the armature impacts the electromagnet to produce an impact force FI . The slight differences are attributed to changes between the coils and the resistance of the non- magnetic shaft.

Figure 1. Load cell measurements from actuator test. In reference to figure 1, the “Thrust Starts” position indicates the start of armature movement, the “End of Thrust & CF” position indicates the end of armature movement, and the “End of Impulse” indicates the end of the force caused by the impact of the attracted pole piece to the electromagnet plus the residual Acceleration Chameleon-force (CF) caused by the movement of the armature, which occurs during the thrust.

Each force trace in Fig. 1 can be defined as the FT 12.5 lbs during movement of the armature and FFTI (  )  20.5 lbs after the end of movement of the armature, such that the net force after movement of the armature is given by FI 12.5 lbs ~ 20.5 lbs , which implies that the impact

238 | P a g e force FI ~ 8 lbs . Given that that the thrust TF~ I the impact force, the acceleration Chameleon- force F  20.5 lbs , which is very close to what was calculated from the Chameleon-acceleration equation.

2  It is noted that the armature acceleration aarm  208 m s with mass marm  0.1093 kg indicates the thrust and impact force would be on the order of  22.73 N . However, the actuator is losing and gaining an equal amount of mass. Therefore, one would think that the thrust be zero and the Chameleon-force just be the impact force. This however does not explain the force traces in Fig.1.

A3. Ballistic Object

3 Let an object near the earth of mass m100 kg and density m  3000kg m be hit with a force

FNF98200  . Neglecting other forces, Newton tells us that the acceleration is given as a F m982 m s2 . Now given the spherical approximation of the object’s radius as

13 3 m Rmm 0.2 ; 4m

41 then the phase factor, using equation (52) with ME 1 . 14 10 m and  8 , is 1   1.7575  105 . 8 MREm From equation (21) with the Chameleon-acceleration aa , the object’s acceleration and ag m  , the earth acceleration of gravity, then

13 g R R0.043 m m a m m to give the Chameleon-acceleration from equation (42) as

12 R a6 32m g 982 m s , m l M p which is the same as given by Newton’s equation F ma , given  8 .

239 | P a g e

TESTS OF FUNDAMENTAL PHYSICS IN INTERSTELLAR FLIGHT

Roman Ya. Kezerashvili

New York City College of Technology, City University of New York, Brooklyn, USA Email: [email protected]

We have considered general relativity (GR) effects related to the curved spacetime and frame dragging on long range trajectories of solar sails. Results prove that small deviations in the initial trajectories of solar sails that are deployed near the Sun can translate to large effects in the long run. It is shown that the Poynting–Robertson effect dominates over other special relativistic effects and decreases the cruising velocity as well as the Heliocentric distance. It is demonstrated that if a solar sailcraft can be used to test fundamental physics related to GR – particularly, the deflections of escape trajectories as the result of the curvature of spacetime and frame dragging in the vicinity of the Sun – then the most interesting orbits are those that are closer to the Sun.

1. Introduction There are different ways for testing fundamental physics: the use of specific scientific instruments on board a spacecraft, tracking the motion of a spacecraft, or a combination of these two approaches. Tracking an interplanetary or interstellar spacecraft is a significant technique for testing the laws of physics and exploring interplanetary or interstellar environments. Nevertheless, adding some instruments, such as an accelerometer on board, could provide orbit determination experts and physicists with further data of great interest: the values of the non-gravitational acceleration acting on the spacecraft, i.e. the deviation of the spacecraft from geodesic motion [1]. In particular, the analysis of spacecraft trajectories for missions where anomalies were already detected - or could be revealed in the future, may provide data related to unknown gravitational and non-gravitational effects. For interstellar missions, we are facing two main conceptual problems: i) how to provide the highest speed to propel a spacecraft to the nearest stars; ii) how to navigate and communicate with the spacecraft. Solar sails have long been considered for an interstellar travel (see Refs. in [2]) and may eventually be applied to interstellar exploration. For such missions, when a solar sail approaches very close to the sun, the effects of curved spacetime in the region near the Sun should be considered. While a solar sail in an escape trajectory is close to the sun for only a short time, perturbations to its motion during this period, when the outward acceleration due to the solar sail propelled is the greatest, can translate into dramatic effects on long-range trajectories. In the general relativistic framework, objects tend to follow geodesics on curved spacetime. However, the Sun emits electromagnetic radiation and one can say that objects move in the photo- gravitational field of the Sun. It is of relevance to analyze how the escape trajectories of a solar sail deviate from geodesics due to the electromagnetic radiation of the sun [3]. It is especially interesting to consider the cases when the solar radiation pressure (SRP) can enhance the relative importance of various general relativistic effects and therefore make them more readily observable. Moreover, solar sail dynamics may display an enhancement of potential anomalies compared with conventional satellite dynamics, which could be detected in the future and may be related to unknown gravitational effects. In that context, the general relativistic equations which describe the motion of a solar sail within the curved spacetime close to the Sun are worked out. Thus, for example, the observation and study of the trajectories of a solar sail could potentially provide tests of various effects associated with general relativity (GR). One can say that fundamental physics may be carried out as a passenger activity on space science missions performed by a solar sail.

240 | P a g e

The roadmap to interstellar flight considers a mission to the heliopause [5,6] and the Sun’s gravitational focus [7-10] as the first stops on the interstellar journey to the nearest star system - the Centauri A/B and Proxima Centauri system. The heliopause represents the outer edge of the solar system and forms a termination shock between the heliosphere and the interstellar medium. According to Einstein’s general theory of relativity, gravitation induces refractive properties on spacetime, causing the sun to act as a lens by bending photon trajectories and collecting them in the Sun’s gravitational focus. Responding to an increasing demand for navigational accuracy [9], we consider general relativistic effects related to space-time curvature and frame dragging as well as Poynting–Robertson effect [11,12] on the escape trajectories of solar sails. There are, of course, many other factors that influence the sail simultaneously and are not considered in this paper. We have specifically considered a number of effects on the escape trajectories of solar sails that are associated with general relativity. We would like to emphasize that these are extremely small effects which can be masked by other features such as the gravitational forces of planets and the fact that the sun is not a point like source of radiation. Nevertheless, in order to provide a description of the solar sail dynamics as accurate as possible, all of these factors and more should be taken into account. Moreover, given that solar sail dynamics shows a relative enhancement of various effects compared to the dynamics of conventional satellites, anomalies due to unknown gravitational effects may be rendered more pronounceable and possibly detectable. The purpose of this paper is to show how small general relativistic effects can be relatively enhanced through solar radiation pressure and longtime duration, and to demonstrate that the Poynting–Robertson effect diminishes the cruising velocity, which has a cumulative effect on the escape distances. The paper is organized in the following way. In Section 2 we present the orbital equations in the exterior spacetime of the sun described by the Kerr metric [13], and also taking into account the solar radiation pressure for GR effects for escape heliocentric trajectories. The description of the Poynting–Robertson effect and orbital equations for a solar sail that include this effect are presented in Sec. 3. The summary of the results and calculations and their discussion are presented in Sec. 4. The conclusions follow in Sec. 5.

2. Orbital Equations in the Exterior Spacetime of the Sun General relativity can have a significant impact on the long-range escape trajectories of a spacecraft. In contrast with the conventional spacecraft, a solar sail deployed near the sun experiences significantly much stronger the effect of solar radiation pressure. The curved spacetime and frame dragging, in conjunction with solar radiation pressure, affects the trajectory of a spacecraft. Specifically, on escape trajectories for a solar sail, for which GR effects and the solar radiation pressure should be considered simultaneously [14]. Let’s focus on the orbital mechanics of a solar sail when it is deployed at the closest approach to the Sun as depicted in Fig. 1. In this figure we distinguish escape trajectory in classical Newtonian dynamics, special relativity with Newtonian gravity and GR. Three different approaches give different escape trajectories. Einstein’s general theory of relativity allows to consider the effect of spacetime curvature and frame dragging due to the slow rotation of the Sun that deflect a solar sail from a Newtonian trajectory and a trajectory that includes special relativistic kinematics.

241 | P a g e

Fig. 1. Escape trajectory in Newtonian theory of gravity, special relativity with Newtonian gravity and general relativity.

The geometry of spacetime in the vicinity of the slowly rotating Sun is described up to linear order in the angular momentum J of the sun by the large-distance limit of the Kerr metric [13], and can be given in spherical coordinates (푟, 휃, 휙) as follows:

4퐺퐽 푑푟2 2퐺푀 푑푠2 = −푓푐2푑푡2 − 푠𝑖푛2휃푑푡푑휙 + + 푟2(푑휃2 + 푠𝑖푛2휃푑휙2), 푓 = 1 − , (1) 푐2푟 푓 푐2푟 where t is time as measured by a distant static observer. When the angular momentum J = 0, this metric reduces to the Schwarzschild metric, which describes the exterior spacetime of a spherical and non-rotating sun. Due to the second term in the metric (1), the rotating sun should exhibit frame dragging—a prediction of GR. To maximize frame dragging effect let us consider the trajectories of the spacecraft that lie within the equatorial plane of the sun. By introducing 푥휇 = (푡, 푟, 휃, 휙) and taking into account 휃 = 휋/2 one can write the 4-momentum of the solar sail as 푝휇 = 푚푑푥휇/푑휏, where is the proper time measured in the frame of reference of the solar sail. For the component of 푝휇 we have:

푚퐸 4퐺푚퐽퐿 푚퐿 2퐺푚퐽퐸 푑푟 푝푡 = − ; 푝휃 = 0, 푝휙 = + , 푝푟 = 푚 (2) 푐2푓 푐4푓푟3 푟2 푐4푓푟3 푑휏 and the constants of motion 퐸 ≡ −푝푡/푚 and 퐿 ≡ 푝휙/푚 are the energy and angular momentum per mass m of the solar sail. Therefore, 푝2 = −푚2푐2 in the absence of the SRP yields

푑푟 퐸2 퐿2 4퐺퐽퐸퐿 ( )2 = − (푐2 + ) 푓 − . (3) 푑휏 푐2 푟2 푐4푟3

One can obtain the radial component of the 4-acceleration by differentiating (3) with respect to τ:

푑2푟 퐺푀 퐿2 3퐺(푐2푀퐿2−2퐽퐸퐿) 푎푟 = + − + , (4) 푑휏2 푟2 푟3 푐4푟4 where M is the mass of the Sun. Eq. (4) describes the motion of the solar sail in the absence of the SRP and is orbital equation in the exterior spacetime of the sun. Now one can include the effect of the SRP and consider the motion of the solar sail in the photo-gravitational field of the sun. The acceleration due to the SRP is given by the same expression as in the Newtonian approximation [2]

휅 휂퐿 푎푟 = , where 휅 = 푠 . (5) 푟2 2휋푐휎

In (5) 푐 = 3 × 108 푚/푠 is the speed of light, σ is the mass per area of the solar sail, which is a key 26 design parameter that determines the solar sail performance, LS = 3.842 × 10 W is the solar luminosity and the coefficient η represents the efficiency of the solar sail used to account for the

242 | P a g e imperfect reflectivity of the sail. Equating the expressions for ar given in (4) and (5), taking the first integral and the φ equation in (2), we finally find the orbital equation 퐸2 퐿2 휅 4퐺퐽퐸퐿 2 −(푐2+ )푓− − 푑푟 푐2 푟2 푟2 푐4푟3 6 2 ( ) = 퐸 푟 푓 . (6) 푑휙 (퐿푓푟−2퐽 )2 푐2 Eq. (6) describes the motion of the solar sail in the photo-gravitational field of the Sun that simultaneously includes the effects of the curved spacetime, frame dragging and the SRP. Therefore, the curved spacetime and frame dragging, in conjunction with solar radiation pressure, affects the trajectory of a sailcraft. In Eq. (6) the angular momentum L per unit mass is a conserved quantity assuming that the force due to the SRP is in the radial direction, while the energy E per unit mass is not a conserved quantity because the sun is transferring energy to the solar sail via the SRP. For example, considering the relation between the proper time interval and the coordinate time interval for the spacetime curvature, assuming J = 0, then one gets 휅 1/2 2퐺(푀− ) 2 2 2 −1/2 2 퐺 퐿 퐿 = 푣0푟0(푓0 − 푣0 /푐 ) , 퐸 = 푐 (푐 − + 2 푓0) , 푟0 푟0 (7) where 푣0 is a speed of the sailcraft at a perihelion 푟0 and 푓0 is the value of 푓 at the perihelion 푟 = 푟0.

3. Escape Trajectories and Poynting-Robertson Effect The absorbed portion of the radiation induces a drag force on the solar sail, thereby diminishing its transversal speed relative to the Sun. The aforementioned drag force is relatively small, nevertheless it can have a long-term cumulative effect on the trajectories of solar sails. This force is related to the Poynting–Robertson effect, which was first investigated for small spherical particles by Poynting [11]. Although it is now realized that this is a special relativistic effect [12] associated with the finite speed of light, Poynting’s paper was actually published a year before Einstein’s paper on special relativity. For simplicity let’s consider a solar sail whose surface is directly facing the Sun and whose motion is restricted to lie within the heliocentric plane. It is obvious that the force due to the SRP is directed radially outwards. However, as a special relativistic effect, the solar radiation has a nonzero transversal component in the frame of reference of the solar sail. This is due to the relative transversal speed 푣휙 = 푟푑휙/푑푡 between the solar sail and the Sun. Therefore, the portion of electromagnetic radiation specularly reflected by the solar sail leads to a radially outwards acceleration, whereas the portion of light absorbed leads to an acceleration directed at an angle with respect to the radial direction. Note that the Poynting–Robertson effect occurs at order v/c, and dominates over other special relativistic effects which are at order (v/c)2. Up to linear order in 푣휙/푐 ≪ 1, the orbital equations which take into account the Poynting–Robertson effect is [15]

푑2푟 퐺푀−휂휅cos2훼 푑휙2 푑 푑휙 (1−휂)휅sinα cos 훼 + − 푟 = 0, (푟2 ) + = 0. (7) 푑푡2 푟2 푑푡 푑푡 푑푡 푟

Solution of the system of Eq. (7) allows to find the speed of the solar sail and demonstrate that the Poynting–Robertson effect decreases its orbital speed.

4. Results In Ref. [16] it was recently suggested to provide the highest speed to propel a spacecraft for extrasolar space exploration taking advantage of space environmental effects, such as solar radiation heating, to accelerate a solar sail coated by materials that undergo thermal desorption at a particular temperature. Three different scenarios, which only differ in the way the sail approaches the Sun, were analyzed and compared. Two more preferable of these scenarios are the following: i. Hohmann transfer plus thermal desorption. In this scenario the sail would be carried as a payload to

243 | P a g e the perihelion with a conventional propulsion system by a Hohmann transfer from Earth’s orbit to an orbit very close to the Sun and then be deployed there. ii. Elliptical transfer plus Slingshot plus thermal desorption. In this scenario the transfer occurs from Earth’s orbit to Jupiter’s orbit. A Jupiter’s fly-by leads to the orbit close to the Sun, where the sail is deployed. The speed reached at the perihelion 푟0 = 0.1 퐴푈 is 푣0 = 316 푚/푠 and 푣0 = 321 푚/푠 for the first and second scenarios, respectively, that corresponds to about 푣0 = 67 AU/year and 푣0 = 69 AU/year. In terms of cruise speed and distance covered per year, the best scenario is always the second one that takes advantage of a profitable planetary flyby. In fact, the cruise speed of 69 AU per year makes it possible to reach a distance of 200 AU within about 3 years, the sun's gravity focus at 547 AU within about 8 years, while to reach the edge of Oort Cloud at 2500 AU it would take about 37 years. For comparison the Voyager 1 spacecraft launched in 1977 with the cruise speed of 17 km/s (3.57 AU/year), finally leaving the solar system after 37 years of flight, traveled 139 AU, while the Voyager 2 is currently in the outermost layer of the heliosphere - in the "Heliosheath" and traveled about 115 AU. In order to reach true interstellar space beyond at about 150 AU the Voyager 1 needs 3 more year. Using these data as initial conditions, we calculated below the deflections of solar sails trajectory from the Newtonian one. The deflection of the trajectory can be find by calculating 푑 = 푅(휑 − 휑푁), where R is the heliocentric distance and 휑 is the angular position of the solar sail as a function of R and 휑푁 is the angular position in Newtonian approximation. We can find the angular position 휑(푅) by integrating Eq. (6) using the perturbation techniques and restricting ourselves by the terms of the first order with respect of J. As a result one obtains 2 2 3 푅 푑푟 2퐺퐸퐽 1 1 퐿 퐿 퐿 ̃ 1 1 2 푓0 푓 휑(푅) ≈ 퐿 ∫ 2 [1 + 4 ( − + 3 − 3 − 4)], ℎ = 2퐺푀 ( − ) + 퐿 ( 3 − 2). 푟0 푟 √ℎ 푐 퐿 푓푟 푓0푟0 ℎ푟 ℎ푟0 퐸푣0푟0 푟 푟0 푟0 푟 (8)

The angular position within the Newtonian gravity is

2 2 −1 푣0 푟0 1 1 휑푁(푅) = 푐표푠 [1 − ( − )]. 퐺푀̃ 푟 푟0 (9)

In Eqs. (8) and (9) 푀̃ = 푀 − 휂퐿푆/(2휋푐휎퐺) is the effective mass of the Sun. Results of calculations of the deflection d of the trajectories are shown in Fig. 2. The discrepancy in the location as predicted by special relativity versus Newtonian mechanics and general relativity versus Newtonian mechanics for v0 = 321 km/s at r0 = 0.1 AU - that are the initial conditions for the second scenario – are shown. Fig. 2 shows the discrepancy in the location due to the spacetime curvature when in (8) 퐽 = 0 obtained by a numerical integration of φ versus R. The deflection due to frame dragging for the 42 2 3 angular momentum of the Sun 퐽 = 10 kg m /s increases to about 1.5 × 10 kilometers. The direction of the deflection depends on whether the solar sail is in a prograde or retrograde orbit relative to the rotation of the sun. GR predicts that the solar sail will undergo a larger deflection than does the Newtonian mechanics.

244 | P a g e

Fig. 2. The discrepancy in the location as predicted by special relativity versus Newtonian mechanics and general relativity versus Newtonian mechanics for the initial condition of the scenario 풗ퟎ = ퟑퟐퟏ 퐤퐦/ 퐬 퐚퐭 풓ퟎ = ퟎ. ퟏ 퐀퐔

Fig. 3. The discrepancy d in the location of a solar sail versus the heliocentric distance R for the following sets of initial conditions: 풗ퟎ = ퟑퟏퟔ 퐤퐦/퐬 퐚퐭 풓ퟎ = ퟎ. ퟏ 퐀퐔 (the first scenario), 풗ퟎ = ퟑퟐퟏ 퐤퐦/퐬 퐚퐭 풓ퟎ = ퟎ. ퟏ 퐀퐔 (the second scenario), 풗ퟎ = ퟒퟐퟎ 퐤퐦/퐬 퐚퐭 풓ퟎ = ퟎ. ퟎퟏ 퐀퐔.

Fig. 4. The decrease in speed ∆풗 due to the Poynting–Robertson effect during the first day of voyage for the following sets of initial conditions: the second scenario 풗ퟎ = ퟑퟐퟏ 퐤퐦/퐬 퐚퐭 풓ퟎ = ퟎ. ퟏ 퐀퐔 (dashed line) and 풗ퟎ = ퟒퟐퟎ 퐤퐦/퐬 퐚퐭 풓ퟎ = ퟎ. ퟎퟏ 퐀퐔 (solid line).

Fig. 5. The decrease in Heliocentric distance ∆풓 as a result of the Poynting–Robertson effect versus the duration of the voyage for the following sets of initial conditions: the second scenario 풗ퟎ = ퟑퟐퟏ 퐤퐦/ 퐬 퐚퐭 풓ퟎ = ퟎ. ퟏ 퐀퐔 (dashed line) and 풗ퟎ = ퟒퟐퟎ 퐤퐦/퐬 퐚퐭 풓ퟎ = ퟎ. ퟎퟏ 퐀퐔 (solid line).

245 | P a g e

As shown in Fig. 3, the discrepancy d in the location of a solar sail dramatically increases for closer 5 flybys, approaching as much as about 9 × 10 kilometers for a solar sail deployed at r0 = 0.1 AU by using the first and the second scenarios traveling to R = 2550 AU. For a solar sail deployed at r0 = 0.01 AU with v0 = 420 km/s, the deflection increases to a million kilometers. Here we consider that the solar sail is deployed at perihelion distances as small as 0.01–0.1 AU, as this may be feasible for solar sails in the near future. In Ref. [17] it was presented a trajectory design for a solar probe,, which includes repeated pole-to-pole Sun flybys at a perihelion of four solar radii.

In order to demonstrate the Poynting–Robertson effect we solve the orbital equations (7) by taking the value for the effective mass per area = 1 g/푚2 and 휂 = 0.9 is used to account for the imperfect reflectivity of the sail. Most of the acceleration of the solar sail takes place during the first day after it has been deployed and the most of the deflection of the solar sail occurs when it is in the vicinity of the sun. We will refer to the difference in the speed between a trajectory with and without the Poynting–Robertson effect as ∆푣. Similarly, ∆푟 is taken to be the difference between the heliocentric distance of the trajectory of the solar sail with and without the Poynting–Robertson effect. In Fig. 4, we show the evolution of ∆푣 during the first day of the voyage for two sets of initial conditions. The Poynting–Robertson effect decreases the speed of the solar sail relative to what it would have been if this effect was not present. For a solar sail deployed at 0.1 AU throughout almost all of the voyage, the speed is about ∆푣~4 푚/푠 less than what it would have been in the absence of this effect and if it is deployed at 0.01 AU the speed is about ∆푣~27 푚/푠 less. This drag force has a cumulative effect on the heliocentric distance. In order to further illustrate this point in Fig. 5 we present results of calculations for the decrease ∆푟 in heliocentric distance. One can see that the Poynting–Robertson effect decreases the Heliocentric distance after a 35-year voyage by an amount 7 6 of ∆푟~3 × 10 kilometers and ∆푟~5 × 10 kilometers when it deployed with the speed 푣0 = 321 km/s at 푟0 = 0.1 AU and speed 푣0 = 420 km/s at 푟0 = 0.01 AU, respectively.

Conclusions We have considered GR effects related to the curved spacetime and frame dragging on long range trajectories of solar sails. Small deviations in the initial trajectories of solar sails that are deployed near the Sun can translate to large effects in the long run. This deflection is primarily due to the curvature of spacetime near the sun, while the kinematic effects of special relativity contribute to a lesser degree. Frame dragging due to the slow rotation of the Sun can result in a deflection, but this effect after a 35-year voyage is about 103 less than the one related to the curved spacetime. The Poynting–Robertson effect occurs at order 푣/푐 and thereby dominates over other special relativistic effects. For escape interstellar trajectories, this effect decreases the cruising velocity as well as the heliocentric distance. If the solar sailcraft can be used to test fundamental physics related to GR–particularly, the deflections of escape trajectories as the result of the curvature of spacetime and frame dragging in the vicinity of the Sun–then the most interesting orbits are those that are closer to the Sun. However, in this case the Poynting–Robertson effect is important as well and should be taken into consideration. Responding to an increasing demand for navigational accuracy [9] we demonstrated that consideration of GR effects as well as Poynting–Robertson do have an impact on the escape interstellar trajectories of solar sails.

References [1] J.D. Anderson, P.A. Laing, E.L. Lau, et al., Study of the anomalous acceleration of Pioneer 10 and 11, Phys. Rev. D 65, 082004/ 1-50, 2002. [2] C.R. McInnes, Solar Sailing. Technology, Dynamics and Mission Applications, Springer, Praxis Publishing, 1998, p. 296.

246 | P a g e

[3] R. Ya. Kezerashvili and J. F. Vazquez-Poritz, Can solar sails be used to test fundamental physics? Acta Astronautica 83, 54-64, 2013. [4] A. Lyngvi, P. Falkner, S. Kemble, M. Leipold, A. Peacock, The interstellar heliopause probe, Acta Astronautica 57, 104 – 111 (2005). [5] M. Leipold, H. Fichtner, B. Heber, P. Groepper, S. Lascar, F. Burger, M. Eiden, T. Niederstadt, C. Sickinger, L. Herbeck, B. Dachwald,W. Seboldt, Heliopause Explorer—a sailcraft mission to the outer boundaries of the solar system, Acta Astronautica 59, 785 – 796 (2006). [6] V. R. Eshleman, Gravitational lens of the sun: its potential for observations and communications over interstellar distances, Science 205, 1133 (1979). [7] J. Heidmann, C. Maccone, Acta Astronautica 32, 409-410 (1994). [8] S. G. Turyshev and B-G. Andersson, The 550-au Mission: a critical discussion, Mon. Not. R. Astron. Soc. 341, 577-582 (2003). [9] C. Maccone C. The Sun as a gravitational lens: proposed space missions, 3rd ed., IPI Press, Boulder Colorado, 2003. [10] S. G. Turyshev, Wave-theoretical description of the solar gravitational lens, Physical Review D 95, 084041 (2017). [11] J.H. Poynting, Radiation in the solar system: its effect on temperature and its pressure on small bodies, Philos. Trans. R. Soc. A 202, 525–552 (1904). [12] H.P. Robertson, Dynamical effects of radiation in the solar system, Monthly Notices of the Royal Astronomical Society 97, 423–438 (1937). [13] R.P. Kerr, Phys. Rev. Lett. 11, 237–238 (1963). [14] R. Ya. Kezerashvili and J. F. Vazquez-Poritz, Escape trajectories of solar sails and general relativity. Phys. Lett. B 681, 387–390, 2009. [15] R.Ya. Kezerashvili, J.F. Vazquez-Poritz, Drag force on solar sails due to absorption of solar radiation, Advances in Space Research 48, 1778–1784 (2011). [16] E. Ancona, R.Ya. Kezerashvili, Orbital dynamics of a solar sail accelerated by thermal desorption of coatings, arXiv:1609.03131v1, 2016; Proceedings of 67th International Astronautical Congress (IAC 2016), Guadalajara, Mexico, 26-30 September 2016. Paper IAC-16-C1.6.7.32480. [17] Y. Guo, R.W. Farquhar, Current mission design of the solar probe mission, Acta Astronautica 55, 211–219 (2004).

247 | P a g e

BREAKTHROUGH PROPULSION CAPABILITY DEVELOPMENT STRATEGY

Ronald J. Litchford Principal Technologist for Propulsion, NASA/STMD – HQ Space Mission Directorate Presented at CUNY City Tech, New York, USA, 13 – 15 June 2017

Author discussed NASA Space Technology; investment flow down, maturation and infusion, development lifecycle, mega-drivers. Also discussed Vision missions and timelines in regards to Cis- Lunar and Mars (HSF 2050), Alpha Centauri probe (interstellar 2069), Outer Solar System (HSF 2100), Habitable Exoplanet (Interstellar 2100). Discussed vision mission case studies; define quantifiable propulsion capability needs and assess advanced propulsion technology landscape. Finally, the author discussed breakthrough propulsion capability development strategy; technology development framework and diversified propulsion R&T portfolio.

[No Abstract since last minute submission]

248 | P a g e

SELF-SUSTAINED TRAVERSABLE WORMHOLES AND CASIMIR ENERGY

Remo Garattini * Initiative for Interstellar Studies, The Bone Mill, New Street, Charfield, GL12 8ES, UK Department of Engineering and Applied Sciences, University of Bergamo, Bergamo, ITALY INFN Sez. di Milano, Milan, ITALY *E-mail: [email protected] In this contribution we review the concept of Self Sustained Traversable Wormholes. We consider configurations which are sustained by their own gravitational quantum fluctuations. The investigation is evaluated by means of a variational approach with Gaussian trial wave functionals to one loop. We interpret the graviton quantum fluctuations as a kind of Exotic Energy. Since these fluctuations usually produce Ultra-Violet divergences, a procedure to keep under control must be introduced. We will discuss two different procedures: firstly, a zeta function regularization is involved to handle with divergences and a renormalization process is introduced to obtain a finite one loop energy. Secondly, we consider the case of Distorted Gravity, namely when either Gravity’s Rainbow or a Noncommutative geometry is used as a tool to keep under control the Ultra-Violet divergences. In this context, it will be shown that for every framework, the self-sustained equation will produce a Wheeler wormhole, namely a wormhole of Planckian size. This means that, from the point of view of traversability, the wormhole will be traversable in principle, but not in practice. Some consequences on topology change are discussed together to the possibility of obtaining an enlarged wormhole radius.

1. Introduction Hendrik Casimir in 1948 [1], discovered the possibility to observe macroscopic forces associated to the energy fluctuations of the vacuum. This discovery was experimentally confirmed in the Philips laboratories [2] [3] and later by Lamoreaux [4]3. The Casimir effect is induced when the presence of electrical conductors distorts the zero point energy (ZPE) of the quantum electrodynamics vacuum. Two parallel conducting surfaces, in a vacuum environment, attract one another by a very weak force that varies inversely as the fourth power of the distance between them. This kind of energy is a pure quantum effect; no real particles are involved, only virtual ones. The difference between the stress-energy computed in presence and in absence of the plates with the same boundary conditions gives

It is evident that separately, each contribution coming from the summation over all possible resonance frequencies of the cavities is divergent and devoid of physical meaning but the difference between them in the two situations (with and without the plates) is well defined. In the nanometre regime the Casimir effect and other vacuum fluctuation induced forces can become significant or

3 See also [24] [25] [26] for further experimental investigations of the Casimir effect.

249 | P a g e even dominant. In particular, the Casimir force poses a challenge for constructing microelectromechanical systems (MEMS) [5], [6]. It causes effects such as stiction [7] [8], which is the permanent adhesion of two nano-structural elements. As we can see the Casimir effect is relevant in the microscopic world, so a legitimate question arises: in which way is it possible to connect the Casimir effect with traversable wormholes which are macroscopically huge? To answer this question we need to describe what a wormhole is. A wormhole can be represented by two asymptotically flat regions joined by a bridge: one example is represented by the Schwarzschild solution. One of the prerogatives of a wormhole is its ability to connect two distant points in space- time. In this amazing perspective, it is immediate to recognize the possibility of traveling crossing wormholes as a short-cut in space and time. Unfortunately, although there is no direct evidence, a Schwarzschild wormhole does not possess this property. It is for this reason that in a pioneering work [9] and subsequently [10] studied a class of wormholes termed traversable4. Unfortunately, the traversability is accompanied by unavoidable violations of null energy conditions, namely, the matter threading the wormhole's throat has to be exotic. Classical matter satisfies the usual energy conditions. Therefore, it is likely that wormholes must belong to the realm of semiclassical or perhaps a possible quantum theory of the gravitational field. Since a complete theory of quantum gravity is yet to come, it is important to approach this problem semiclassically. On this ground, Hochberg, Popov and Sushkov considered a self-consistent solution of the semiclassical Einstein equations corresponding to a Lorentzian wormhole coupled with a quantum scalar field [11]. On the other hand, Khusnutdinov and Sushkov fixed their attention to the computation of the ground state of a massive scalar field in a wormhole background. They tried to see if a self-consistent solution restricted to the energy component appears in this configuration [12]. Nevertheless, nothing forbids to consider gravitons instead of scalars and in particular, the quantum fluctuations generated by the wormhole itself. On this side, the idea that quantum fluctuations around a traversable wormhole background have been investigated. This investigation has led to the definition of Self Sustained Traversable Wormhole. (SSTW) A traversable wormhole is said to be “Self Sustained” if

푇푇 퐸0 = −퐸 (1)

푇푇 where 퐸 is the total regularized graviton one loop energy and 퐸0 is the classical term [13] [14]. The apex “TT” stands for Transverse-Traceless which is the feature that the tensor perturbation must have since the graviton is a spin-2 particle. This procedure is quite similar to computing the Casimir energy on a fixed background. Before going on we need to introduce some of the features of a traversable wormhole.

2. Traversable Wormholes In Schwarzschild coordinates, the traversable wormhole metric can be cast into the form 푑푟2 푑푠2 = − exp(−2휙(푟))푑푡2 + + 푟2푑Ω2 푏(푟) (2) 1 − 푟 where 휙(푟) is called the redshift function, while 푏(푟) is called the shape function and where 푑Ω2 = 푑휃2 + 푠𝑖푛2 휃 푑휙2 is the line element of the unit sphere. A proper radial distance can be related to the shape function by 푟 푑푟′ 푙(푟) = ± ∫ ′ 푟 √1 − 푏 (푟 )/푟′ 0 ± (3) where the plus (minus) sign is related to the upper (lower) part of the wormhole or universe. Two coordinate patches are required, each one covering the range [푟0,+∞). Each patch covers one

4 See also Ref. [27] for completeness.

250 | P a g e universe, and the two patches join at 푟0, the throat of the wormhole defined by 푟0 = 푚𝑖푛{푟(푙) }. Using the Einstein field equation

(4) in an orthonormal reference frame, we obtain the following set of equations

(5)

12br  b pr1   r   3 (6) 8G r r r and

(7)

in which 휌(푟) is the energy density, 푝푟(푟) is the radial pressure, and 푝푡(푟) is the lateral pressure and G is the Newton’s constant. Using the conservation of the stress-energy tensor, in the same orthonormal reference frame, we get

(8)

As a specific example we consider the Ellis wormhole defined by

2 푏(푟) = 푟0 /푟. (9)

For this special case, the line element (2) simply becomes

(10) while Eq.(3) simplifies into

(11)

The energy density, the radial pressure and the transverse pressure simplify into 1  r  ,  0  2 (12) 8Gr0

251 | P a g e

1 pr r  0  2 (13) 8Gr0 and 1 pr , t  0  2 (14) 8Gr0 where we have evaluated the components of the stress-energy tensor on the throat. As we can see, both 휌(푟) and 푝푟(푟) are negative and violate the Null Energy Conditions (NEC) which is a prerogative of the exotic matter. This means that 휌(푟) + 푝푟(푟) < 0. Of course different forms of the shape functions lead to the different expressions for the energy density which, in some cases, can even be positive. For example Lobo [15] [16], Kuhfittig [17] and Sushkov [18] have considered the possibility of sustaining the wormhole traversability with the help of phantom energy. To this purpose we need to introduce an equation of state (EoS) 푝푟(푟) = 휔휌(푟) with w ÎÂ. When 휔 < −1 we are in the phantom energy regime and 휌(푟) > 0. A rearrangement of Eqs.(5)-(8) leads to

 2 b 8 G r r (15) and b8 Gp r3 b r  b' r r  r , 2r22 1 b r / r 2 r 1 b r / r (16) where we have used the EoS and the Eq. (5). By imposing 휙′(푟) = 0, one finds the following solution for the shape function 1 푟0 휔 푏(푟) = 푟 ( ) . (17) 0 푟 ′ In order to satisfy the flare-out condition 푏 (푟0) < 1 and the asymptotic flatness 푏(푟)/푟 → ∞ when 푟 → ∞, we have to impose 휔 > 0 or 휔 < −1. The proper radial distance is related to the shape function by

(18) where the plus (minus) sign is related to the upper (lower) part of the wormhole or universe and where 2퐹1(푎, 푏, 푐; 푥) is a hypergeometric function. When 휔 = 1, one finds the Ellis wormhole. Of course it is always possible to generalize the EoS into an inhomogeneous EoS of the form 푝푟 = 휔(푟)휌. The corresponding shape function becomes

(19)

and solutions for the SSTW can be found as shown in Ref. [19], without fixing a specific form for 휔(푟). It is also immediate to generalize the inhomogeneous EoS to a polytropic EoS of the form 훾 푝푟 = 휔휌 , whose shape function is   1  1   1 8G  33 (20) b r  r00  1  r  r  .  

252 | P a g e

It is straightforward to see that the solution is not asymptotically flat. Indeed 푏(푟) ≅ 푟3, for 푟 → ∞, ∀훾, and therefore this case will be discarded. Fixing our attention on the Ellis wormhole and its generalization induced by the homogeneous and inhomogeneous EoS, in the next section we will explore how the self-sustained equation (1) works.

3. Self-Sustained Traversable Wormholes As advanced in the introduction, a SSTW is defined by Eq.(1) and in a sense, the equation governing quantum fluctuations behaves as a backreaction equation. The SSTW equation has its origin in perturbing the Einstein’s Field Equations. The classical term of Eq.(1) can be obtained with the calculation of the Hamiltonian density on the wormhole background. In practice, one gets

푔 0 3 푖푗 푘푙 √ 퐸 = ∫ 푑 푥 [(16휋퐺)퐺푖푗푘푙휋 휋 − 푅] Σ 16휋퐺

1 1 ∞ 푑푟푟2 푏′(푟) = − ∫ 푑3푥√푔푅 = − ∫ , 16휋퐺 Σ 2퐺 푟0 √1−푏(푟)/푟 푟2 (21)

푖푗 where 퐺푖푗푘푙 is the super-metric and 휋 is the super-momentum. Since the wormhole metric (2) is independent on time, only the curvature term is not vanishing, namely the kinetic term disappears. Note that the curvature is represented by the scalar curvature in three dimensions in terms of the shape function. Note also that boundary terms become important when one compares different configurations like Wormholes and Dark Stars [20] or Wormholes and Gravastars [21]. If 푏(푟) is represented by Eq.(9), then 휋푟0 퐸0 = (22) 2퐺 and the SSTW equation becomes r 0 ETT . (23) 2G

On the other hand, if 푏(푟) is represented by Eq.(17), then the SSTW equation is

r   1  퐸0 = AEA0  TT where  1 ,    1, (24)     3 G 1  22   where Γ(푥) is the gamma function. For the special value of 휔 = 1, one finds Eq.(23). Concerning the r.h.s. of Eq.(1), the general structure to one loop assumes the following form  1  2 2 2 112  2 E E m r dE  4 mr1     , (25)

 1  2 2 2 222  2 E E m r dE  4 m2 where we have considered the energy density instead of the total energy and where

253 | P a g e

 2 63br  1 m r 21   2 b r  3 b r  1 r r  22 r r   . (26)

 2 6br  3 3 m r 21   2 b r  3 b r  2 r r  22 r r 2 2 푚1(푟) and 푚2(푟) represent two 푟-dependent effective masses. It is clear that the integrals in Eq.(25) are divergent. The evaluation method for such integrals is equivalent to the scattering phase shift method and to the same method used to compute the entropy in the brick wall model. To keep under control the divergences a zeta function regularization method can be considered. Technical details can be found in Refs. [13] [14]. Note that this procedure is also equivalent to the subtraction procedure of the Casimir energy computation where ZPE in different backgrounds with the same asymptotic properties is involved. Here we report only the case in which 퐺0(휇0) is identified with the squared Planck length. Then the wormhole radius can be approximated by 105 1 449 2 1  420  2ln 2 Olp   5      r . 0  (27)  30 Ol1/ 2 0  12    p

As we can see, from the previous expression, the radius is divergent when 휔 → 0. At this stage, we cannot establish if this is a physical result or a failure of the scheme. When 휔 → ±∞, 푟0 approaches the value 1.16푙푃, while for 휔 = 1, we obtained 푟0 = 1.16푙푃. It is interesting to note that when 휔 → +∞, the shape function 푏(푟) in Eq. (17) approaches the Schwarzschild value, when we identify 푟0 with 2푀퐺. It is interesting to note that outside the phantom range we have wormhole solutions. This is not unexpected since the graviton quantum fluctuations play the role of the exotic matter. The positive 휔 sector seems to corroborate the Casimir process of the quantum fluctuations supporting the opening of the wormhole. Although a Regularization/Renormalization procedure is the standard technique to deal with UV divergences which normally appear in a Quantum Field Theory approach, it is interesting to consider what happens if a deformation of the space-time can alleviate or even cure this plague. Different proposal can be taken under consideration, namely a Non-commutative geometry approach, a Generalized Uncertainty Principle approach and last but not least Gravity’s Rainbow. In the next section we will introduce such a space-time deformation to see how the usual Regularization/Renormalization procedure can be avoided.

4. Gravity’s Rainbow Gravity's Rainbow is a distortion of the spacetime metric at energies comparable to the Planck scale. A general formalism for a curved spacetime was introduced in [22], where two unknown functions 푔1(퐸/퐸푃) and 푔2(퐸/퐸푃), denoted as the Rainbow's functions modify the basic line element (2). They have the following property

lim 푔1(퐸/퐸푃) = 1 and lim 푔2(퐸/퐸푃) (28) 퐸/퐸푃→0 퐸/퐸푃→0 = 1 and the line element (2) becomes

254 | P a g e

푒(−2휙(푟)) 푑푟2 푑푠2 = − 푑푡2 + 2( ) 푏(푟) (29) 푔1 퐸/퐸푃 2( ) (1 − 푟 ) 푔1 퐸/퐸푃 2 푟 2 + 2 푑Ω 푔1 (퐸/퐸푃)

The distorted wormhole background (22) comes into play at the classical level and also for the graviton one loop. To one loop, the SSTW equation becomes [19]

(30)

The integrals 퐼1 and 퐼2 are defined as

(31)

and

(32)

∗ respectively. 퐸 is the value which annihilates the argument of the root. In 퐼1 and 퐼2 we have included an additional 4휋 factor coming from the angular integration and we have assumed that the effective mass does not depend on the energy 퐸. It is important to observe that 퐼1 and 퐼2 are finite only for some appropriate choices of 푔1(퐸/퐸푃) and 푔2(퐸/퐸푃). Indeed, a pure polynomial cannot be used without the reintroduction of a regularization and a renormalization process. It is immediate to see that integrals that 퐼1 and 퐼2 can be easily solved when 푔1(퐸/퐸푃) = 푔2(퐸/퐸푃). However the classical term keeps a dependence on the function 푔2(퐸/퐸푃) that cannot be eliminated except for the simple case of 푔2(퐸/퐸푃) = 1 . For instance, if we assume that the shape function is represented by the Ellis wormhole in Eq. (9) and 훼퐸2 (33) 푔1(퐸/퐸푃) = 푒푥푝 − ( 2 ), 푔2(퐸/퐸푃) = 1 퐸푃 with 훼 ∈ ℝ, the classical term is not distorted. Then Eq. (25) has the following solution at

푟0퐸푃 = 2.97√훼 푤𝑖푡ℎ 훼 ≅ 0.242. (34)

This means that 푟0퐸푃 = 1.46 , to be compared with the roots given in the previous section. One can also adopt a relaxed form for the Rainbow's functions described by

255 | P a g e

to obtain the following result 푟0퐸푃 = 4.12. On the other hand, if we take into account an EoS, the shape function (17) can give interesting results only in the range 1 4.5, 2.038 r E 1.083. 0 P It is interesting to note that the condition

푏(푟) + 휔푏′(푟)푟 = 0 (35) obtained by Eq.(16) works also for an inhomogeneous EoS. Indeed, the presence of the rainbow's function does not affect the form of (30). The situation appears completely different when a polytropic with an inhomogeneous parameter 휔 is considered. Indeed, when the polytropic EoS, i.e.,

, is plugged into the expression

b8 Gp r3   r , 2r2  1 b r / r (36) one finds

(37)

We can always impose 휙(푟) = 퐶, but this means that

(38) , and a dependence on 푔2(퐸/퐸푃) appears. For this reason this case will be discarded.

Conclusions and Outlooks In this contribution we have established a connection between the Casimir Energy and a Traversable Wormhole. In particular we have examined the possibility that a traversable wormhole can be sustained by its own gravitational quantum fluctuations. The fluctuations, contained in the perturbed Einstein tensor, substitute the exotic matter considered in Ref. [12] which is the fundamental ingredient for the existence of the wormhole. To do calculations in practice, a variational approach with the help of gaussian trial wave functionals has been used to compute the one loop term. To handle the divergences appearing in such a calculation we have proposed two different procedures: (a) a standard Regularization/Renormalization process, and (b) the distortion of gravity at the Planck scale.

256 | P a g e

For the standard Regularization/Renormalization process, a zeta function calculation has been used. This procedure is formally equivalent to a Casimir energy subtraction procedure. The renormalization is performed promoting Newton's constant 퐺 as a bare coupling constant to absorb the ultraviolet divergencies. To avoid dependences on the renormalization scale a renormalization group equation has been introduced. While the renormalization process is not new in the context of the semiclassical Einstein field equations, to our knowledge it is the use of the renormalization group equation that seems to be unknown, especially concerning self-consistent solutions and the traversability conditions of the wormhole. The procedure has been tested on the prototype of 2 traversable wormholes, namely, the Ellis wormhole with 푏(푟) = 푟0 /푟. The result shows that the obtained traversability has to be regarded as in principle rather than in practice because the size of the wormhole radius is of the Planckian order. On the other hand if we adopt Gravity’s Rainbow, the result is slightly improved. The introduction of an EoS with 휔 ∈ ℝ shows that the phantom energy range is forbidden. Indeed phantom energy works in the range 휔 < −1. However, the classical term is well defined in the range −1 < 휔 < +∞ and the interval −1 < 휔 < 0 is connected to a dark energy sector. Nevertheless, the dark energy domain lies outside the asymptotically flatness property. So, unless one is interested in wormholes that are not asymptotically flat, i.e. asymptotically de Sitter or asymptotically Anti-de Sitter, we also have to reject this possibility. Therefore, the final stage of computation has been restricted only to positive values of the parameter 휔. On the other hand, the positive 휔 sector seems to corroborate the Casimir process of the quantum fluctuations supporting the opening of the wormhole. Even in this region, we do not know what happens approaching directly the point 휔 = 0, because it seems that this approach is ill defined, even if the wormhole radius becomes much more large than the Planckian size. Note that the situation is always slightly better when we use Gravity's Rainbow as a regulator procedure. Indeed, in this framework, every shape function analyzed is traversable. The bad news is that the traversability is always in principle but not in practice as the wormhole radius in of the Planckian size, even if the radii are greater that the radius discovered in Ref. [13]. One way to obtain a larger radius is to reinterpret the self-sustained equation as an ignition equation. Indeed, one possibility is to use the self-sustained equation in the following manner

(39)

where 푛 is the order of the approximation. In this way, if we discover that fixing the radius to some value of a fixed background of the r.h.s., and we discover on the l.h.s. a different radius, we could conclude that if the radius is larger that the original, the wormhole is growing, otherwise is collapsing. Note that in Ref. [23], Eq.(39) has been used to show that a traversable wormhole can be generated with a topology change starting from a Minkowski spacetime. This is because we are probing a region where the gravitational field develops quantum fluctuations so violent to be able to suggest a topology change. To conclude, in this contribution we have shown that a traversable wormhole exists in principle and that the Casimir-like energy generated by the quantum fluctuations of the wormhole itself can be thought as the right energy source. The next step will be about the possibility to have a traversable wormhole also in practice. A serious analysis of Eq.(39) could be a beginning, but also the addition of rotations could be an interesting improvement.

257 | P a g e

References

[1] H. Casimir, "On the attraction between two perfectly conducting plates," Proc. Kon. Ned. Akad. Wetenschap, vol. 51, p. 793, 1948. [2] M. Sparnaay, "Attractive forces between flat plates," Nature 180, p. 334, 1957.

[3] M. Sparnaay, "Measurement of attractive forces between flat plates," Physica 24, p. 751, 1958.

[4] S. Lamoreaux, "Demonstration of the Casimir Force in the 0.6 to 6 mm Range," Phys. Rev. Lett., vol. 78, p. 5, 1997. [5] F. Serry, D. Walliser and G. Maclay, "The anharmonic Casimir oscillator (ACO)-the Casimir effect in a model microelectromechanical system.," J. Microelectromechanical Syst., vol. 4, p. 193–205, 1995. [6] H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop and F. Capasso, "Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force," Science, vol. 291, no. 5510, pp. 1941-1944, 2001. [7] N. Tas, T. Sonnenberg, H. Jansen, R. Legtenberg and M. Elwenspoek, "Stiction in surface micromachining.," J. Micromechanics Microengineering, 6(4), p. 385–397, 1996. [8] E. Buks and M. L. Roukes, "Stiction, adhesion energy, and the Casimir effect in micromechanical systems.," Phys. Rev. B, vol. 63, p. 033402, 2001; ArXiv:cond-mat/0008051 [cond-mat.mes-hall]. [9] M. Morris and K. Thorne, "Wormholes in spacetimes and their use for interstellar travel: A tool for teaching general relativity," Am. J. Phys., vol. 56, p. 395, 1988. [10] M. Morris, K. S. Thorne and U. Yurtsever, "Wormholes, Time Machines, and the Weak Energy Condition," Phys. Rev. Lett., vol. 61, p. 1446, 1988. [11] D. Hochberg, A. Popov and S. Sushkov, "Self-consistent Wormhole Solutions of Semiclassical Gravity," Phys. Rev. Lett., vol. 78, p. 2050, 1997; Arxiv: gr-qc/9701064. [12] N. R. Khusnutdinov and S. Sushkov, "Ground state energy in a wormhole space-time," Phys. Rev. D, vol. 65, p. 084028, 2002; Arxiv: hep-th/0202068. [13] R. Garattini, "Self Sustained Traversable Wormholes?," Class.Quant.Grav., vol. 22, p. 1105, 2005; Arxiv gr-qc/0501105. [14] R. Garattini, "Self sustained traversable wormholes and the equation of state," Class.Quant.Grav., vol. 24, p. 1189, 2007; Arxiv: gr-qc/0701019. [15] F. S. N. Lobo, "Phantom energy traversable wormholes," Phys. Rev. D, vol. 71, p. 084011, 2005; Arxiv: gr-qc/0502099. [16] F. Lobo, "Stability of phantom wormholes," Phys. Rev. D, vol. 71, p. 124022, 2005; Arxiv: gr- qc/0506001. [17] P. Kuhfittig, "Seeking exactly solvable models of traversable wormholes supported by phantom energy," Class.Quant.Grav., vol. 23, p. 5853, 2006; Arxiv: gr-qc/0608055. [18] S. Sushkov, "Wormholes supported by a phantom energy," Phys. Rev. D, vol. 71, p. 043520, 2005; Arxiv gr-qc/0502084. [19] R. Garattini and F. S. N. Lobo, "Self-sustained wormholes in modified dispersion relations," Phys. Rev. D, vol. 85, p. 024043, 2012; ArXiv:1111.5729 [gr-qc].. [20] A. DeBenedictis, R. Garattini and F. Lobo, "Phantom Stars and Topology Change," Phys. Rev. D, vol. 78, p. 104003, 2008; ArXiv:0808.0839 [gr-qc]..

258 | P a g e

[21] R. Garattini, "Wormholes or Gravastars?," JHEP, vol. 52, p. 1309, 2013; ArXiv:1001.3831 [gr-qc]..

[22] J. Magueijo and L. Smolin, "Gravity's Rainbow," Class. Quant. Grav., vol. 21, p. 1725, 2004 ArXiv:gr-qc/0305055. [23] R. Garattini and F. Lobo, "Gravity`s Rainbow induces topology change," Eur. Phys. J. C., vol. 74, p. 2884, 2014; ArXiv:1303.5566 [gr-qc].. [24] A. Roy and U. Mohideen, "Demonstration of the Nontrivial Boundary Dependence of the Casimir Force," Phys. Rev. Lett., vol. 82, p. 4380, 1999. [25] A. Roy, C.-Y. Lin and U. Mohideen, "Improved precision measurement of the Casimir force," Phys. Rev. D, vol. 60, p. 111101, 1999. [26] U. Mohideen and A. Roy, "Precision Measurement of the Casimir Force from 0.1 to 0.9 micrometers," Phys. Rev. Lett., vol. 81, p. 4549, 1998. [27] M. Visser, "Lorentzian Wormholes," AIP Press, New York, vol. 64, 1995.

[28] R. Garattini and F. Lobo, "Self sustained phantom wormholes in semi-classical gravity," Class.Quant.Grav., vol. 24, p. 2401, 2007; ArXiv:gr-qc/0701020..

259 | P a g e

HUMAN EXPLORATION OF THE SOLAR SYSTEM AS A PRECURSOR TO INTERSTELLAR TRAVEL: OUTLOOK AND REALITIES

Ralph L. McNutt, Jr. * Johns Hopkins University Applied Physics Laboratory, Laurel, MD, USA *Corresponding author, [email protected] [Abstract Only]

Abstract Technical speculation about the possibilities of space travel began with Konstantin E. Tsiolkovsky at the beginning of the 20th century [1], building upon notions of rockets from centuries earlier [2]. Only with the Second World War and the competition in space between the U.S. and the Soviet Union during the ensuing Cold War were sufficient funds available to develop what has become known as astronautics to the point that robotic and human spacecraft became possible. To date, the culmination of the human program has been the Apollo landings on the Moon and the building and permanent habitation of the International Space Station (ISS). At the same time there has been a recurrent backdrop of the idea of humans traveling out from the solar system to the stars, with the topic developed somewhere between science [3] and science fiction [4], given the enormity of that task [5]. Nonetheless, it seems prudent to examine the realities and requirements of the “easier” problem of human travel throughout the solar system, to inform both the longer-term possibility of human travel beyond the asteroid belt, as well as the shorter-term goal of the human exploration of the Mars system [6]. While missions to Mars can be accomplished with chemical and/or nuclear thermal propulsion [7], continuous, low-thrust missions will be required to decrease flight times to acceptable durations for more distant targets [8, 9]. For human flight the duration, living space, and expendables (food, water, and air) all become part of a significant trade space, which also reflects risk postures, both with respect to radiation tolerance and contingency strategies. In the absence of some type of induced, artificial hibernation (for which no near-term technologies currently exist) mission lifetimes will likely be limited to ~5 years. Provision of supplies, if not forward positioned, recycling efficiencies and reliabilities, living volume, and the target system all then drive the required mass and, hence, required propulsion [10]. Closure of the engineering design depends upon physical characteristics of the means of propulsion, bookkept as the specific mass of that system, which must include propulsion hardware, energy generation conversion and efficiency, and radiation of waste heat [11]. Implementation is highly dependent upon materials and system reliabilities, preplaced infrastructure, and the adopted form of nuclear energy for power and propulsion. Significant structural masses will be required for such missions with assembly in space or on Earth and/or with materials brought from Earth or mined at the Moon or Near-Earth Asteroids (NEAs). The approach taken also become part of the trade space [12]. None of these issues is new. What is new is now- available space technology, the role of even newer technologies, and the development and implementation costs, all of which we have real experience over the past five decades. In the absence of disruptive, implementable, propulsion technologies, we can visit the types of requirements that may then be needed for recurrent human Mars travel [13], and for initial human forays to the asteroid belt and the planets of our solar system beyond. The experiences of actual human expeditions throughout the solar system – not unlike the initial expeditions to Antarctica – will inform us of what the possibilities for homo ad astra might be when the coming century dawns [6]. Keywords: Interstellar Travel, Human Space Exploration, System Engineering

260 | P a g e

References [1] Tsiolkovskiy, K. E. Study of outer space by reaction devices. 742 (National Aeronautics and Space Administration, Washington, D.C., 1967). [2] Gruntman, M. Blazing the Trail: The Early History of Spacecraft and Rocketry. (AIAA, 2004). [3] Goddard, R. H. The ultimate migration. Journal of the British Interplanetary Society 36, 552-554 (1983). [4] Bernal, J. D. The World, the Flesh, and the Devil: an Enquiry into the Future of the Three Enemies of the Soul. 2nd edn, (Indiana Univ. Press, 1969). [5] Asimov, I. in The 1966 World Book Year Book 148-163 (Field Enterprises Educational Corporation, Publishers, 1966). [6] McNutt, R. L. Solar system exploration: A vision for the next 100 years. Johns Hopkins Apl Technical Digest 27, 168-181 (2006). [7] Drake, B. G. & Watts, K. D. Human Exploration of Mars Design Reference Architecture 5.0 - Addendum #2. 598 (NASA, Washington, D.C., 2014). [8] Ehricke, K. A. in Handbook od Astronautical Engineering (ed H. H. Koelle) 47 (McGraw-Hill Book Company, Inc., 1961). [9] Troutman, P. A. et al. Revolutionary concepts for Human Outer Planet Exploration (HOPE). AIP Conf. Pro. 654, 821-828 (2003). [10] McNutt, R. L. ARGOSY: ARchitecture for Going to the Outer solar SYstem. Johns Hopkins Apl Technical Digest 27, 261-273 (2007). [11] McNutt, R. L., Horsewood, J. & Fiehler, D. I. Human Missions Throughout the Outer Solar System: Requirements and Implementations. Johns Hopkins Apl Technical Digest 28, 373-388 (2010). [12] Koelle, H. H. & Huber, W. G. in Handbook of Astronautical Engineering (ed Heinz Hermann Koelle) (McGraw-Hill Book Company, Inc., 1961). [13] McNutt, R. L., Jr. et al. in 10th International Workshop on Combustion and Propulsion: In-Space Propulsion. (eds L. T. de Luca, R. L. Sackheim, & B. A. Palaszewski) Paper 33 (grafiche g. s. s., Arzago d'Adda (BG) Italy).

261 | P a g e

THE EQUIVALENCE OF INTERNAL AND EXTERNAL ENERGY SOURCE INTERPRETATIONS OF THE CASIMIR EFFECT AND THEIR IMPLICATIONS FOR INTERSTELLAR TRAVEL Robert L. DeBiase1* 1 Independent Researcher, Staten Island, NY, USA * Corresponding author, [email protected]

Multiple interpretations exist as to the source of the Casimir effect. In one, the force results from an extension of the van der Waals forces between atoms making up the bulk matter of the plates, implying an internal energy source. In yet another, the force results from a difference in radiation pressure between the inside and outside of the cavity. Since the vibrating modes inside the cavity are restricted, there is a net pressure from outside pushing the plates together. The implied energy source for this interpretation is external to the plates. The extension of van der Waals interpretation is encompassed in the Casimir-Polder equation expressing the potential energy between two polarizable atoms. The radiation pressure interpretation is encompassed in the famous energy per unit area and force per unit area formulas for perfectly conducting parallel plates. It is believed that these interpretations are equivalent. Calculating lateral and normal forces for a pair of sinusoidally corrugated flat plates with conductors spanning full and partial wavelengths, using two approximations will test the equivalence. The proximity force approximation (PFA) can be implicitly premised upon an external energy source interpretation while the pair-wise summation (PWS) approximation is explicitly based upon the bulk matter internal energy source interpretation. For plates having conductors spanning the full corrugation wavelength, the results of the two approximations are remarkably equivalent. However plates with partial corrugation wavelength conductors produce lateral forces that are not only not equivalent, the PFA produces anomalous external forces. The anomaly can be tested with current technology using an atomic force microscope. If the anomaly should prove to be true it has great implications for interstellar space travel. Keywords: Casimir effect, non-parallel plates, proximity force approximation, pair wise summation

1. Introduction There are many interpretations as to the source of energy behind the Casimir effect. In one, the source is considered to come from the potential energy of atoms in the bulk matter making up the plates. In another, the energy source is considered to be the zero-point fields in the vacuum of space between and around the plates. These interpretations are as old as the Casimir effect itself since they date back to two papers published in 1948, one authored by Hendrik Casimir and coauthored with Dirk Polder, entitled: “The Influence of Retardation on the London-van der Waals Forces” [1]. Van der Waals forces occur between atoms and molecules at distances typically less than 1 nm and are responsible for the cohesion of most solid materials. If the forces result from two instantaneous induced dipoles, they are called London-van der Walls forces and if the bulk matter making up the plates are composed of dielectric material and separated by distances of from about 100 nm to ), the effects of retardation must be included and this extension is also called a Casimir force. This interpretation explicitly depends upon the zero-point fluctuations of the

262 | P a g e polarizable atoms in the bulk matter making up the plates. At plate separations somewhat greater than 1 micron at room temperature, thermal fluctuations must be included as well. The second paper was by Casimir himself entitled: “On the attraction between two perfectly conducting plates” [2]. This paper is premised upon the difference in the sum of the resonant frequencies of all virtual photons within the cavity between perfectly conducting plates and the sum of the virtual photon frequencies outside the cavity. Where these virtual photons originate from is not explicitly stated. They could result from the tails of molecular potentials of matter nearby [3], but they could also originate from the zero-point fluctuations of fields within a perfect vacuum [4]. Regarding the equivalence of these interpretations, Maclay [5] observes that these approaches differ in how they visualize the fluctuations of the electromagnetic field, but give consistent results in the few cases of simple geometries that have been computed. Pinto [6] is even more explicit about the equivalence of multiple interpretations of the Casimir effect saying: “These differing interpretations are all logically acceptable, although mutually incompatible. Regardless, the results are mathematically equivalent and indistinguishable from one another.” For most authors the equivalence is taken for granted. Approximations exist that can be used as proxies to mathematically test the equivalence of the vacuum and bulk matter interpretations. Pair Wise Summation (PWS) is an approximation based upon the Casimir-Polder equation, which can be viewed as an extension of the van der Waals forces and thus is a proxy for the bulk internal energy interpretation. The Proximity Force Approximation (PFA) descends from the parallel plates derivation of the Casimir forces. As such it is a good proxy for the vacuum external energy interpretation of the Casimir effect. Both of these approximations are commonly used and are conceptually simple. The bad thing about them is that their simplicity may make them incomplete.

2. The Pair Wise Summation Approximation (PWS) With the Pair Wise Summation approximation, the interaction energy potentials of pairs of polarizable atoms from two plates are added together as shown in Fig. 1. 1 2 j Plate 2 rij

1 2 3 i Plate 1 Fig. 1 The summation of the energy potentials of pairs of atoms from the two plates

The energy potential of the atom pair i, j is described by the Casimir-Polder equation [7, 8]: hc c 2 (1) urij   7 23   E1 E 2   M 1 M 2  7   E1 M 2   M 1 E 2   7  4  rij 4  rij

2 Where   23   E1 E2  M1 M 2  7   E1 M 2  M1 E2 

The parameter rij is the distance between atoms i and j, M are the electrostatic and magnetic polarizability of the atoms respectively While there is no restriction on the shape of the plates with PWS, forces calculated by it will always be equal and opposite.

3. The Proximity Force Approximation (PFA) The Proximity Force Approximation (PFA), sometimes called the Derjaguin approximation [9, 10], is based upon the forces between two perfectly conducting parallel plates. The conducting plates

263 | P a g e suppress vibration modes of virtual photons between the plates but not outside the plates resulting in there being less energy inside the cavity than outside. The subsequent energy difference between outside and in results in an attractive force pushing the plates together.

The Casimir energy per unit x, y area epp derived from the zero point fields in a vacuum for two perfectly conducting parallel plates is:

hc 2 e z   (2) pp 720z3 where z is the distance between plates. The normal force per unit area on the plates is:

ez   hc 2  hc 2 f z            3  4 (3) z z  720z  240z In a paper by Milonni, Cook and Goggin [11] the Casimir forces are calculated explicitly from the radiation pressure of the vacuum. The result for perfectly conducting parallel plates is the classical Casimir formulation of the force per unit area as given in Eq. 3. 3.1 The proximity force approximation for non-parallel plates Non-parallel plates can be thought of as multiple parallel plates as is shown in Fig. 2. z Plate 2 Z2(x) z0 Z2(x) – Z1(x) Z1(x) Plate 1 x Fig. 2 Dividing non-parallel plates into a set of parallel plates

The energy per unit x, y area epp can generally be easily determined for a general volumetric pixel given the geometry of the plates. From that the total plate energy can be determined by integrating over x, y area in terms of some geometric parameter for distance between plates, z0. The normal direction is the direction between the plates, perpendicular to the parallel platelets - in the z direction. The lateral direction is along the plates in the x direction (or y direction). Given the energy epp per unit x, y area at some location on the plate, forces per unit x, y area at that location can be determined in the following way:   e e e dF pp ˆ pp ˆ pp ˆ  f  epp   i  j  k dAxy x y z The PWS approximation had no restriction on shape but the PFA does. The geometries and parameters that will be considered here are similar to those used in the Chen, Mohideen experiment of 2001 that demonstrated lateral forces [12], and thus are within the domain of the PFA.

3.2 Direction of lateral + normal force vector resultant

C Z A 

fn  fl B Fig. 3 The direction of the lateral plus normal vector resultant relative to the local area 264 | P a g e

In Fig. 3, if the normal plus lateral vector resultant is perpendicular to the local area, then the slope of line AB will be the negative reciprocal of the slope of line AC, which is the tangent to the curve at A. Starting with the energy per unit x, y area at some x (y is irrelevant): 2  ch e pp   3 720Z 2 x  X 2  Z1 x  X 1  e 2 Then the normal force per unit x, y area for Plate 2 is: pp  ch , f n2     4 Z 2 240 Z 2  Z1  dZ  2ch 2 e dX While the lateral force per unit x, y area for Plate 2 is: pp 2 f l 2     4 X 2 240 Z 2  Z1  f 1 Then Slope(AB)  n2  . Now let x = x - X 2 2 f l 2 dZ2

dX 2 dZ dZ dx dZ Then by the chain rule: 2  2  2   2 dX 2 dx2 dX 2 dx2 dZ dZ dx dZ On the other hand: SlopeAC   2  2  2  2 dx dx2 dx dx2

Thus: 1 1 1 1 SlopeAB         dZ   dZ   dZ  SlopeAC   2   2   2         dX 2   dx 2   dx  Thus, the resultant force is perpendicular to the local plate area, making it consistent with a radiation pressure. Similar results are found for Plate 1.

4. Test of equivalence for parallel plates A full analytic calculation can be done for parallel plates using PWS and then compared with the vacuum oriented calculation, the purpose of which is to come up with a scaling factor, sometimes called a calibration factor [9] or a normalization factor [8, 9]. Fig. 4 shows a diagram defining the parameters for the PWS calculation of two parallel flat plates.

d z Plate 2 - conducting (x2, y2, z2)

Casimir cavity - vacuum r(x1,y1,z1,x2,y2,z2) a y

x Plate 1 - parallel plates (x1, y1, z1) d

X Y Fig. 4 Diagram for deriving PWS equation for parallel plates The interaction energy between a pair of atoms in Plates 1 and 2 can be found from the Casimir- Polder equation first shown in Eq. 1 and here repeated with some modifications:

265 | P a g e

hc  2 urx1 , y1 , z1 , x2 , y2 , z2    7 where 4  rx1 , y1 , z1 , x2 , y2 , z2  2 2 2 rx1 , y1 , z1 , x2 , y2 , z2   x2  x1   y2  y1   z2  z1  and

2 = 23   E1 E2  M1 M 2  7   E1 M 2  M1 E2 . The total energy between plates is found by integrating over the volumes of both plates:

2 2 d 2d a Y Y X X hc   dx2  dx1  dy2  dy1  dz2  dz1 Ua,d    7 (4)       2 2 4 z 0 z d a y 0 y 0 x 0 x 0 2 1 2 1 2 1 2 x2  x1   y2  y1   z2  z1 

After much calculation the normal force on plate 2 becomes:

Ua, d hc  2  2   1 2 1  F a, d       XY      SmallerTerms (5) PWS    4 4 4  a 4 10  a a  d a  2d 

When d is much greater than a, but much less than macroscopic dimensions X and Y, FPWS along the z direction, becomes like the vacuum centric Casimir equation because the terms with d in them go to zero. For X and Y both being of macroscopic dimension, SmallerTerms can also be considered zero. 4.1 Comparing the PWS with the vacuum centric solution for parallel plates

2 2 hc   XY hc 2 XY For d much greater than a, F   and Fpp   , PWS 40a 4 240a4

2 Fpp  Resulting in a scaling factor of: for gold. (6) S pp   2 2  5.814 FPWS 6 

-24 3 Where the cm M is assumed to be zero. 22 3 atoms/cm (for gold [8]) The bulk and vacuum calculations for parallel plates are equivalent in that both are inverse forth power relations and both are directly proportional to the area of the plates but that F >> F . This pp PWS difference can’t be accounted for by corrections for temperature and conductivity.

The scaling factor Spp will be used in subsequent calculations comparing PWS and PFA calculations for sinusoidal corrugated plates.

5. Test of equivalence for various sinusoidal corrugated plates 5.1 A mathematical model for sinusoidal corrugated plates using the PFA The geometry for sinusoidal corrugated plates being calculated by the PFA is depicted in Fig. 5. The parameters used in the mathematical model based upon this geometry are contained in Table 1:

266 | P a g e

Parameter Parameter Name Value L Corrugation wavelength 1.2

A1 Corrugation amplitude of plate 1 Variable – A2 * A2 Corrugation amplitude of plate 2

X1 Phase displacement for plate 1 Set to 0 X2 Phase displacement for plate 2 Variable z0 Parametric distance between plates 0.233 Y Plate widths (plates 1 & 2) 1 cm

Table 1: Parameters and values used calculation of sinusoidal corrugated plates model using the PFA and PWS

A2

Plate 2 X2 x z0

A1 z La Plate L y b

x L

Fig. 5 Geometry for sinusoidal corrugated plates model using the PFA

The parameter values in the table with asterisk were those used in the Chen, Mohideen, et. al. experiment of 2001 demonstrating the lateral Casimir force [12]. The x and z coordinates in Fig. 5 are in units of L, the corrugation wavelength. The equations for Z1 and Z2 describe the x, z cross- section of plates 1 and 2 respectively.

For all the tests of lateral and normal forces, the bottom Z1 plate will serve as the test plate. Amplitude A1 will be varied as well as Plate 1 start and stop locations La and Lb. The corrugation phase X2 of the Z2 upper plate will be changed while the bottom Z1 plate remains stationary. Changing the corrugation phase of the upper plate is equivalent to moving it from left to right. Only that part of the upper plate that is directly above the stationary lower plate participates in the Casimir effect as calculated by the PFA.

5.1.1 Using the PFA model to calculate lateral forces on plates versus varying corrugation phase X2

Substituting z = Z2 – Z1 = the values from Fig. 5 into Eq. 2 one obtains the following energy per unit x, y area  2ch (7) e pp x, X 1 , X 2 , A1    3   2 x  X   2 x  X    2 1  720  A2 cos   A1 cos   z0    L   L  

Next, calculate the lateral force per unit x, y area for Plates 1 and 2, fX1 (x,X1,X2, A1) and fX2 (x,X1,X2, A1) After which X1 can be set to 0 because plate 1 is stationary.

The total PFA lateral force on Plate 1 when the conductor is between the limits of La to Lb:

267 | P a g e

Lb Y FX 1 X 2 , A1   f X 1 x, X 2 , A1 dy  dx Repesented by black dots in subsequent figures. (8) xL y0 a

The total PFA lateral force on plate 2 when the conductor is between the limits of La to Lb:

Lb Y FX 2 X 2 , A1   f X 2 x, X 2 , A1 dy  dx Represented by gray dots in subsequent figures. (9) xL y0 a 5.1.2 Using the PFA model to calculate normal forces on plates versus varying corrugation phase X2

Substituting z = Z2 – Z1 into Eq. 2 one obtains the following energy per unit x, y area: hc 2 e pp   3 (10) 720 Z 2  Z1 

After calculating the normal force per unit x, y area for Plates 1 and 2 the values of Z1 and Z2 from Fig. 5 can be substituted giving fZ1 (x, X1, X2, A1) and fZ2(x, X1, X2, A1), after which X1 can be set to 0 because plate 1 is stationary.

The total PFA normal force on Plate 1 when the conductor is between the limits of La to Lb is:

Lb Y FZ1 X 2 , A1   f Z1 x, X 2 , A1 dy  dx Repesented by black dots in subsequent figures. (11) xL y0 a

The total PFA normal force on Plate 2 when the conductor is between the limits of La to Lb is:

FZ2(X2, A1) = - FZ1(X2, A1). Represented by gray dots in subsequent figures.

5.2 A mathematical model for sinusoidal corrugated plates using PWS The geometry for sinusoidal corrugated plates being calculated by PWS is depicted in Fig. 6. The parameters used in the mathematical model based upon this geometry are contained in Table 1 with the addition of the parameter for the plate thickness d m.

A2 d Plate 2 (x2, y2, z2) X2 rx, y, z A1 L a (x1, y1, z1) Plate 1 Lb L Fig. 6 Geometry for sinusoidal corrugated plates model using PWS

The parameter values in the table with asterisk were those used in the Chen, Mohideen, et. al. experiment of 2001 demonstrating the lateral Casimir force [12]. The x and z coordinates in Fig. 6 are in units of L, the corrugation wavelength. The equations for Z1 and Z2 describe the x, z cross- section of plates 1 and 2 respectively. For all the tests of lateral and normal forces, the bottom Z1 plate will serve as the test plate. Amplitude A1 will be varied as well as Plate 1 start and stop locations La and Lb. The corrugation phase X2 of the Z2 upper plate will be changed while the bottom Z1 plate remains stationary. Changing the corrugation phase of the upper plate is equivalent to moving the upper plate to the left and right. Unlike the PFA, with PWS atoms in the lower plate can interact with atoms in the upper plate beyond the x, y area bounded by the lower plate.

268 | P a g e

5.2.1 Using the PWS model to calculate lateral forces on plates versus varying corrugation phase X2 Since the intension is to compare the PWS calculation with the PFA calculation the parallel plate scaling-factor will be included in the calculation. Thus the Casimir-Polder equation (Eq. 1) becomes, after incorporating the scaling factor, Equation 6: B' c  2  2 c B' B  S    u   7 , Where pp 2 2 2 (12) 2 2 2 2 4 6  24 x2  x1   y2  y1   z2  z1   The lateral force per unit of volume for Plate 1 then becomes:

u c 7x2  x1  (13) f x1    2  9 2 2 2 x1 24 2 x2  x1   y2  y1   z2  z1   The lateral force per unit of volume for Plate 2 is: fx2 = - fx1 To find the total lateral force on each plate the lateral force per unit volume needs to be integrated over the volume of both plates. An intermediate analytic solution can be obtained by integrating over y1, y2, z1 and z2. Call this intermediate solution for Plate 1, gx1.

Z1 Z2 d Y Y g  2 f dy  dy  dz  dz (14) x1     x1 2 1 2 1 z1 Z1 d z2 Z2 y1 0 y2 0

 2 2 2   W   V   U  3 2 2 2 2 2 2 2 2 2 5 2 2 2 2 2 2  15P Q R W atan 2V atan U atan 5x P Q W 2P R V Q R U 7x Q R 2P R P Q  c  x   x   x   Y 2  x 2     12 15x6P2Q2R2 2 2  x  X  P  U  x U  Z 2  Z1 2 2 Z 2  z0  A2 cos2   2 2 Where: Q  V  x , V  U  d ,  L  and x  x2  x1 2 2 W  U  2d  x1  R  W  x Z1  A1 cos2    L 

The total PWS lateral force on Plate 1 is found by integrating Eq. 14 by x2 from –L to 2L, to account for edge effects, and x1 from La and Lb:

2L Lb F X , A  g dx  dx Represented by solid black lines in subsequent figures. (15) x1  2 1    x1 1 2 x2 L x1 La The total PWS lateral force on Plate 2:

Fx2(X2, A1) = - Fx1(X2, A1) Represented by solid gray lines in subsequent figures. The total PWS lateral force from Plates 1 and 2 is:

Fx(X2, A1) = Fx1(X2, A1) + Fx2(X2, A1) = 0

5.2.2 Using the PWS model to calculate normal forces on plates versus varying corrugation phase X2 Since the intension is to compare the PWS calculation with the PFA calculation the parallel plate scaling-factor will be included in the calculation. As with the lateral force calculations Equation 1 becomes a repeat of Equation 12:

269 | P a g e

B' c  2  2 c , Where B'  B  S    u   7 pp 2 2 2 2 2 2 2 4 6  24 x2  x1   y2  y1   z2  z1   The normal force per unit of volume for Plate 1 then becomes:

u c 7z2  z1  (16) f z1    2  9 2 2 2 z1 24 2 x2  x1   y2  y1   z2  z1   The normal force per unit of volume for Plate 2 is: fz2 = - fz1 To find the total normal force on each plate the normal force per unit volume needs to be integrated over the volume of both plates. An intermediate analytic solution can be obtained by integrating over y1, y2, z1 and z2. Call this intermediate solution for Plate 1, gz1.

Z1 Z2 d Y Y g  2 f dy  dy  dz  dz (17) z1     z1 2 1 2 1 z1 Z1 d z2 Z2 y1 0 y2 0

 2 2 2   W   V   U  2 2 2 2 2 2 2 2 2 2 2 2  3P Q R  atan 2atan atan  xP Q W 3W 5x 2xP R V 3V 5x  xQ R U 3U 5x  c  x x x    Y 2  x2          12 15x5P2Q2 R2

2 2  x2  X 2  P  U  x U  Z 2  Z1 Z 2  z0  A2 cos2   2 2  L  Where: Q  V  x , V  U  d , and x  x2  x1 x 2 2 W  U  2d  1  R  W  x Z1  A1 cos2    L 

The total PWS normal force on Plate 1 is found by integrating Eq. 17 by x2 from –L to 2L, to account for edge effects, and x1 from La to Lb:

2L Lb F X , A  g dx  dx Represented by a solid black line in subsequent figures. (18) z1  2 1    z1 1 2 x2 L x1 La The total PWS normal force on Plate 2:

Fz2(X2, A1) = - Fz1(X2, A1). Represented by a solid gray line in subsequent figures. The total PWS normal force from Plates 1 and 2 is:

Fz(X2, A1) = Fz1(X2, A1) + Fz2(X2, A1) = 0

270 | P a g e

6. Results: PFA and PWS Plate Forces vs. Corrugation Phase

6.1 Full Wavelength – A1 = 8 nm

L

/ / z

X2 = .3L A2 = 0.059 m

A1 = 0.008 m x / L

Dotted line: PFA

Lateral x: L = 0 to L = L forces on a b plates Solid line: PWS with parallel plate Scaling factor

x : L = 0 to L = L 1 a b Corrugation Phase X2 / L Normal Dotted line: PFA

forces on

x: La = 0 to Lb = L plates Solid line: PWS with parallel plate Scaling

factor

Corrugation Phase X2 / L x1: La = 0 to Lb = L Fig. 7 Lateral and normal forces on plates with Plate 1 having full corrugation wave-length

and amplitude A = 8 nm 1

6.2 Full Wavelength – A1 = 59 nm

L

/ / z A2 = 0.059 m X2 = .3L

A = 0.059 m 1 x / L

Lateral Dotted line: PFA forces x: La = 0 to Lb = L on

plates Solid line: PWS with parallel plate Scaling factor

x1: La = 0 to Lb = L Corrugation Phase X2 / L

Normal Dotted line: PFA forces on plates x: L = 0 to L = L a b

Solid line: PWS with parallel plate Scaling factor

x1: La = 0 to Lb = L

Corrugation Phase X2 / L Fig. 8 Lateral and normal forces on plates with Plate 1 having full corrugation wavelength and 271 | P a g e amplitude A = 59 nm 1

6.3 Half Metallized Wavelength – A1 = 59 nm

L

/ / z A2 = 0.059 m X2 = .3L A1 = 0.059 m x / L

Dotted line: PFA Lateral forces on x: La = 0 to Lb = 0.5L plates

Solid line: PWS with parallel plate Scaling factor

x1: La = 0 to Lb = 0.5L Corrugation Phase X2 / L Dotted line: PFA Normal forces on x: L = 0 to L = 0.5L plates a b Solid line: PWS with parallel plate Scaling factor

x1: La = 0 to Lb = 0.5L Normal Forces(dynes) Corrugation Phase X2 / L

Fig. 9 Lateral and normal forces on plates with Plate 1 having half metallized wave-length and

amplitude A1 = 59 nm

6.4 Partially Metallized Wavelength, La = 0.1L to Lb = 0.9L, A1 = 59 nm

L A2 = 0.059 m / /

X2 = .3L z A = 0.059 m 1

x / L

Dotted line: PFA Lateral forces x: La = 0.1L to Lb = 0.9L on (dynes) Forces

plates Solid line: PWS with parallel plate Scaling factor

Lateral

Corrugation Phase X2 / L x1: La = 0.1L to Lb = 0.9L

Normal Dotted line: PFA

forces on x: La = 0.1L to Lb = 0.9L plates

Solid line: PWS with parallel plate Scaling factor

Normal Forces (dynes) Forces Normal

x1 La = 0.1L to Lb = 0.9L Corrugation Phase X2 / L

Fig. 10 Lateral and normal forces on plates with Plate 1 having a partially metallized wavelength

from La = 0.1L to Lb = 0.9L, with corrugation amplitude A1 = 59 nm.

272 | P a g e

For all test cases an arbitrarily drawn vertical dashed line shows a corrugation phase of 0.3L along with the appropriate lateral and normal forces associated with that corrugation phase. It will be noted that the normal PFA and PWS calculated forces are virtually on top of each other, showing their equivalence when the parallel plates scaling factor is included for the PWS calculation. Additionally for all cases the Plate 1 test plate is kept static while the corrugation phase of Plate 2 (X2) is changed. Figs. 7 and 8 show lateral and normal total forces on Plates 1 and 2, for a full corrugation wavelength test plate. In Fig. 7, the test plate corrugation amplitude (A1) equals 8 nm, while in Fig. 8, the test plate corrugation amplitude is 59 nm. Though the lateral forces shown in Figs. 7 and 8 are not on top of each other as are the normal forces. They are none-the-less both similarly skewed (Fig. 8) or not skewed (Fig. 7) showing equivalence save for the additional scaling factor. This equivalence is quite extraordinary considering the differences in the calculation methods for the two approximations. Also to be noted is that the Plate 1 and 2 forces, lateral and normal, are equal and opposite. Fig. 9 show the total forces on Plates 1 and 2, both lateral and normal, when the test plate, is a half metallized corrugation wavelength with a corrugation amplitude of 59 nm. Fig. 10 shows the total forces on Plates 1 and 2, both lateral and normal, when the test plate, is a partially metallized corrugation from 0.1L to 0.9L, having a corrugation amplitude of 59 nm. The PWS and PFA calculated lateral forces shown in both Fig. 9 and Fig. 10 are not similar at all. While the PWS calculated lateral forces for Plates 1 and 2 are equal and opposite for all corrugation phases, the PFA calculated lateral forces show a PFA vector sum that is non-zero for most of the corrugation phase domain meaning that it is predicting an anomalous external force. The fact that the full wavelength plots for both lateral and normal forces shown in Figs. 7 and 8 as well as the plots for normal forces in Figs. 9 and 10 show equivalence means that the implementation of the approximations were correct and that the anomalous external forces evident for the plots of lateral forces in Figs. 9 and 10 cannot be summarily written off because the same mathematical methodology was used in all cases. Indeed the same Equations 8, 9, 11, 15 and 18 were used for the plots in Figs. 9 and 10 as were used for the plots in Figs. 7 and 8. The only difference being the use of different integration limits La and Lb.

7. Implications for Interstellar Travel 7.1 Intrinsic Acceleration

Insulator with low dielectric constant L Metallizin  Metallized surface g angle  Active part of z0 = p cavity d Metallized surface A Insulator with low dielectric constant

FIG. 11 CROSS SECTION OF A TYPICAL SAW TOOTH GROOVE WITH PARAMETERS Assuming that the external forces predicted by the PFA are true, one can construct a propulsion mass consisting of multiple grooves patterned after the sinusoidal plates in Fig. 9 having half metallized wavelength with the Plate 2 phase (X2) set to 0. Instead of sinusoidal plates however, saw tooth shaped grooves make constructing the propulsion mass much easier.

273 | P a g e

The lateral force for a typical groove can be derived directly from the PFA given the minimum distance between plates z0, which in the case of the saw tooth groove shown in Fig. 11 is assumed to be the same as the plasma wavelength p, and amplitude A. Groove lateral force can also be derived from the sinusoidal plates lateral force by making suitable transformations for amplitude and plate distance. The groove lateral force so derived is:

2 2 2  c  AA  3z0 A  3z0  FGrooveLatA, z0   Y  3 3 where Y is groove length. (19) 720 z0 A  z0  For a ‘back of the envelope’ calculation of a propulsion mass comprising, for lack of a better term, a force cell, assume that the amplitude A is 80 nm, the minimum distance between active parts of the plates z0 is 130 nm, the groove width L is 1000 nm and that the groove length Y is 1 cm. The propulsive force can then be computed for a 1 cm x 1 cm x 1 cm cube as follows: 3 -4 FProp / cm = [FgrooveLat = 1.5 x 10 dynes / (1 cm long groove)] x 10,000 grooves / cm x 5000 layers / cm = 7,500 dynes / cm3 Further assume that the 1 cm3 force cell has an average density of water, 1 gram / cm3, then: 2 FProp / gram = 7,500 dynes / gram = 7,500 cm / sec = 7.6 gE (where gE is an Earth gravity) which can be considered the intrinsic acceleration of the propulsion mass or force cell. Divide that number by 2 or 3 to account for corrections for conductivity and temperature and other sins and then a possible intrinsic acceleration available to propel a spaceship would be about 3.8 gE or 2.6 gE. 7.2 Making a spaceship

Our putative spaceship with mass MSpaceShip consists of propulsion mass MProp, and everything else - spaceship structure and payload, as shown in Fig. 12.

F = IntrinsicAcc [= 3.8 g or 2.6 g ] * M Prop E E Prop aSpaceShip = [3.8 gE or 2.6 gE] * (MProp / MSpaceShip ) MProp

MSpaceShip

FIG. 12 A CONCEPTUAL SPACESHIP With such an intrinsic acceleration it is possible to make a spaceship with an acceleration greater than one Earth gravity so that it can lift off from Earth and maneuver and still have a mass ratio that is favorable compared to rockets of today. Constant ratio of propulsion to spaceship mass means spaceship can be scaled to almost any size, from grams to metric tons

7.3 Trip times Assume that once outside Earth’s atmosphere the spaceship accelerates and decelerates at a constant one Earth gravity. Then a trip to the Moon, with a distance of about 380,000 km would take about 3.5 hours. A trip from Earth to Mars at its nearest (a distance of about 79 million km) would take about 2 days. A trip from Earth to Mars at its furthest (a distance of about 377 million km) would take about 4.5 days. A trip from Earth to Alpha Centauri (a distance of about 4 light-years) would take about 5 years Earth time, with a much shorter ship time because of time dilation. Such a mission would have a five year travel time with an additional four years for first data return, which would be equivalent to the New Horizons flyby of Pluto in 2015. While New Horizons was a flyby, the probe powered by Casimir force

274 | P a g e cells would be capable of exploring the entire Alpha Centauri system. Moreover, because of the constant ratio of propulsion to spaceship mass, the probe could be scaled to almost any size, from grams to metric tons. The performance of a spaceship powered by the quantum vacuum seems unbelievable, which is probably part of the reason why the hypothesis has never been experimentally tested. To the authors knowledge non-parallel discontinuous conducting plates have not been analyzed by a more exact technique [13, 14] that is consistent with radiation pressure [15] than the proximity force approximation, such as the technique outlined in the Milonni, Cook and Goggin paper of 1988 [11], let alone experimentally tested.

8. An Atomic Force Microscope Test of the Anomalous Forces

Photo Laser diodes Metallized surface Mirror Cantilever Mirror Cantilever Un-corrugated flat plate Sphere corrugations, half Sphere metallized saw tooth cantilever/sph x x x, y, z piezoere> x, y, z piezo

y Side View Detecting lateral forces Front z

Fig. 13 Conceptual setup of atomic force microscope to detect anomalous lateral forces

Fig. 13 shows the conceptual setup of an atomic force microscope to detect anomalous lateral forces. The setup is patterned after the Chen, Mohideen, et al experiment of 2001 [12], that successfully detected lateral forces between sinusoidally corrugated sphere and flat plates. The setup is designed to avoid false positives in that the lateral forces are observed through the up and down flexing of the cantilever and not the usual torsional rotation. The setup to detect anomalous lateral forces differs from Chen, Mohideen in that the corrugated sphere has grooves with a saw tooth cross section (shown greatly exaggerated in Fig.13) that are partially metallized on the smaller sloped portion of the saw tooth. Additionally the flat plate is un-corrugated because both PFA and PWS approximations predict zero lateral force on the flat plate when it is un-corrugated. Thus if there is any lateral force detected on the partially metallized grooved sphere, they are the result of an anomalous lateral force.

Conclusions The anomalous external lateral forces resulting from the PFA calculations for partially metallized corrugation wavelengths depend upon the reality of a number of assumptions. First, zero point fields must originate from the vacuum of space itself, which most researchers believe is true because of the predictions of quantum mechanics [3, 4, 5, 16]. It is not sufficient that the fields originate just from zero point fluctuations of the atoms and molecules of the bulk matter making up the plates. The energy source needs to be external to the plates in order for the system of plates to be an open system. Second, the radiation pressure assumption needs to be true for non-parallel plates and not just for parallel plates. Indeed, the PFA seems to be inherently consistent with a radiation pressure as was shown in Section 3.2. The PWS approximation, on the other hand, inherently assumes lateral and normal forces are equal and opposite, which is entirely appropriate for a system where the potential energy is internal to the plates. That model can never predict external forces without the assumption of external energy being pumped into the system [3].

275 | P a g e

Is the PFA prediction of external lateral forces for certain plate configurations necessarily wrong? It is after all based upon an approximation and both the PFA and PWS approximations have known deficiencies. As previously mentioned, the equivalence of results for other plate configurations argues against that conclusion. Moreover, the parameters used in the calculations were chosen so as to be in a regime where both the PFA and PWS approximation were applicable. According to a paper by Cole and Puthoff [17], extracting energy, in this case mechanical energy, from the vacuum does not intrinsically violate the conservation of energy. It also does not intrinsically violate entropy because while the energy outside the plates is random, the energy between the plates is less random because of the Casimir effect. Moreover, it is a testable and falsifiable conjecture and is therefore scientific. A negative result would strongly argue against the radiation pressure assumption, since it is the weaker of the two assumptions (vacuum origination and radiation pressure). It would certainly eliminate radiation pressure as calculated from the PFA. But is it possible for radiation pressure to be a valid mechanism for the Casimir effect and external forces not result? A positive result would be the dream of science fiction aficionados but it could also provide a new probe into the nature of the Casimir effect. It would also exacerbate the controversy regarding the nature of the quantum vacuum and the expansion of the universe. It is not necessary that if one of these models is true the other must necessarily be false. Indeed, both could be true because the PWS approximation requires a scaling factor to make it equivalent to the PFA. Indeed, while much is known about the Casimir effect, the fact that a popular approximation can predict anomalous external forces shows perhaps that there is yet much that is still unknown and not knowing is not the same as knowing not.

References [1] H. B. G. Casimir and D. Polder, “The Influence of Retardation on the London-van der Waals Forces,” Physical Review 1948; 73(4). [2] H. B. G. Casimir, “On the attraction between two perfectly conducting plates,” Proc. K. Ned. Akad. Wet. 1948; 51: 793-795. [3] G. J. Maclay, R. L. Forward, “A gedanken spacecraft that operates using the quantum vacuum (dynamic Casimir effect),” Foundations of Physics 2004; 34(3): 477-500. [4] A. Lambrecht, “The Casimir effect: a force from nothing,” Physics World, September 2002. [5] G. J. Maclay, “The role of quantum vacuum forces in microelectromechanical systems,” In: Krasnoholovets V., editor, Progress in Quantum Physics Research, New York, NY: Nova Science; 2003. [6] F. Pinto, “System for dispersion-force-based actuation,” US Patent 8,174,706 B2, 2012. [7] O. Kenneth, I. Klich, A. Mann, M. Revzen, “Repulsive Casimir Forces,” Physical Review Letters 2002; 89(3), 033001 [8] M. Tajmar, “Finite Element Simulation of Casimir Forces in Arbitrary Geometries,” Int. J. Mod. Phys. C 2004; 15: 1387-1395 [9] D. A. R. Dalvit, P. Neto, A. Lambrecht, S, Reynaud, “Lateral Casimir–Polder force with corrugated surfaces,” J. Phys. A: Math. Theor. 2008; 41: 164028 (11pp). [10] T. Ederth, “Template-stripped gold surfaces with 0.4-nm rms roughness suitable for force measurements: Application to the casimir force in the 20-100-nm range,” Physical Review A 2000; 62: 062104-1. [11] P. W. Milonni, R. J. Cook, M. E. Goggin, “Radiation pressure from the vacuum: Physical interpretation of the Casimir force,” Phys Rev A. 1988; 38: 1621-3. [12] E. Chen, U. Mohideen, G. L. Klimchitskaya, V. M. Mostepanenko, “Demonstration of the lateral Casimir force,” PhysRevLett 2002; 88(10): 101801. [13] A. Lambrecht, P. A. M. Neto, S. Reynaud, “The Casimir effect within scattering theory,” New Journal of Physics 2006; 8: 243.

276 | P a g e

[14] K. A. Milton, J. Wagner, “Multiple scattering methods in Casimir calculations,” J. Phys. A: Math. Theor. 2008; 41: 155402. [15] H. C. Chiu, G. L. Klimchitskaya, V. N. Marachevsky, V. M. Mostepanenko, U. Mohideen, “Demonstration of the asymmetric lateral Casimir force between corrugated surfaces in the nonadditive regime,” Phys. Rev. B 2009; 80, Issue 12, id. 121402. [16] M. G. Millis, “Assessing Potential Propulsion Breakthroughs”, Ann. N.Y. Acad. Sci. 2005; 1065: 441-461. [17] D. C. Cole, Puthoff H. E., “Extracting energy and heat from the vacuum,” Phys Rev E; 1993, 48: 1562-1565.

277 | P a g e

FIRST STOP ON THE INTERSTELLAR JOURNEY: THE SOLAR GRAVITY LENS FOCUS

Louis Friedman 1, Slava G. Turyshev2 1 Executive Director Emeritus, The Planetary Society 2 Jet Propulsion Laboratory, California Institute of Technology [email protected]

Whether or not Starshot [1] proves practical, it has focused attention on the technologies required for practical interstellar flight. They are: external energy (not in-space propulsion), sails (to be propelled by the external energy) and ultra-light spacecraft (so that the propulsion energy provides the largest possible increase in velocity). Much development is required in all three of these areas. The spacecraft technologies, nano-spacecraft and sails, can be developed through increasingly capable spacecraft that will be able of going further and faster through the interstellar medium. The external energy source (laser power in the Starshot concept) necessary for any flight beyond the solar system (>~100,000 AU) will be developed independently of the spacecraft. The solar gravity lens focus is a line beginning at approximately 547 AU from the Sun along the line defined by the identified exo-planet and the Sun [2]. An image of the exo-planet requires a coronagraph and telescope on the spacecraft, and an ability for the spacecraft to move around the focal line as it flies along it. The image is created in the “Einstein Ring” and extends several kilometers around the focal line – the spacecraft will have to collect pixels by maneuvering in the image [3]. This can be done over many years as the spacecraft flies along the focal line. The magnification by the solar gravity lens is a factor of 100 billion, permitting kilometer scale resolution of an exo-planet that might be even tens of light-years distant. The value of such an image would be enormous and is examined in this paper.

Key words: Gravity Lens Focus, interstellar precursor mission

1. Introduction

A mission to 500-1000 AU is a small fraction of interstellar flight, approximately 0.3%. Yet, its requirements are beyond current spacecraft state-of-the-art. A 50-kg spacecraft with a solar sail of 300x300 meters, capable of flying to 0.1 AU perihelion distance can reach 600 AU in 20 years and 1000 AU in about 33 years. Achieving this is a tall order: we do not have sails of this size, we do not have materials for this close a flyby of the Sun, and we do not have working smallsat (<100 kg) spacecraft for a 20-40 year journey. But meeting these requirements are necessary soon, if we are going to create even lighter spacecraft to capture the external energy which can enable interstellar flight. Other types of sails besides solar sails may also be considered – for example, e-sails, drawing power from the interaction of the solar and interstellar wind with charged wires on the spacecraft. Hybrid propulsion with sails and nuclear electric propulsion are also to be considered as is a new idea for laser electric propulsion since the spacecraft will likely require a small nuclear power source for operating hundreds of AU from the Sun. Studies are needed both for their cost-effective application to a solar gravity lens focus mission and their technology applicability as an interstellar precursor.

The solar gravity lens focus is the only destination in the interstellar medium (except for possible unknown rogue planets) that can serve as a milestone for interstellar flight. Beyond the heliopause

278 | P a g e

(~120 AU) there are no natural objects which have compelling science and mission goals. If we can operate a spacecraft on the focal line created by the solar gravity lens we can in principle provide high resolution images of an identified interesting exo-planet, one that might itself be itself a fundamental interstellar goal. Because the spacecraft technologies necessary to operate such a mission are those which must be developed for interstellar flight it also serves as a technology driver. These include laser communications, deep-space/long-lived power, autonomy and reliability over long flight times, precise attitude control and stability and the materials and thermal technologies for very close flyby of the Sun. Thus, a putative solar gravity lens focus mission is both a scientific interstellar precursor (imaging the identified potentially habitable exo-planet) and a technology precursor for interstellar flight. No other such precursor has been identified.

2. Rationale The question of life on other worlds is perhaps the key question of space exploration. The discovery of a huge number with huge diversity of planets around other stars strongly suggests that putatively habitable planets will be discovered soon, perhaps even with bits of data suggesting that there is extraterrestrial life. But even if there are such discoveries no telescope we can imagine construction on Earth or in the accessible solar system will be powerful enough to resolve or characterize life. For example the angular size of an Earth-sized planet at 4.5 light-years (the closest star) is of the order of one milli-arcsecond, which would require a telescope on Earth (or anywhere in the inner solar system) with diameter of tens of kilometers. And that would provide only a one pixel resolution!

Fortunately, nature provides an alternative – a natural lens with a magnification power at 1 micron wavelength of 100 billion and extreme angular resolution of one billionths of an arcsecond! It is the solar gravity lens (SGL) which focuses light from a distant planet or star at along a semi-infinite line emanating away from the Sun beyond 547 AU (Fig. 1).

Figure 1. Illustration of Solar Gravity Lens

A modest telescope equipped with a coronagraph could operate at the SGL’s focus to provide a direct high-resolution image and spectroscopy of an exoplanet. Because of the high magnification and tremendous resolving power of the SGL, the entire image of an exo-Earth is compressed by the SGL into a small region with diameter of 2 km in the immediate vicinity of the focal line [3]. While all currently envisioned NASA exoplanetary concepts aim at getting just a single pixel to study an exoplanet, a mission to the SGL focus opens the breathtaking possibility of direct imaging (at 103 × 103 linear pixels, or ∼10 km in resolution) and spectroscopy of an Earth-like planet up to 30 pc away, enough to see its surface features and signs of habitability. Such a possibility is truly unique and should be studied in the context of a realistic deep space mission.

To derive an image with the SGLF, including contributions from the Sun (the parent star will be resolved at the anticipated resolution), and zodiacal light. A conventional coronagraph would block just the light from the Sun, but here we want the coronagraph to transmit light only at the Einstein ring where the planet light would be. Imaging with SGLF will be done on a pixel-by-pixel basis. It is

279 | P a g e likely that we would have to conduct a raster scan moving the spacecraft in the image plane. For the light received from an exoplanet, each pointing corresponds to a different impact parameter with respect to the Sun, thus, one image pixel. Between the adjacent pointings (i.e., pixels) the impact parameter changes, bringing in the light from the adjacent surface areas on the planet. To build a (103×103) pixels image, we would need to sample the image pixel-by-pixel, while moving in the image plane with steps of 2 km/103 = 2m. This can be achieved, for instance, by relying on a combination of inertial navigation and 3 laser beacon spacecraft placed in 1 AU solar orbit whose orbital plane is co-planar to the image plane.

Considering the plate scale: with SGL, the image at the exo-Earth is reduced by a factor of ~6103, meaning the orbit of 1 AU becomes ~2.25104 km and orbital velocity of 30 km/s becomes 5 m/s. For comparison, the solar gravity accelerates the Earth at 6 mm/s2. Similarly, the imager spacecraft needs to accelerate at ~6 m/s2 to move in a curved line mimicking the motion of the exoplanet. If the telescope is ~103 kg, the force is 6 mN, which maybe achieved with electric propulsion. Whether it is feasible for interplanetary propulsion, electric propulsion maybe sufficient for maneuvering to sample the pixels in the Einstein ring needed for imaging.

The instrument should implement a miniature diffraction-limited high-resolution spectrograph, enabling Doppler imaging techniques, taking full advantage of the SGL amplification and differential motions (e.g. exo-Earth rotation). In fact, relying on the enormous amplification and angular resolution of the SGL, a mission to the SGLF should also do spectroscopic research of the exoplanet, even spectro-polarimetry. Ultimately, it will not just be an image of the alien world, but potentially a spectrally resolved image over a broad range of wavelengths, providing a powerful diagnostic for the atmosphere, surface material characterization, and biological processes on an exo-Earth.

Given that interstellar flight to an exoplanet is beyond any known capability in any reasonable time frame this may allow us to unambiguously determine and characterize life on a planet around anther star. Even if interstellar flight is proved feasible it is almost certain that its imaging and data return properties will be very limited, insufficient for life determination on a target exo-planet. In short: imaging a putative habitable exo-planet at the solar gravity lens focus is likely the most practical way we will ever be able to accurately see such another world. A mission to the SGL will enable a breakthrough in exploration of habitable or better yet inhabited planets – decades, if not centuries, before being able to visit them.

3. How Can We Reach the Focus → 547 AU? The Voyager spacecraft has gone the furthest and fastest exiting the solar system at a speed slightly more than 3 AU/year. It will not reach 547 AU until after the year 2400 – long past its operating lifetime. A study at the Keck Institute for Space Studies (KISS) in 2014-15 considered the question of faster missions to go deeper into the interstellar medium to explore it, Kuiper Belt Objects and perhaps reach the solar gravity lens focus (SGLF) [4]. A mission design using an Oberth maneuver (applying a Δv at perihelion) with a large solid rocket motor can provide a much larger exit velocity. Figure 2 (from the KISS Study) shows the exit velocity in AU/year as a function of the amount of Δv applied at perihelion (an Oberth maneuver) and the perihelion distance (from N. Arora in [5]). Applying this maneuver at low perihelion requires a significant heat shield. The system design sized for a SLS launch described in [5] provided a Δv=5.5 km/s at a perihelion of 3 solar radii (requiring heat shields totaling nearly 300 kg). The resulting exit velocity is ~13 AU/year.

280 | P a g e

Figure 2. Delta.V versus Solar Radii at Perihelion

Arora, Strange, Alkalai [5] expanded the consideration of ballistic trajectories to include multiple gravity-assists for missions encountering Kuiper Belt Objects on the way into the Interstellar Medium literally examining thousands of trajectories. The result was a highest exit velocity of about 14 AU/year – insufficient for a practical mission to the SGLF. They also considered hybrid designs with a solar sail deployed on the trajectory after the close solar flyby while still in the inner solar system, after jettisoning the solid rocket motor and heat shields. For the designs, they considered they found that that exit velocities near 18 AU/year might be possible.

John Brophy at JPL has studied electric propulsion to reach that distance and found that a two-stage SEP/NEP system, with 30 kW SEP and 20 kW NEP can achieve 20 AU/year in about 20 years flight time [6]. It requires a small nuclear reactor for the NEP and would take at least 40 years to reach 547 AU. Brophy is now studying a new concept; powering an electric propulsion spacecraft with a 100-megawatt laser (space based) to reach an exit velocity of 40 AU/year, enabling a flight time of about 14 years to 547 AU [7]. The use of a space-based 100 MW laser is a big assumption, but pales compared to the suggestion of the 50 GW laser in Starshot.

Friedman and Garber [8] first considered the SGLF as an interstellar precursor. They studied solar sail requirements to reach exit velocity speeds > 20 AU /year. The results are summarized in Figure 3. Garber has extended this analysis to consider the area/mass requirements to reach an exit velocity of up to 40 AU/year. His result (private communication) is given in Figure 4.

Sail area to spacecraft mass ratios of 900 m2/kg yield a speed of 25 AU/year, 30 AU/year requires A/m=1400 and 40 AU/year requires A/m= 2550. Since any spacecraft will need power – presumably a small radioisotope generator, we consider that radioisotope electric power (REP) thrusters can provide an additional boost to the solar sail spacecraft as well as propulsion for in-space maneuvers, such as midcourse navigation and maneuvers in the Einstein Ring to collect the image pixels. A JPL study 15 years ago [9] cited an Advanced Radioisotope Power System delivering 106 watts weighing 8.5 kg (~12.5 watts/kg). A system this small would be insufficient for boosting spacecraft velocity but might provide enough propulsion for small maneuvers and attitude control. Quantitative studies need to be done in a system design. N. Arora (private communication during the KISS study op. cit. estimated the REP boost might be as much as 20%, e.g. 5 AU/year. Albeit, likely with a heavier system.

281 | P a g e

Perihelion (AU) 0.2 0.15 0.1

30

25 20 15 10

5

(AU/YR) YEARS 10 AFTER VELOCITY EXIT 0 100 300 500 700 900

SAIL AREA TO MASS RATIO (M2/KG)

Figure 3. Exit Velocity with Sail Area to Mass Ratio

Exit Velocity (AU/y) vs. Sail area/SC mass (m2/kg) with perihelion =0.1 AU 50 40

30 20

10

0 0 500 1000 1500 2000 2500 3000 3500

Figure 4. Exit Velocity with Sail Area to Mass Ratio

Thus, a 200 x 200 meter sail might achieve a solar system exit velocity of 25 AU/year with a notional mass statement for this example of - 30 kg spacecraft bus; - 13 kg for REP system providing 100 watts of electric power and possibly a small maneuver capability. It remains to be determined if the REP system can be smaller, or can add to exit velocity with a propulsive boost - 1.6 kg sail whose density is on the order 0.04 g/m2 (equivalent to 0.25-micron polyimide or a possible sail on carbon nanotubes). Of note is an interesting analysis of possible carbon nanotubes sails for extremely fast space flight, possibly as high as 0.001c (63 AU/year) [10]. The solar sail numbers are promising, although it must be emphasized that the largest area to mass designs that ever been built is ~8 m2/kg; a long way below 900 or 1170 m2/kg. (For comparison purposes we note that JPL mid-1970s proposal for a Halley Comet Rendezvous Mission used a solar sail spacecraft with an area to ass ratio of 711 m2/kg,) Neither have any large sail areas been made with thickness <2.5 microns (one order of magnitude than that assumed above). Further study of practical solar sail sizes for a 20-30-year deep spaceflight and of the minimal mass for long-lived

282 | P a g e interplanetary spacecraft remains to be done. If the spacecraft mass can be smaller, the sail area will correspondingly decrease (the sail linear dimension proportional to the square root of the mass).

A new consideration for space-sailing is the electric sail (or E-sail) [11]. This uses the solar wind instead of solar pressure and long charged tethers to propel the spacecraft by the created electrodynamics force resulting from the electric tethers flying through the charged particles of the solar wind. The advantage of e-sailing is that the force drops off much more slowly than the r-2 law of solar photons energy, due to a current sheath enlargement partially compensating for the decrease in solar wind energy. Pekka Januhen, the originator of the concept, made a preliminary estimate of the size required to reach 550 AU in 25 years with a 50 kg spacecraft: 20 tethers, 10 km each (200 km of total tether length). But E-sails are entirely theoretical at this point and many details about materials and spacecraft dynamics need to be considered. It would also of course require a radioisotope electric power source.

One might ask about laser sailing – it is, after all, a necessary technology for interstellar flight. It would be desirable to have the interstellar precursor be a laser sail. Phil Lubin is comprehensively studying (and experimenting with) laser sailing, with the goal of producing an interstellar roadmap [12]. Figure 5 (presented by Lubin in the KISS study, op. cit.) shows that to achieve even 20 AU/year (~105 m/s) that the laser would require more than 100 GW with a telescope of 1km in order to propel a 10 kg spacecraft. This would be an interstellar precursor, but we do not want to wait for the long-desired (by some) but very problematical huge laser array. That same objection applies to the laser electric propulsion being studied by Brophy [7].

We conclude that solar sails are the only technology ready now to be considered for an interstellar precursor mission to the SGLF. Studies of E-Sail, and considerations of electric propulsion should continue, but no designs are practical now.

Figure 5 - Speed in m/s from Lubin [12); 105 m/s= approx.. 20 AU/year

283 | P a g e

4. What Do We Have to Do There? When we reach the SGLF we must continue to fly along the focal line for a flight time as long as it took us to get there, e.g. another 25 years. Images of the exo-planet will have to be constructed through a complicated de-convolution process of pixels sampled in the Einstein Ring around the focal line (cf. fig.1). That is the spacecraft will have to sample in a moving annulus some tens of kilometers in width while travelling at speeds ~25 AU/year. Tethering or electric propulsion could be used to perform raster-scanning with a spacecraft located >550 AU away. For an exo-Earth 30 pc away, the planet's image moves in a 45,000-km diameter 1-year orbit. Its image at the SGLF is 2 km in diameter. One way to scan the image of an exo-Earth is a spiral scan to follow the planetary motion using a 2-km tether and the RTG on the other end of it. This reduces the fuel requirement for raster scanning the image.

The relatively small amount of propulsion for such maneuvers cannot come from the sail (indeed, it may be jettisoned by then), but will have to come from the radioisotope power source being carried on-board. In addition the data will have to be communicated continuously back to Earth – likely with an optical system, although consideration of radio communication using the sail as an antenna remains to be done. A very high degree of stability and control will also be required.

Another approach for maneuvering in the Einstein Ring would be to have a sub-satellite to the main satellite to carry the camera and collect the pixels. The sub-satellite could be tethered to the main spacecraft or perhaps, as suggested by Darren Garber (private communication) electrostatic forces between the main spacecraft and the sub-satellite could be used with very modest power in this plasma-free area of the interstellar medium. This novel means of propulsion control (for the sub- satellite) should be studied.

Implicit in the mission design is the a priori identification of the exo-planet which is our imaging target. The spacecraft can only go to one solar gravity lens focus. Thus, from the outset, the building of multiple small spacecraft should be planned both for reliability and to enable missions to image different exo-planets.

Conclusions Ever since Galileo invented a telescope, astronomical telescope making has been an evolving discipline. The task of designing of a modern telescope is complex, involving consideration of materials, detectors, precision manufacturing, tools for optical and thermal analysis, and etc. The largest telescope so far is the European Extremely Large Telescope with aperture of 39.3 m that is currently under construction in Chile. A telescope with diameter of tens of kilometers in space is beyond our technological reach. Although very exciting, the SGL still needs a structure to support its use.

It remains to be determined just how complex will be the capturing and creation of exo-planet images using the solar gravity lens. It also remains to be determined what would be the cost of a mission to its focus. But if it does prove to be a feasible mission, there may be cost and science trade-off between remote sensing using the solar gravity lens and flying to, operating and returning data from an exo-planet in another star system. This is especially true if the most interesting exo- planet to explore happens not to be at the nearest star but perhaps somewhere further away. In any case, the first job is to simulate creating the image in the SGLF. This is being done by Turyshev in his current NIAC study. We plan to investigate spacecraft design questions of how to reach the extremely large regions outside the solar system, but the primary emphasis will be placed on the feasibility of mission operations in support of the primary science objectives – the high-resolution imaging and spectroscopy.

284 | P a g e

The solar gravity lens may offer a unique means for imaging exo-planets and determining their habitability. The requirements to use it to create such an image remain to be determined. A comprehensive study of a Solar Gravity Lens Focus mission is needed. Theoretical considerations are promising, both for getting there and for capturing high resolution images and spectra of potentially habitable exo-planet. The mission would be an interstellar precursor advancing technologies ultimately necessary for interstellar flight and investigating the chief objective of an interstellar mission: the questions of life on other worlds.

This work, in part, was performed at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

References [1] A. Finkbeiner, “Near Light-Speed Mission to Alpha Centauri”, Sci Am, March 2017 [2] S.G. Turyshev, B-G. Anderson, “The 550 AU Mission: A Critical Discussion”, Mon.Not.Roy.Astron.Soc. 341 (2003) 577-582, gr-qc/0205126 [3] S.G. Turyshev, “Wave-Theoretical Description of the Solar Gravity Lens Focus”, Phys. Rev. D 95, 084041 (2017); arXiv:1703.05783 [gr-qc]; Slava G. Turyshev, Viktor T. Toth, “Diffraction of electromagnetic waves in the gravitational field of the Sun”, arXiv:1704.06824 [gr-qc] [4] E. Stone, L. Alkalai, L. Friedman, “Science and Technology for Exploring the Interstellar Medium”, Keck Institute for Space Studies Report, 2015. [5] N. Arora, N. Strange, L. Alkalai, “Trajectories for a Near-Term Mission to the Interstellar Medium”, AAS 758, 2017 [6] J. Brophy, private communication [7] J. Brophy, “NASA Innovative Advanced Concepts Study”, in progress, 2017 [8] L. Friedman, D. Garber, “Science and Technology Steps into the Interstellar Medium”, IAC-14,D4,4,3,x22407 , International Astroanutical Congress 2014 [9] R. Medwaldt, P. Liever, “An Interstellar Probe Mission to the Boundaries of the Helisosphere and Interplanetary Space”, AIAA Space Forum, 2000 [10] S. Santoli, “Carbon Nanotube Membrane Solar Sails”, in Marulanda, Carbon Nanotubes, 2012 [11] P. Janhunen et. al., “Overview of Electric Solar Wind Sail Applications”, Proceedings of the Estonian Academy of Sciences, 2014, 63, 2S, 267–278 [12] P. Lubin, “A Roadmap to Interstellar Flight”, JBIS, 2016.

285 | P a g e

286 | P a g e

287 | P a g e

288 | P a g e

289 | P a g e

290 | P a g e

291 | P a g e

292 | P a g e

293 | P a g e