Electromagnetically Driven Fusion Propulsion

Anthony Pancotti John Slough, David Kirtley, George Votroubek, Christopher Pihl

IEPC 2013 MSNW LLC, Redmond, WA 98052 Why We Are Not on Mars Yet? Takes too long Costs too much

Safety Direct cost

Radiation exposure Operational costs Complexity Cancer risk Pre-deploy assets Bone & muscle loss Space assembly Mental fatigue Increased risk of critical failure Launch costs Large space structures Huge fuel Governmental support Mass Public interest Political Solution: New method of propulsion is needed Short trip time Reduced IMLEO

2 High (α) High Exit Velocity (Isp) Determining the Optimal Mars Mission Opposition-class Conjunction-class • short surface stay times at Mars • long-duration surface stay times • typically 30 to 90 days • 500 days or more • relatively short total round-trip mission times • long total round-trip times • 500 to 650 days • approximately 900 days • minimum-energy solutions for a given launch opportunity Both options are well outside the current permissible exposure limit of radiation*

Mission down design approach (1) shortest overall mission to reduce the associated human health and reliability Mission Architecture Goal risks (Short Trip Time) 90 Transit times to and from Mars (2) adequate time on the surface in which Adequate stay time (30+ days) to maximize the return of mission Single launch (130 MT IMLEO) objectives and science No pre-deployed assets (3) low mission mass, which, in turn, DRA 5 Payload mass (63 MT) reduces the overall cost and mission Full propulsive MOI & EOI complexity (Reduced IMLEO) Reusable spacecraft

“ideal mission does not exist”* 3 FDR offers the first realistic approach to fusion-based propulsion

Benefit Result Direct transfer of High efficiency, 1 fusion energy to the low mass engine propellant 2 solid propellant No significant tankage High exhaust Short trip time, 3 velocities (2000- high mass fraction 5000s Isp) Low IMLEO Magnetic insulated No significant physical 4 nozzle interaction Minimal thermal mass MIF’s Low energy Low mass (single launch) 5 requirements and greatly reduced cost Fusion energy yield Fundamental physics is 6 has been proven and understood demonstrated

4 210 day Round-trip (COPERNICUS)

Maneuver ΔV (km/s) ΔT (days) Near Body Simplified Near Body Simplified TMI 12.7 7.3 8.9 7.1 MOI 8.5 13.2 4.7 10.5 TEI 16.6 16.5 1.7 2.9 EOI 11.2 12 1.6 1.6 Total 49.0 49.0 16.8 22.1

TMI MOI TEI TOI

5 Spacecraft Scaling

Mission Assumptions Payload mass 63 MT Spacecraft mass 15 MT IMLEO ~130 MT Earth Orbital Altitude 407 km Mars park orbit 1 sol 250 x 33793 km Total Mission Time 210 days Stay Time 30 days

Mission 8000 COPERNICUS Architecture Design 6000 Propulsion Requirements 4000 Isp (s) Isp 5000 s 2000

Jet Power 36 MW 0 100 200 300 Specific Power 2.4 kW/kg Fusion Gain 6 Power System Scaling

Gain of 200

2.8 MJ Liner Energy at 45% coupling

6.2 MJ of Capacitors @ 2.5 kJ/kg STORAGE ENERGY

2.5 MT of Energy Storage

Solar panels have flown on 99% of all space mission. 36 MW Jet Power 180 kW of Input power OR 400 kW at Mars Gain of 200 200 W/kg

POWER SOURCE 500 W/kg to 1000 W/kg are speculated for the future Direct energy recovery from fusion reaction possible 2 MT of Solar Panels 7 PowerDiagram Flow 211 kW

Charging

Solar Panels

Power

MJ 2.8 Energy

6.2 MJ

Energy MJ 3.4 Thermal Loss

Recovery 4 MW Gain Fusion Frozen Flow 564 MJ

2 MW 36 MW Jet Power

Mass Budget

Mass Mission Fusion Spacecraft Component TRL Switches and cables equal to (MT) Dependent Dependent Spacecraft structure 3.4 4 X energy storage mass Propellant tank 0.1 5 X X FRC Formation 0.5 4 X Simple aluminum coil, but Propellant Feed 1.2 2 X Energy storage 2.5 7 X most likely composites with Liner driver coils 0.3 3 X We, Be, or Cu liners Switches and cables 1.2 6 X Solar Panels 2.0 8 X X Thermal control, 10% heat Thermal Management 1.1 5 X Nozzle 0.2 2 X rejection @ 1 kW/kg with a Margin (20%) 2.5 margin of 3X Spacecraft Mass 15 X X Crew habitat 63 X FRC formation based of lab Propellant 56 X X equipment Total Mass 134 X X Propellant Feed – roll of film Payload mass fraction 47% – ring formation and injection 1. Fairings, support structure, communication, data handling ACS, Batteries 2. Hardware responsible for formation and injection of Fusion material (FRC) 3. Capacitors (6.2 MJ @ 2.5 kJ/KG) 4. Electromagnetic coil used to drive inductive liner 20% Margin 5. Pulsed power electronic components need to charge and discharge capacitor bank 6. 180 kW @ 200 W/kg 9 Spacecraft Layout Considerations 1.6 m 36 caps 9 m 12 /ring 9.7 MT 4.8 m Propellant spool Packing Energy Storage Packing

5 m

45 m

10 210-Day Architecture Summary

61 MT payload 27 MT Isp = 5000 s 83 MT α = 2.4 kW/kg Jet power = 36 MW

Gain = 200 Spacecraft Mass = 15 MT

15 MT 134 MT FDR DRA 5.0 (NTP) 1 launch 9 launches 134 MT 848.7 MT (IMLEO) (IMLEO) (May 19, 2018) 210 days 1680 days Refuel, Re-crew for future missions Fusion Approach 1. Analytical

4 −12 2 4 3 −42 2 2 r0 fus 2.1E 10 0 vn r0 D 1.1 ×=τεπ〉σ〈×≅ 10 0 Tn 0 ε 3 vL 2 1 2 4 3 B0 3 E = LLL = Tkn3vM r000 =επ⋅ r0 επ 2 3 µ0

E fus −3 M L − 8/112/18 G ×== 1073.1 B0 = 103.4 EMx LL EL l0 2. Computational • 1D Liner Dynamic + Circuit • 3D Structural compression • (ANSYS) • Neutronics

3. Experimental Validation 12 FRC Fusion at MSNW

“Creation of a High Temperature Plasma through Merging and Compression of Supersonic Field Reversed Configuration Plasmoids” . Journal of Nuclear Fusion, 2011

• Fusion with this technique is proven • $5 M DOE-funded programs demonstrated high field compression of FRC to fusion conditions o 2.3 keV Deuterium Ions o >100 microsecond lifetimes of 1E22 plasma o >1E12 D-D neutrons created in this program o At only 1.2 Tesla! • FRC programs at similar size demonstrated >3 ms lifetime 13 Experimental

IDL Unity Gain Validation Experiment at MSNW

CAD rendering of the Foil Liner Compression (FLC) test facility at MSNW Picture of the FDR validation experiment construction now underway.

14 Experimental Results

400 400 0.6 ANYSIS Max R μs μs 0.5 Exp. R(30349) 40 cm Exp. R(30331) 0.4 Exp. R(30351) 410 410 ¼ Power 6 cm ANSYS Min R 0.3 1D Code R μs μs Aluminum Liner 0.4mm 0.2

Testing for code 20 kV Liner Radius (m) 420 420 0.1 μs μs Validation 840 μF 0 0 1 2 3 4 5 6 -4 Time (s) x 10 430 430 μs μs

440 440 200 μs μs 1-D model Discharge 30581 160 10.3 cm Linear extrapolation 450 450 5 cm Light-up from liner collapse μs μs 120 0.4 mm on axis 20 kV 460 460 80 μs μs 840 μF 40 Internal Magnetic Field (T) Field Magnetic Internal 470 470 μs μs 0 -10 0 10 20 30 40 50 60 Time (µsec) 15 FDR Validation Exp Mk III 5.5 cm, 5 cm, 0.6 mm, 20 kV, 840 μF Summary Mission Architecture Goal 90 Transit times to and from Mars Halfway through Phase 2 NIAC Single launch to Mars (130 MT IMLEO) • Mission Architecture No pre-deployed assets • Spacecraft Design 63 MT Payload mass Full propulsive MOI • Fusion Physics Full propulsive EOI • Analytical Reusable spacecraft • Computational • Experimental • 60 T measured Mission Assumptions • corresponds to 100-200 T Payload mass 63 MT Spacecraft mass 15 MT IMLEO 130 MT Earth Orbital Altitude 407 km Mars park orbit 1 sol Total Mission Time 210 days Stay Time 30 days

Propulsion Requirements Isp 5000 s Jet Power 36 MW Specific Power 240 W/kg Gain 200 17 The Fusion Driven Rocket is being developed by MSNW and The University of Washington

With Support from NASA’s Innovative Advanced Concepts 18 BACK-UP SLIDES

19 Anticipated Parameters from FDR Validation Experiment

FRC adiabatic scaling laws

In experiment, FRC radial and axial compressions would occur simultaneously

Final field similar to that achieved Initial FRC size, temp in several density and energy flux same as past FRC’s compression expts. Sub MJ FRC FRC lifetime Requires only

>> τdwell ~ 4 µs 33% bank eff.

• Final FRC parameters yield a fusion gain G = 1.6 (ML=0.18 kg Al) 20 Power Flow

Diagram

4 MW Thermal Loss Thermal 2 MW Frozen Flow Frozen 180 kW

Jet Power 6.2 517 36 MW MJ MJ Charging 2.8 MJ 3.4 MJ

Fusion Gain

Recovery Energy Field Reversed Configuration (FRC) Magnetic Field lines and Pressure Contours

r Be x = s s Bvac r rc rc L r =ε s R s SOL 2rs Ls z

Bvac Flux Conservation Bext = External measurements of B yield − x1 2 s FRC separatrix radius rs(z), FRC length Ls ⇒ volume, position, velocity Key B2 Equilibrium kTnP == ext Radial Pressure Balance 00 Simple cross-tube interferometric 2µ0 Relations: measurement with rs from yields 〈n〉 and T

1 Axial Pressure Balance 1−=β x2 2 s With above obtain plasma energy, Inventory, confinement times FRC equilibrium constraints and the diagnostic measurements that together with the equilibrium relations that are employed to determine the basic parameters of the FRC equilibrium 22 Fusion Based on Inductively Driven Liner Compression of the FRC The energy within the FRC separatrix at peak compression is dominated by plasma energy that is in pressure balance with the edge magnetic field B0, so that one can write: 1 4 B2 E = 2 = Tkn3vM r3 =επ⋅ 0 r3επ 2 LLL 3 000 µ 0 (1) 0

The zero subscript indicates values at peak compression where rs ~ r0 and 2 magnetic pressure balance (2n0kT0= B0 /2µ0).

Fusion energy produced in the FRC during the liner’s dwell time τD at peak compression: 4 − 4 − r 2.1E 10 12 2 vn r3 1.1 ×=τεπ〉σ〈×≅ 10 42 2 Tn 2 0 ε (2) fus 0 3 0 D 0 0 v L where n0 and T0 are the peak density and temperature, and where the liner shell dwell time at peak compression, τD, ~ 2r0/vL

23 Fusion Based on Inductively Driven Liner Compression of the FRC (cont.) The usual approximation for the D-T fusion cross section in this temperature range: 〈σν〉 ≅ 1.1x10-31 T2(eV) was also assumed. Pressure balance, together with expressions (1) and (2) yields for the fusion gain:

E M G fus ×== 1073.1 −3 L B = 103.4 − EMx 8/112/18 0 LL EL l0

where l0 (= 2r0⋅ε) is the length of the FRC at peak compression. The last expression is obtained from adiabatic scaling laws ⇒

2 2 5/4 5/2 − 5/1 L 0 0 ~~ BlrBE 00 and 00 ~~ Brl 0

to express G in terms of the liner kinetic energy EL and mass ML only. Fusion Ignition will amplify gain by large factor. It is estimated that the total fusion gain GF ~ 5-10⋅G. For a large margin of safety, it is assumed that: GF = 2.5G or, -7 1/2 11/8 GF = 1.1×10 ML EL 24 Comp - 1D Liner Code Source Free RLC Circuit Circuit Parameters R=3 mΩ Liner Parameters dI dL L=20 nH + dV r=0.41 m L=V I IR+ C=I 420 uF dt dt dt w=6 cm 40,000 V l=0.2 mm

) 9 2 x 10 changing 1 0.015 inductance 0 0.01

-1 0.005 Solved as 2 First Order equations Thickness (m) Thickness -2 0 0 1 2 3 0 1 2 3 Liner Acceleration (m/s Time (s) -4 Time (s) -4 x 10 • Various Current waveforms x 10 • Ringing ) 0.04

2000 Ω • Crowbar Phase change • Diode 0 0.02 Increasing • Magnetic flux diffusion Cross-section • Resistivity - ρ(T) Latent heat Liner resistance ( Liner Velocity (m/s) -2000 0 0 1 2 3 0 1 2 3 Time (s) -4 • Latent heats Time (s) -4 x 10 x 10 • Radiative cooling 1500 0.4 • Energy conservation 1000

0.2 500 Data for actual coil and Temperature (K)

Liner Radius (m) collector plate used 0 0 0 1 2 3 In Foil Liner Compression 0 1 2 3 Time (s) -4 Time (s) -4 x 10 (FLC) Test bed x 10 25 ANSYS Explicit Dynamics® Calculations  Three 0.4 m radius, 5 cm wide, 0.2 mm thick Aluminum liners converging onto T = 0 µs T = 120 µs a stationary test target.

 First 3D structure compression of metallic liner

 No gross instabilities were observed T = 40 µs T = 160 µs due to the structure rigidity of the material

 Forces are well beyond the plastic deformation limit of the material, resulting in a uniform compression T = 80 µs T = 195 µs

 Low internal energy from the liner compression which is different from plasma or thick liner compression

Liner behavior agreed very well with 1D Liner Code 26 FDR Spacecraft Layout

Solar Panels

Transit Liner/Propellant Habitat Spline Truss

Fusion Driven Rocket Energy Mars Lander Storage

Radiators The Fusion Driven Rocket

(a) Thin hoops of metal are driven at the proper angle and speed for convergence onto target plasmoid at thruster throat. Target FRC plasmoid is created and injected into thruster chamber.

(b) Target FRC is confined by axial magnetic field from shell driver coils as it translates through chamber eventually stagnating at the thruster throat

(d) Vaporized and ionized by fusion neutrons and alphas, the plasma blanket expands against the divergent magnetic field resulting directed flow of the metal plasma out of the magnetic nozzle.

Schematic of the inductively driven metal propellant compression of an FRC plasmoid for propulsion 28 Estimated Total Equivalent Doses

Current technology (210 days) Mars sortie mission (30 days stay) NTP/NEP (150 days) Long stay at Mars base (525 days) Fusion Driven Rocket (30 days)

Solid bars – calculation for spacecraft with a minimum shield (5 g/cm2 Al) Dashed bars – calculations for a thick shield (20 g/cm2 Al)

 The career limit is 400 mSv for a 25 year old for a 3% risk of fatal cancer  There is still great uncertainty as to what the actual risk is for long term low level exposure 29 Lindl-Widner Diagram with Magnetic Field Confinement Of the Fusion Alphas

FDR

The BR form of the L-W diagram. Ignition curves for different product BR. When the BR parameter exceeds the threshold value, the dT/dt > 0 region extends to infinitely small ρR and ignition becomes possible at any ρR. 30 Material Constraints with Inductively Accelerated Liners • The material properties relating to this resistive heating (electrical conductivity, melting point, heat capacity, etc.) can be characterized by a

parameter gM defined by the “current integral”: t m 2 2 = M AgdtI ∫0 I - current flowing through the material cross-sectional area A = w×δ, where w is the liner width and δ is the liner thickness.

2 • The driving force is simply the magnetic pressure (B /2µ0) applied over the surface area of the metal facing the coil when in close proximity to the driving coil. • The current can be related to the force through Ampere’s law which can be reasonably approximated as B = µ0I/w. One finds for the maximum velocity for a given shell thickness δ:

4 vm (m / s) = 2.5x10 δ Al (mm) − Alu minum 6061 4 vm (m / s) =1.6x10 δ Li (mm) − Lithium 31 ANSYS Maxwell® Calculations of the 3D Electromagnetic Fields B (T) R 8

• Solution for a 0.4 m radius coil driving a 6 cm wide, 0.2 mm thick Al liner. • The circuit was based on the capacitor bank currently available at the UW Plasma Dynamics Laboratory. • The spatial forces on the liner at various times and radii are calculated and used as input into the dynamic calculation similar to the one shown above. • Mutual interaction between coils and liners will also be investigated. 32 Magneto-Inertial Fusion Two Approaches Shell (liner) implosion driven by Bθ from large Liner implosion from j x B force between axial currents in shell. external coil and induced liner currents Foil Liner Compression FRC plasmoid Magnetic Nozzle

FRC Injector

MTF FDR Liner Driver System Issues: Advantages: • Extremely low inductance load difficult to drive • Large driver coil easy to power with ample (massively parallel HV caps and switches) standoff • Close proximity and electrical contact ⇒ major • Driver electrically isolated from liner and collateral damage with each pulse magnetically from fusion process • Small FRC must be formed close to implosion ⇒ • Large FRC can be formed external to implosion marginal B for ignition w injector destruction with abundant B for ignition • Only inefficient 2D compression possible ⇒ • Full 3D compression can be realized for requires much larger driver energy efficient compression and translation John Slough, David Kirtley, George Votroubek, and Chris Pihl, “Fusion Based on the Inductively-Driven 33 Lithium Liner Compression of an FRC Plasmoid”, 20th ANS TOFE, Aug 2012 Theoretical Validation of Key FDR Elements (peer reviewed papers)  Importance of 3D compression  Superiority of high β FRC target  Magnetic field limits thermal and particle loss - even with (cold) wall confinement and β > 1

 Ignition possible with magnetized plasma where ρR <<1 but BR > 60 T-cm.  Magnetic field well within range of larger FRCs.

 Method for producing 3D liner Fusion Based on the Inductively-Driven Lithium Liner implosions with stand-off Compression of an FRC Plasmoid  Generation of FRC plasma target with sufficient magnetization and John Slough, David Kirtley, Anthony Pancotti, Christopher Pihl, confinement for ignition George Votroubek (Submitted to Journal of Fusion Energy 2012)  Method for efficient conversion of plasma, radiation, and fusion energy in a manner that protects and magnetically isolates reactor 34 Initial Mission Studies

350 0.8 Fusion Assumptions: 0.7 • Ionization cost is 75 MJ/kg 300 Higher fusion gain • Coupling Efficiency to liner is 50% and longer trip times 0.6 250 0.5 • Thrust conversion ηt ~ 90% result in higher • Realistic liner mass are 0.28 kg to 0.41 kg 200 payload mass fraction 0.4 • Corresponds to a Gain of 50 to 500 0.3 • Ignition Factor of 5 Fusion Gain 150 0.2 • Safety margin of 2: GF =GF(calc.)/2 Paylod Mass Fraction

100 Mass FractionPayload 0.1

50 0 Mission Assumptions: 20 40 60 80 100 120 • Mass of Payload= 61 MT Trip Time (Days) • Habitat 31 MT 200 0.8 • Aeroshell 16 MT 0.7 • Descent System 14 MT 150 0.6 • Specific Mass of capacitors ~ 1 J/g 0.5 • Specific Mass of Solar Electric Panels 200 W/kg Burn time of ~10 days • Tankage fraction of 10% (tanks, structure, 100 0.4 is optimal

radiator, etc.) Total Gain 0.3 • Payload mass fraction =Payload Mass/Initial 0.2

50 Mass FractionPayload Mass Paylod Mass Fraction 0.1 • System Specific Mass = Dry Mass/SEP (kg/kW) 0 • Analysis for single transit optimal transit to Mars 20 40 60 80 • Full propulsive braking for Mars Capture - no Burn Time (Days) aerobraking Anthony Pancotti, John Slough, David Kirtley, Micheal Pfaff, Christopher Pihl, George Votroubek, “Mission Design Architecture 35 for the Fusion Driven Rocket”, AIAA 48th JPC, July 2012 Theoretical Validation of Key FDR Elements (peer reviewed papers)

• Demonstrated inductively driven liner compression

of Bz fields > 1 Mbar

• Demonstrated the stable formation, merging and magnetic compression of the FRC • FRC lifetime better than previous scaling

• Demonstrated successful FRC liner compression with a xenon plasma liner

Hope to publish in the near future! Experimental demonstration of fusion gain with inductively driven metal liners 36 Magneto-Inertial Fusion Best of Both Worlds

Solid stars signify fusion gain conditions w Ti = Te = 10 keV 1012 ICF electron thermal conduction

Plasma Pressure MFE Exceeds Material ICF Yield Strength 109 (ITER) MIF (NIF) (FDR) Plasma Energy (J) Stored Energy (J) Energy Stored 106

FRC Scaling Tokamak ITER89-P 103 1020 1022 1024 1026 1028 1030 1032 Plasma Density (m-3) ITER MFE Issues: NIF ICF Issues: . Enormous magnetic energy requires • Enormous storage energy (~400 MJ) due to Cryogenic Magnets very low driver efficiency . Low power densities leads to large scale, • Even with stand-off , reactor wall and is capital and development costs bombarded by primary fusion products . Devastating transient instabilities defy • Intricate and minute target with sub-nsec solution timing make for challenging technologies37 1D Liner Code: Maxwell® Data

-6 x 10 3 Data for actual coil and 2 collector plate used Total Inductance of coil with liner at various locations. Liner 1 In Foil Liner Compression inductance was determined

theoretically Coil Inductance (H) (FLC) Test bed 0 0 0.1 0.2 0.3 0.4 0.5 Liner Radius (m) -5 x 10 Physical Parameters 1.5

Description Value B avg Average Magnet field in the gap 1 B(I,R) = Circuit resistance 0.002 Ω between coil and liner divided Ic Magnet resistance 0.001 Ω by the current in the coil for 0.5 Circuit inductance 20e-9 H various liner locations 0 Density of liner (Al) 2710 kg/m^3 0 0.1 0.2 0.3 0.4 0.5 Width of liner 0.06 m Liner Radius (m)

Magnetic Field as funciton of and I R -7 Radius of coil 0.41 m x 10 6 Initial radius of liner 0.403325 m Accurate definition of resistivity of Solid-liquid Voltage 40,000 V 4 Aluminum based on NIST data. transition Capacitance 420 u F Data only went to 2000 K. Data 2 Liner thickness 0.2 mm was linear extrapolated out to vaporization temperature Resistivity (Ohms/m) Resistivity 0 0 500 1000 1500 2000 2500 3000 r=0.41 m Temperature (K) w=6 cm 38 l=0.2 mm 1D Liner Code Conservation of Energy

mc KE R+R+R+R=R T equivalent resistance value Resistance of the coil equivalent resistance need to remove value to remove the energy equal to Resistance of the circuit energy from the circuit ohmic dissipation equal to the kinetic (heating) of the liner energy gained by the 5 x 10 3.5 liner EKE 3 ETherm 2.5 E cap • Energy recovery 2 E coil • All thermal losses E 1.5 resist • drive current E Energy (J) 1 circ • inner field current Etotal 0.5 • Pressure balance of inner Einner field 0 Ecap and outer fields -0.5 0 1 2 39 Time (s) -4 x 10 Research Plan Technology Roadmap for the Fusion Driven Rocket

2015 2020 2025 2030

180 W/kg 300 W/kg 600 W/kg 1000 W/kg

Solar Power

Energy Storage 1 kJ/kg 2 kJ/kg Gain of 200 Charging Spaceflight Rep Rate > 0.01 Hz Shielding Gain of 40 R = 1 m Thermal Li Liner L EL = 3.5 MJ Rep Rate > 0.1 Hz FRC Formation Thruster with Nozzle Al Liner Magnetics Gain > 5 R = 0.4 m Milestones Propellant L EL = 2 MJ Concept Validation Experiments Gain < 1 ML = 0.38 kg Subscale Ground Demonstration Chamber/Nozzle RL = 0.4 m D-T Operation Rep Rate > 0.01 Hz EL = 0.5 kJ Full-Scale Ground Prototype ML = 0.18 kg D-D Operation In-Space Demonstration Mission Single Pulse FDR ENGINE Manned Mars Mission (Complete System) Phase I Phase II $10 M/year $50 M/year Manned Mars Spaceflight Program

Technology Game Changing NIAC Demonstration NASA Mars Flight Program Technology Development

TRL Mission Future Mission Studies

 Mars • Single launch to Mars (Opposition Class) • Mission refinement • Long Stay Mission (>500 day) (Conjunctive Class) • Single trip – on orbit assembly • Larger s/c (fuel launched separate) • Pre-deploy mission architecture • Classic DRA style with pre-curser cargo mission • Ultra-fast (30 day) transfers  Jupiter • Enter and exit gravity well • Moon mission  NEO • Sample return • Redirection?

41 Analytical Model (Fusion Side)

From action Integral constraint where RL= 1.2 m, w = 0.15m Min. ML required to trap fusion products: 0.28 kg Energy loss in ionization of liner (~75 MJ/kg)

For known Liner Mass a Drop off in Isp at low gains is due to Specific Impulse ionization losses is determined

Isp links fusion conditions with mission equations 42 Fusion Driven Rocket Engine

Main Compression Coils Shadow Shield Magnetically Insulated Expander

FRC Formation

Shock Engine Truss Absorbers Liner/Propellant Injector 43 Fusion Driven Rocket Engine

Main Compression Coils Shadow Shield Magnetically Insulated Expander

FRC Formation

Shock Engine Truss Absorbers Liner/Propellant Injector 44 Analytical Model (Mission side)

Rocket Equations MR = Mass Ratio ∆   V  Mf = Final mass   7 Equations gI 0sp M = Initial mass = eMR   7 Unknowns i MP = Pr opellant mass M = Structural mass Mi s MR = f = Frequency M f αcap = Specific mass of capacitors

αSEP = Specific mass of solar panels f PL += MMM S PSEP = Solar panel power i PL ++= MMMM PS

Isp from fusion conditions LP ∆= TfMM

Ein PSEP Delta V requirement as a function of Ms = + + MPL1.0 αcap αSEP trip time: Solution to Lambert Problem P E = SEP in f

 It is assumed that initially FDR employs solar panels for house keeping power  Eventually it would be derived directly from nozzle flux compression