sign in sign up
<<
Home , Pair production

NASA/CRw2001-211116 AIAA-2001-3361

f Production at a Potential Boundary

Michael R. LaPointe Ohio Aerospace Institute, Brook Park, Ohio

August 2001 The NASA STI Program Office... in Profile

Since its founding, NASA has been dedicated to CONFERENCE PUBLICATION. Collected the advancement of aeronautics and space papers from scientific and technical science. The NASA Scientific and Technical conferences, symposia, seminars, or other Information (STI) Program Office plays a key part meetings sponsored or cosponsored by in helping NASA maintain this important role. NASA.

The NASA STI Program Office is operated by SPECIAL PUBLICATION. Scientific, Langley Research Center, the Lead Center for technical, or historical information from NASA's scientific and technical information. The NASA programs, projects, and missions, NASA STI Program Office provides access to the often concerned with subjects having NASA STI Database, the largest collection of substantial public interest. aeronautical and space science STI in the world. The Program Office is also NASA's institutional TECHNICAL TRANSLATION. English- mechanism for disseminating the results of its language translations of foreign scientific research and development activities. These results and technical material pertinent to NASA's are published by NASA in the NASA STI Report mission. Series, which includes the following report types: Specialized services that complement the STI TECHNICAL PUBLICATION. Reports of Program Office's diverse offerings include completed research or a major significant creating custom thesauri, building customized phase of research that present the results of data bases, organizing and publishing research NASA programs and include extensive data results.., even providing videos. or theoretical analysis. Includes compilations of significant scientific and technical data and For more information about the NASA STI information deemed to be of continuing Program Office, see the following: reference value. NASA's counterpart of peer- reviewed formal professional papers but • Access the NASA STI Program Home Page has less stringent limitations on manuscript at http://www.sti.nasa.gov length and extent of graphic presentations. • E-mail your question via the Internet to TECHNICAL MEMORANDUM. Scientific [email protected] and technical findings that are prelimina D" or of specialized interest, e.g., quick release • Fax your question to the NASA Access reports, working papers, and bibliographies Help Desk at 301-621-0134 that contain minimal annotation. Does not contain extensive analysis. • Telephone the NASA Access Help Desk at 301-621-0390 CONTRACTOR REPORT. Scientific and technical findings by NASA-sponsored Write to: contractors and grantees. NASA Access Help Desk NASA Center for AeroSpace Information 7121 Standard Drive Hanover, MD 21076 NASA/CRm2001-211116 AIAA-2001-3361

Antimatter Production at a Potential Boundary

Michael R. LaPointe Ohio Aerospace Institute, Brook Park, Ohio

Prepared for the 37th Joint Propulsion Conference and Exhibit cosponsored by the AIAA, ASME, SAE, and ASEE Salt Lake City, Utah, July 8-11, 2001

Prepared under Cooperative Agreement NCC3-860 and SBIR Contract NAS8--98109

National Aeronautics and Space Administration

Glenn Research Center

August 2001 Acknowledgments

Funding for this research was provided through NASA SBIR Contract NAS8-98109 during the period April-November 1998.

This report is a formal draft or working paper, intended to solicit comments and ideas from a technical peer group.

This report contains preliminary findings, subject to revision as analysis proceeds.

Available from

NASA center for Aerospace Information National Technical Information Service 7121 Standard Drive 5285 Port Royal Road Hanover, MD 21076 Springfield, VA 22100

Available electronically at ht_: / / gltrs.gr¢.nasa.gov/GLTRS ANTIMATTER PRODUCTIONAT A POTENTIALBOUNDARY

MichaelR. LaPointe Ohio Aerospace Institute Brook Park, Ohio 44142

ABSTRACT curtailed by an inability to collimate the energetic . With the experimental discovery of the anti- Current production techniques rely on high- in 1955, attention turned to the use of proton- collisions between beam particles and target antiproton as an energy source for nuclei to produce particle and pairs, but spacecraft propulsion. The higher rest energy of inherently low production and capture efficiencies ren- the proton-antiproton pair yields 1877 MeV per der these techniques impractical for the cost-effective annihilation event, compared with 1.02 MeV released production of antimatter for space propulsion and other by - annihilation. Equally important, a commercial applications. Based on Dirac's theory of significant fraction of the proton-antiproton annihilation the field, a new antimatter production concept energy appears in the kinetic energy of charged is proposed in which particle-antiparticle pairs are cre- particles, 35 which may be collimated for direct thrust or ated at the boundary of a steep potential step formed by used to heat an expellant more effectively than electron- the suppression of the local vacuum fields. Current an- positron gamma radiation. Several antiproton-powered timatter production techniques are reviewed, followed rocket designs have been proposed over the past few by a description of Dirac's relativistic quantum theory decades, ranging from low thrust, high specific impulse of the vacuum state and corresponding solutions for pion engines to higher thrust, lower specific impulse particle tunneling and reflection from a potential bar- solid and gas core thermal rockets. 62° Recent modeling tier. The use of the Casimir effect to suppress local efforts have simulated the performance of magnetically vacuum fields is presented as a possible technique for confined hydrogen plasma engines heated by charged generating the sharp potential gradients required for proton-antiproton annihilation byproducts -'_24 and have particle-antiparticle pair creation. investigated antiproton-boosted fission reactions as a driver for an inertial confinement fusion rocket. 25"26 INTRODUCTION Although a number of potential antiproton propulsion Present chemical engines and electric propulsion concepts have been analyzed, their transition from theo- thrusters are well suited for near-Earth applications and retical design to experimental validation and practical robotic space flight, but advanced propulsion use has been constrained by the prohibitive cost of cre- technologies must be developed to enable fast piloted ating and storing the . The following section and robotic deep space missions. Of all the known discusses current antiproton production methods, and energy sources, none provides more specific energy outlines near-term prospects for efficient antiproton than the annihilation of matter and antimatter. The production and storage. energy released per kilogram of combined matter and antimatter is nearly 250 times the specific energy Current Antiproton Production Methods released in nuclear fusion, and over 8 orders of magnitude greater than the specific energy released in The two leading facilities for antiproton production and chemical combustion) The possibility of producing storage are the European Laboratory for Particle Phys- rockets using gamma rays from electron- ics (formerly CERN, the Center for European Nuclear positron annihilation was investigated over half a Research) in Geneva, and the Fermi National Accelera- century ago," but the efficiency of the engines were tor Laboratory (FNAL) in the United States. At the

NASA/CR--2001-211116 1 CERNfacility,protonsareacceleratedbya linearac- number of upgrades to the current facilities could be celeratorto50MeV(8x10-_:J),injectedintoabooster made to improve antiproton production and storage ringandacceleratedto 800MeV,andthensentto a capabilities. Magnetic fields produced by electric cur- protonsynchrotron,wheretheyarefurtheraccelerated rents flowing through the metal wire targets could be to26GeV.Thehigh-energyprotonsarethenfocused used to keep the spray of antiprotons closer to the target intoa2-mmbeanaanddirectedintoa3-mmdiameter, axis, reducing their angular spread. Multiple targets 1l-cmlongcopperwiretarget.Therelativisticprotons could be employed, with magnetic lenses used to refo- collidewith thetargetnuclei,producinga sprayof cus the antiprotons between each section. Angular cap- gammas,pions,kaons,andbaryons,includingantipro- ture efficiencies could be improved by going to higher tons.Onleavingthetarget,theantiprotonshaveapeak beam , creating a forward-peaked distribution momentumof 3.5GeV/c,correspondingto apeaken- that allows more antiprotons to be captured. Material ergyof roughly3GeV. A shortfocallength,pulsed lenses could be replaced with current-carrying plasma magnetichornisusedtocaptureantiprotonsthathave lenses, which are less likely to absorb the antiprotons momentawithin1.5%of theirpeakvalue,atanglesup and would not need active cooling. Using linear rather to 50 mradfromthetargetcenterline.Thecaptured than synchrotron accelerators to produce the initial antiprotonsaresenttoastorageringin burstsof about high-energy proton beams could increase the accelera- 10 7 antiprotons every few seconds, and around 10 I1 tor energy efficiency by an order of magnitude over the antiprotons can be accumulated before space charge current 5% wall plug efficiencies. effects scatter the circulating beam. The antiprotons are sent back to the proton synchrotron, which decelerates Taken together, the potential facility improvements them to an energy of 200 MeV, and then to the low could result in the yearly production and storage of mi- energy antiproton ring, where the circulating beam is crogram quantities of antiprotons at a potential cost 27 of further decelerated, stochastically cooled, and stored. around $6.4x106/_g ($6.4xl09/mg). While these pro- Similar techniques are used to create antiprotons at duction numbers and costs are approaching those re- FNAL. quired for ground testing antimatter propulsion con- cepts, they are not adequate for antimatter-based pro- During the high-energy collisions, approximately one pulsion systems. Forward 1"2°calculates that antiproton antiproton is created for every 105-106high-energy pro- propulsion becomes cost competitive with chemical tons incident on the target. The energy efficiency, de- propellant systems at an antiproton production cost of fined as the energy released in a proton-antiproton an- approximately $107/mg, and antiproton propulsion be- nihilation event (1.88 GeV at rest) divided by the en- comes the most cost effective propulsion source avail- ergy required to create an antiproton, is abysmally low. able if the production costs can be lowered to On average, CERN creates 1 antiproton for every $2xl06/mg. Because the near term facility modifica- 2.5x106 ; at an average energy of 26 GeV per tions outlined above are unlikely to produce the neces- proton, the corresponding energy efficiency is ap- sary reduction in antiproton production costs, a number proximately 3x10 8. FNAL, which uses a 120 GeV of alternative antiproton production techniques have proton beam to strike the target, creates 1 antiproton for been suggested. Chapline 2s has proposed colliding every 3.3x 104 protons, corresponding to an energy effi- heavy ion beams, made up of singly charged uranium ciency of around 4x10 7. Assuming a "wall-plug" effi- atoms, to produce up to 10t8 antiprotons/sec. Unfortu- ciency for each accelerator of around 5%, the total anti- nately, the antiprotons will be emitted isotropically and proton production efficiencies are roughly 1.5x10 "° for will be very difficult to collect. Equally problematic, CERN and 2x10 -8 for FNAL. The total annihilation the colliding heavy ion beams will produce a significant energy contained in 1-mg of antiprotons (roughly amount of nuclear debris and radiation, which would 6xl02° antiprotons) is 1.8x1011 J; an efficiency of have to be safely and efficiently removed from the 1.5x10 -° means that it would take nearly 1.2x10 :° J spray of antiprotons. Cassenti '9 has suggested that the (3.3x10 t3 kW-hr) to create 1 mg of antiprotons. As- pions generated during the collision of high-energy suming a conservative energy cost of $0.05/kW-hr, the protons with heavy target nuclei could be redirected estimated production cost is a staggering $1.6xl0 H per toward the target to increase the number of antiprotons milligram of antiprotons. Most antimatter propulsion and improve the efficiency of current antiproton pro- concepts require milligrams to grams of antiprotons, duction techniques. Although promising, the collection indicating that current antiproton production techniques and redirection of the pions and antiprotons remains a are inadequate for future spacecraft propulsion applica- major challenge to this concept. uons.• However, as discussed. by Forward 1 a nd Schmidt et aL, 27 neither CERN nor FNAL were designed as Hora 3° proposed the use of a high intensity laser that dedicated antiproton production facilities. As such, a could generate sufficiently strong electric fields to

NASA/CR--2001-211116 2 V produceproton-antiprotonpairsfromthevacuum,and Crowe3j separatelyproposedtheuseof highintensity lasersto produceelectron-positronpairs. At present, however,therearenoknownlasersthatcanproducethe ;mo C2 highintensityelectricfieldsneededforpairproduction. Forward1"2°andHaloulakosandAyotte32haveinvesti- gatedthepossibilityof buildingand operating an anti- 2 proton factory in space, where the proton accelerator :-moc could be powered by solar energy. However, the esti- mated cost to produce and store the antiprotons is still nearly $109/mg, which is a factor of 102 too high for :? cost-effective space propulsion applications. 32

Rather than rely on high-energy proton beam collisions Figure 1. Energy Levels of the with a stationary target, this paper outlines a new con- cept that may lead to the more efficient production of More generally, in Dirac's theory the vacuum repre- antimatter in quantities sufficient for propulsion and sents a continuum of negative energy states occupied by other commercial applications. The proposed technique negative energy particles. Pair creation is the process in is based upon particle-antiparticle pair production at the which sufficient energy is given to a particle in the steep potential boundary created by the suppression of negative energy state to raise it to a positive energy local vacuum field energies. The premise is based on state (creating a real panicle and leaving behind a hole, Dirac's relativistic theory of the vacuum state, which is or antiparticle); annihilation occurs when the particle outlined in the following section. The theory underly- falls back into the hole, with the energy carried away as ing particle-antiparticle pair creation at a potential radiation. The vacuum itself should have zero energy, boundary is discussed, followed by an explanation of zero mass, and no charge, which is clearly not satisfied the technique proposed to create the required potential by the simple form of the theory. Instead, there are step. The paper concludes with an overview of an ex- infinitely many negative energy states, which together perimental approach designed to demonstrate the feasi- have an infinitely large negative energy, and, in the bility of this new antimatter production concept. case of populating the negative energy con- tinuum, an infinitely large negative charge. These dif- DIRAC'S THEORY OF THE VACUUM STATE ficulties are removed by renormalizing the zero point of charge and energy in such a way that the vacuum has Dirac was the first to develop a relativistic wave equa- no mass, energy, or charge. This renormalization proc- tion that correctly describes the interaction of spin-l/2 ess is not pleasing from an aesthetic viewpoint, but it panicles, such as electrons and protons. 33 Dirac's equa- does satisfy the constraint that only departures from the tion contains both positive and negative energy solu- vacuum state are observable and hence relevant. tions, the latter identified with the continuum energy of the vacuum state (Fig. 1). As defined by Dirac, the vac- TUNNELING AND POTENTIAL BARRIERS uum state is characterized by the absence of all real electrons in positive energy states, but has electrons Related to Dirac's theory of the vacuum is the quantum filling all negative energy states (the "Dirac sea"). Be- mechanical process of particle tunneling in the presence cause of the Pauli exclusion principle, real electrons of a steep potential st_p. An overview of this process is cannot transition into negative energy states since all provided by Greiner, the salient features of which are such states are already occupied; however, an electron given here. in a negative energy state can absorb radiation and tran- sition to a positive energy state, leaving behind a "hole" Consider a spin-l/2 particle (for example, an electron or in the negative energy continuum. The hole behaves proton) with energy, E, and , p, traveling like a positive electron and represents the antiparticle of along the z-axis (Figure 2). The particle encounters a the electron. The creation of an electron and an an- step potential of magnitude V0 that rises to full value in tielectron (positron) is identified as pair creation and a distance equal to the Compton wavelength of the par- requires a minimum energy of 2moC 2. Pair annihilation ticle, _,_: occurs when an electron drops back into the (unoccu- h pied) hole, with the resulting transition energy emitted _ =-- (1) as radiation. moC

NASA/CR--2001- 211116 3 whereh is Planck's constant (6.626xi0 34 J-s), mo is the particle rest mass, and c is the . 0 Iffl = A pti c exp (7) E + m0c 2 V o II 0

i ":?i...... where A is a constant and the particle momentum, p,, is given by: E Plc 4E 2 -- m o-"C 4 (8)

At the potential boundary, part of the particle wave will be reflected and part will be transmitted. The reflected Z v wave solution in Region I is: Figure 2. Particle incident on a potential step.

0 " _

The Dirac equation describing the propagation of the _;=B. -p_I c expL n j (9) particle in Region I is: E + ,moC2 0

3 q_ hc 3 3 3 _ , and the transmitted solution in Region II is: ot ki k ox "ox ox ) 1 where _ is the particle wave function, h is the reduced 0 (h/2n), Hs is the Hamiltonian, andr,/_ YJ. =D -p2c exq ] ,,0, are the standard Dirac matrices. Noting that the Vo -E-moc:1 momentum operator/j is given by:

where again B and D are constants. The particle mo- mentum in Region II is given by: _ hc( a a +& a +a a ]_hv (3) P=T[ '_x' -_ _7)-7 p2c=4(E-Vo) _ -moc 4 (11) the Dirac equation can be written in the more compact The incident and reflected wave functions must equal form: the transmitted wave function at the step boundary (z=0): ,,, q',l:=0 + _,l:=0r =vz,/l:=o (12) The Hamiltonian for Region I (zero potential) is the from which the following conditions are obtained for total particle energy, E, while in Region II the Hamilto- the coefficients A, B and D: nian becomes (E-V0). The Dirac equation for a particle wave traveling along the +z direction in Region I is A+B=D (13) then:

[c(a3. _,)+ fimoc2]ll/= Elff (5) A-B;-D p'( E+m°c2 ] ] (14) In Region II, the Dirac equation for the traveling parti- cle wave becomes: =-D_ I(Vo(vo _- E_mocZE + moc 2_(E_mocZXE + moc: I =-Dy

[c(6/3 • _,)+ l_moc2]qt=(E-Vo)v (6) where _,is defined as:

The solution for the particle wave function in Region I (15) is:

NASA/CR--2001-211116 4 Uponrearrangement,Equations13and14yield: __ = _ Vo _oc 2 DD* Y

DD* 2p'-c2 ] -_=_l--_y) (16) ] E + moc- (24) Dividing Equation 14 by the coefficient A and substitut- ing Equation 16 for (B/A) yields:

D 2 (17) A 1-y For a potential step V0 > (E+m0c2), the value y>i. From Equation 23, this indicates that the reflected par- The particle current j is defined to be: ticle current exceeds the incident particle current in Region I dJlq>lJtl)- It appears that electrons are entering j(z) =clg *(z)a_(z)^ (18) Region I from Region II, but there are no electrons ini- tially present in Region II. This result, known as where _ut(z) is the adjoint of _(z). The values of lif t& Klein's Paradox, is most often interpreted as particle- in Region I are: antiparticle pair creation at the potential boundary.

Discussion of Results. _g_a_ = A* p_c ,0,1 exp • ^ I0, E+m0 c2 /) L n j Applying a potential V0 > E + m0c 2 raises the energy in Region II sufficiently for there to be an overlap be- lffla 2 = A* p__c (19) tween the negative energy continuum (z>0) and the E + moC" positive energy continuum (z<0), as shown in Figure 3:

I_rlt_t ^ 3 = A* pjc ,0,1,0 exp (E+moc: I) L n j from which jb the incident particle current in Region I, is: .) 2 Jl =-AA" "PlC (20) E + rno c2

Similarly, the reflected (.j[) and transmitted (Jn) particle currents are: E Jl.r = -BB" 2p_c- E +mo cz (21) mo c2

jo = DD,I Vo --2p,E- c2moc2 I (22) -moe _

Equations 20-22 can now be used to calculate the re- flection and transmission coefficients for the particle wave function impacting the potential boundary. Tak- ing the ratio of the reflected current to the incident par- Figure 3. Energy Continuum of the Dirac Equation at a ticle current yields: Potential Barrier. 34 (x) = particle, (o) = antiparticle

When V0 > E + m0c", the particles striking the barrier from the left are able to knock additional particles out J; E + moc 2" BB" B 2 _ (1+ ),)2 (23) of the vacuum on the right, leading to an antiparticle current flowing from the left to the right in Region II E--+moc--_" and a particle current flowing from right to left in Region I. This pair creation is depicted schematically The ratio of the transmitted current to the incident cur- in Figure 3, with the additional particles entering rent is given by: Region I from the right accounting for the increase in

NASA/CR--2001-211116 5 returncurrent.Asnotedby Greiner,34thisprocessis mostreadilyunderstoodasparticle-antiparticlepair creationat thepotentialbarrierandis relatedto the decayof thevacuumin thepresenceof supercritical I lI " fields.WhenthepotentialfunctionV0islessthanE + moc",theparticlemomentumin RegionII isimaginary moc 2 (Eq.11)andthewavesolutionwill beexponentially damped(Eq.10);all of theincidentcurrentis then _ -mo c2 reflectedbackintoRegionI, andnoparticlecurrentis -_l "U° transmittedintoRegionII. It isonlywhenV0> E + E _. --m---m- m0c2thatthemomentumin RegionII becomesrealand _Uo+moC_ 1-'-_ theparticlewavefunctioninRegionII againbecomesa travelingwave. _Uo_moc2_.,- Theabovederivationsmaybesummarizedasfollows: • TheDiracequationisusedtorepresenttheevolu- tionofspin-l/2particlewavefunctions. • Dirac'sequationpermitsbothpositiveandnegative Figure 4. Lowering the vacuum energy via the Casimir energysolutions;thenegativeenergystatesare effect. filledwithvirtualparticles,whichpreventparticle transitionsfrompositiveenergystatesto negative energystatesviathePauliexclusionprinciple. • Particleswillbecompletelyreflectedfromapoten- VACUUM FIELDS AND THE CAS1MIR EFFECT tial barrier(¥0)whentheirenergyE < Vo;the transmittedparticlewavefunctionisexponentially Dirac's vacuum is a negative energy continuum popu- dampedwithinthepotentialbarrier. lated by particles that prevent positive energy particles • ForpotentialstepswithV0> E+ rn0c2,anincident from transitioning into the negative energy states. To particlewill inducepaircreationat thepotential avoid obvious problems associated with infinite vac- boundary,resultingin a (real)returnparticlecur- uum charges and energies, the vacuum state is renor- rentanda(real)transmittedantiparticlecurrent. malized to zero; only deviations from the vacuum state are measurable. As such, the potential step shown in Thequestionnowarisesasto whetherthiseffectcan Figure 3 represents an applied field measured with re- actuallybeappliedtotheproductionofantimatter.The spect to the background vacuum; the energy in Region potentialstepmustbegreaterthanE+ moc2, where E is II has been raised by the applied field such that the the total particle energy (rest mass plus kinetic), and the negative energy states now overlap the positive energy potential must rise to its full value over a distance com- states in Region I. However, raising the background parable to the Compton wavelength of the particle, vacuum in Region II requires a tremendous amount of h/(moc). For an electron, the minimum potential step energy (V0>E+m0c 2) over a very small distance, which height is 1.02 MeV (plus the kinetic energy of the elec, is clearly beyond present capabilities. Rathe r than .rais- tron), and the Compton wavelength is approximately ing the vacuum energy in_Region ffl _it _s proposedtha t 2.4x10 -12 m. For a proton, the minimum potential step the same effect can be generated by suppressing the height is 1876 MeV and the Compton wavelength is relative vacuum energy in Region I, as shown in Fig- approximately 1.3x10 16 m. These supercritical poten- ure 4. This process can be viewed either as lowering the tials are too large to be generated over such short dis- positive energy states such that they now overlap with tances using laboratory electric fields, but there may be the negative energy states in Region ii, or the back- another option: rather than use externally applied fields ground vacuum in Region I can be renormalized to zero to raise the vacuum energy in Region II, it may be pos- to yield an energy diagram similar to Figure 3. in either sible to use the Casimir effect to lower the vacuum en- instance, a particle wave traveling from Region I into ergy in Region I. This concept, shown schematically in Region II will be described by the same Solutions out- Figure 4, may be able to produce the same pair creation lined in the section above, leading to particle- effects depicted in Figure 3 without requiting the appli- antiparticle pair creation at the potential boundary. cation of supercritical external fields. A brief discus- Unlike Figure 3, pair production is achieved not by sion of the Casimir effect is provided below, followed raising the potential but by lowering the relative vac- by an outline of a possible experimental test of the pro- uum energy, an effect that might be accomplished posed antimatter production mechanism. through the use of a Casimir cavity.

NASA/CR--2001-211116 6 BeforediscussingtheCasimireffect,it shouldbenoted constitutes a force of attraction, F, per unit area, given thatDirac'sinterpretationofthevacuumasacontinuum by: F ! dUt. hc of negativeenergystatesoccupiedbynegativeenergy A L-" dr. z4 (26) particles,thoughsomewhatdated,is notin disagree- mentwiththecurrentquantumelectrodynamic(QED) A more careful analysis leads to the exact relationship interpretationof thevacuumasaninfiniteseaof elec- for the force per unit area between the parallel conduct- tromagneticradiationpopulatedwith virtualparticle ing plates: 39 pairs.Becauseexchangeinteractionsoccurin Dirac's F /r 2 hc theory,virtualelectron-positronpairsarecontinuously A 240 z.4 (27) createdandannihilatedin thevacuum;anelectronin a boundorfreestatecanfill a virtualholein theDirac In other words, the vacuum energy density between the sea,withavirtualelectrontakingitsplace.Renormali- plates is lower than the vacuum energy density outside zationof thevacuumenergyandchargeis required the plates by an amount equal to the right hand side of bothin Dirac'soriginaltheoryandin QED,andas Equation 27. For reasonable plate sizes and small notedby Greiner,34thephysicalcontentof theDirac separation distances, the change in the vacuum energy theoryformsthebasisof currentquantumelectrody- density can be appreciable. Assuming the plates have namics.ThisismentionedbecausetheCasimireffectis length L=0.1 m and are separated by a distance of l-gm generallydiscussedin termsof theQEDinterpretation (10 nm), the change in the vacuum energy density is ofthevacuumstate,andit isnecessarytopointoutthat approximately 1.3x10 -_ J/m 3, corresponding to an boththeDiracandQEDvacuuminterpretationsare inward pressure of 1.3x10 -4 N/m-" on the plates. For a complementary. separation distance of 0.1-1am (10 -7 m), the change in the vacuum energy density is equal to 1.3 J/n'l 3, The Casimir Effect corresponding to an inward pressure of 1.3 N/m". The calculations can be carried down to separation distances As in the Dirac theory, the vacuum state in quantum that are approximately equal to the cut-off wavelength of the conducting material, at which point the plates can electrodynamics is interpreted to be the state of lowest no longer be considered good electromagnetic energy. This lowest energy state is not at rest, but fluc- reflectors. tuates with a "zero-point" energyY 39 The vacuum fluc- tuations have measurable effects, including the experi- mentally observed Lamb-Retherford shift between the s Equations 26 and 27 demonstrate that the vacuum en- and p energy levels of the hydrogen atom, and the at- ergy density between the conducting plates is lower than the external vacuum energy density. Multiplying tractive Casimir force that occurs between closely Equation 27 by the plate surface area (L 2) and the sepa- spaced uncharged conductors. As discussed by Moste- panenko et aL, 35 the Casimir effect can be accounted ration distance between the plates (z) yields an expres- for by assuming the force is a consequence of the sepa- sion relating the decrease in the vacuum energy be- tween the plates compared to the external vacuum field ration-dependent vacuum field energy trapped between energy: the conductors. For example, assume that two square rc2 hcL 2 conducting plates with side dimensions L, separated by AE_ac - 720 _3 (28) a distance z, are placed in a vacuum. In the QED inter- pretation, the vacuum is teeming with electromagnetic For square plate dimensions of L = 0.1 m and a separa- radiation (although mathematically the vacuum state is tion distance of 0. l-lam, the change in vacuum energy is renormalized to zero), hence the plates may be consid- calculated to be 4.3x10 9 J, or roughly 2.7x10 l° eV (27 ered to constitute a cavity that supports vacuum fluctua- GeV). The vacuum energy between the plates is thus tion modes with wave numbers down to about z-1. The substantially lower than the vacuum energy external to vacuum energy trapped between the plates is approxi- the plates, or conversely, if the vacuum energy between mately given by: the plates is renormalized to zero, the vacuum energy external to the plates is substantially higher than the U : hw = (L-z) hckk2dk ---1L2hc[zK4 _:-3] ±l i vacuum energy between the plates. By adjusting the _ 2 _, 4 (25) plate dimensions and separation distance, it may thus be 2 = Uu _ UL possible to significantly suppress the vacuum energy in a given region and generate a condition similar to that where Uv is the upper energy bound, UL is the lower shown in Figure 4. A particle generated in the sup- energy bound, and K represents a high frequency cut- pressed vacuum fields of Region I will see a higher off to make the total energy finite. The negative rate of vacuum field energy outside of the plates, and if the change of the lower cut-off energy UL with separation z relative change in the vacuum energy exceeds E+moc 2,

NASA/CR--2001-211116 7 it may be possible to generate particle-antiparticle pairs Equation 32 expresses necessary conditions for a flat at the vacuum energy step. Because the Dirac solutions parallel plate geometry to form a sufficiently steep po- hold equally well for electrons or protons, the possibil- tential gradient for particle-antiparticle pair production ity exists that low energy proton-antiproton pairs might to occur. For electrons, this condition can be written: be created at the steep potential boundary created by L-_ vacuum field suppression in a Casimir cavity. s----z ff ---1.56x 1026(m --_) (33)

Creating a Potential Gradient Assuming a plate separation distance z = 10-7 m and a gradient length d = 10"6m, the required plate area, L-', is The Casimir effect provides an avenue for creating suf- around 0.156 m-'; for square plates this corresponds to a ficiently large potential steps, but the question arises as side length of approximately 0.4 m. Plates of this size to whether these steps can be generated over a distance and flatness are well within current manufacturing ca- comparable to the Compton wavelength of the particle. pabilities, offering some encouragement for experimen- From Equation 1, the Compton wavelength for elec- tal verification of the proposed concept. For protons, trons is 2.42x10 12 m, while for protons the Compton L: wavelength is 1.32x10 _5 m. Either distance is several 3----z ff 5.26x10 -(m ") (34) orders of magnitude smaller than any realistic plate thickness separating the interior and exterior vacuum Using the same plate separation and gradient distances fields, hence typical fiat plates will not provide a suffi- above would require a plate length of 725 m to provide ciently steep potential step for pair creation to occur. a suitable potential gradient. However, a number of Casimir force experiments have been performed over A possible solution to this dilemma is to create a suit- the past several years with plate separations down to able potential gradient over a distance larger than the several nanometers, and a reasonable lower limit of 10.8 Compton wavelength, such that the required step m can be assumed for the plate separation z. The dis- change in potential occurs over a distance comparable tance over which the potential gradient is formed, d, to the Compton wavelength. Assuming the required can also be reduced by locally thinning the plate sup- potential step has magnitude V and the change in vac- port structure; a realistic lower bound on d is thus as- uum field energy due to the Casimir effect has magni- sumed to be 10 -9 m. Given these values, the plate size tude AE,,,, the gradient relation can be expressed: for producing the required potential step for proton- antiproton pair production is around 0.73 m, which is v _ .... (29) difficult but not impossible to manufacture. ;_, d where Acis the Compton wavelength of the particle and Ideally, the potential gradient would be formed in a d is the plate thickness, or more properly the thickness region devoid of plate material; this can be accom- of the region over which the change in vacuum field plished by designing the Casimir plate with a small hole energy occurs. For pair production to occur at the step whose diameter is of the same order or smaller than the boundary, the potential V must exceed E+m0c:, where E plate separation distance. Vacuum electromagnetic is the total energy of the particle (rest mass plus kinetic fields with wavelengths larger than the hole diameter energy). Assuming the particle kinetic energy at the will still be blocked by the cavity, but the potential gra- boundary is small compared to its rest mass energy, the dient formed by the plates is now in a material-free requirement for V becomes: region that more faithfully reproduces the assumptions behind Figures 3 and 4. Possible effects due to the V > 2mo c2 (30) fringing of vacuum electromagnetic fields at the hole boundaries remain to be evaluated, but this method ap- Inserting Equations 28 and 30 into Equation 29 yields pears promising to provide the required potential gradi- the following expression for the plate area, thickness, ents in a material-free region. and separation as a function of particle mass and Comp- ton wavelength: Summary. In summary, it appears possible to produce 2moc2 rc2hcL 2 a Casimir cavity geometry that will provide sufficiently steep potential gradients for particle-antiparticle pair Z_ = 720_-_d (31) creation. By introducing a small hole in the plate which reduces to: material with a diameter similar to the plate separation distance, a potential step may be created in a material- L-" -- 4.15x10 44m° (32) free region, as depicted in Figure 4. Electron-positron pairs and proton-antiproton pairs can conceivably be

NASA/CR--2001-211116 generated using this technique, with significantly less target placed outside the central plate hole can be used infrastructure and presumably lower cost than current to intercept any emitted at the potential antimatter production methods. boundary. The resulting annihilation of the positrons with the target material will produce 0.511-MeV EXPERIMENTAL DESIGN gamma rays that can be measured with a detector lo- cated behind the target. The following experiment is proposed to evaluate the possibility of producing particle-antiparticle pairs at a Proton-Antiproton Production potential boundary created within a Casimir cavity. The proposed experiment is a modified version of a If successful, the experimental arrangement outlined similar experiment performed by the author under a above will demonstrate the basic feasibility of the pro- prior contract to the NASA Marshall Space Flight Cen- posed pair production process. However, for propul- ter. 4° In that experiment, flat parallel plates were used sion applications it is desirable to produce antiprotons to form a Casimir cavity to investigate pair creation, but rather than positrons. As previously discussed, the con- the plate geometries were not properly designed to gen- straints on plate size, flatness, and separation become erate sharp potential gradients. Based on that effort and significantly more demanding, but remain within the the additional analysis in this report, the following ex- capability of current manufacturing techniques. For periment is suggested as a proof-of-concept test. proton-antiproton pair production, square plates with areas of 0.526 m2 (L = 0.725 m) would have to be sepa- Electron-Positron Production rated by a distance of l0 -8 m, indicating that the surface flatness of the plates would have to be on the order of To investigate the formation of electron-positron pairs, nanometers. Larger plate areas would relax this con- it is proposed that a Casimir cavity be constructed from straint by allowing larger separation distances, and the two flat, square metallic plates, each with an area of ability to machine flat surface areas must be traded 1.61xl0 2 m 2 (L = 12.7 cm). From Equation 33, spacing against the fabrication of larger plate dimensions. The the plates a distance z = l0 -7 m apart should provide a central hole diameter would again be on the order of the suitably steep potential gradient for electron-positron plate separation distance to provide a material-free po- pair creation to occur. To create a material free region tential step, and the electron source would be replaced for the steep potential step, the central region of one with a proton source to provide the particles within the plate should be thinned down to a material depth d _< cavity. If this scheme is successful, the antiprotons can 10.7 m, into which a central hole should be drilled per- be captured upon exiting through the hole in the pendicular to the plate boundary. The diameter of the Casimir plate and stored in portable Penning traps for hole should be on the order of the plate separation dis- later use. tance, so that vacuum electromagnetic fields with wave- lengths larger than the hole diameter will still be CONCLUDING REMARKS blocked by the cavity plates. On the opposite plate, a small amount of radioactive material can be deposited A new concept has been described for creating matter- to act as a source of electrons within the cavity; Ni 63is antimatter particle pairs at a steep potential boundary. a readily available commercial source, and the kinetic The potential step is created using the Casimir effect to energy of the emitted electrons (0.067 MeV) are suffi- suppress the vacuum energy between parallel conduct- ciently below the rest mass energy of the electron that ing plates. Preliminary calculations indicate that a suf- Equation 30 remains a viable approximation. Alterna- ficiently steep potential gradient can be formed for rea- tively, the metallic plate can be irradiated to produce sonable plate dimensions and separation distances. A subsequent electron emissions within the cavity. preliminary experimental design is outlined as a proof- of-concept test for the proposed antimatter production The plate surfaces must be aligned and moved to within scheme. Additional analysis remains to be performed 10 -7 m to form the required potential step, which can be to validate the concept, including an evaluation of ma- accomplished using commercially available piezoelec- terial and temperature effects on the plate boundaries, tric transducers. The close separation distance requires the effect of fringing fields on the potential step at the & that the surface flatness of the plates not exceed 108 m, plate central hole, and the consequences of imperfect which is a stringent but commercially attainable con- parallel plate alignment on the required potential gradi- straint. The entire system should be mounted in a vac- ent. Nevertheless, based on the preliminary analysis uum system capable of achieving a hard vacuum (_< 10.8 presented in this paper, the proposed concept appears to torr), and isolated from vibrations. To evaluate whether be a potentially viable alternative to the high-energy the proposed pair production method works, a small antimatter production methods currently in use.

NASA/CR--2001-211116 9 REFERENCES 13. Cassenti, B.N., "Energy Transfer in Antiproton An- nihilation Rockets," in Antiproton Science and Tech- 1. Forward, R.L., Antiproton Amlihilation Propulsion, _, B.W. Augenstein et al., eds., World Scientific, AFRPL-TR-85-034, Forward Unlimited, Oxnard, CA, Singapore, 1988, pp. 574-602. 1985. 14. Cassenti, B.N., "Conceptual Designs for Antiproton 2. Sanger, E., "Zur Theorie der Photoneraketen" ("The Propulsion Systems," AIAA Paper No. 89-2333, pre- Theory of Photon Rockets"), blgenieur-Archiv., 21, sented at the 25th Joint Propulsion Conference, Mon- 1953, pp. 213-226. terey, CA, Jui 10-12, 1989

3. Morgan, D.L. and Hughes, V.M., "Atomic Processes 15. Vulpetti, G., and Pecchioli, M., "Considerations Involved in Matter-Antimatter Annihilation," Phys. About the Specific Impulse of an Antimatter-Based Rev., D-2 (8), 1979, pp. 1389-1391. Thermal Engine," J. Propulsion and Power, 5 (5), I989, pp. 591-595. 4. Agnew, L.E., Jr., Elioff, T., Fowler, W.G., Lander, R.L., Powell, W.M., Segre, E., Steiner, H.M., White, 16. Howe, S.D., and Metzger, J.D., "Antiproton-Based H.S., Wiegand, C., and Ypsilantis, T., "Antiproton In- Propulsion Concepts and Potential Impact on a Manned teractions in Hydrogen and Carbon Below 200 MeV," Mars Mission," J. Propulsion and Power, 5 (3), 1989, Phys. Rev., 118 (5), 1960, pp. 1371-1391. pp. 295-300.

5. Morgan, D.L., Annihilation of Antiplvtons in Hea_3' 17. Forward, R.L., 21st Century Space Propulsion Nuclei, AFRPL TR-86-OII, Lawrence Livermore Na- Study, AL-TR-90-030, Forward Unlimited, Malibu, tional Laboratory, Livermore, CA, Apr 1986. CA, Oct 1990.

6. Massier, P., "The Need for Expanded Exploration of 18. Tarpley, C., Lewis, M.J., and Kothari, A.P., "Safety Matter-Antimatter Annihilation for Propulsion Applica- Issues is SSTO Spacecraft Powered by Antimatter tions," J. Br. hlterplanetary Soc., 35 (9), 1982, pp. 387- Rocket Engines," AIAA Paper No. 90-2365, 26th Joint 390. Propulsion Conference, Orlando, FL, Jul 16-18, 1990.

7. Forward, R.L., "Antimatter Propulsion," J. Br. hTter- 19. Cassenti, B.N., "High Specific Impulse Antimatter planetal 3' Soc., 35 (9), 1982, pp. 391-395. Rockets," AIAA Paper No. 91-2548, presented at the 27th Joint Propulsion Conference, Sacramento, CA, 8. Cassenti, B.N., "Design Considerations for Relativis- June 24-26, 1991. tic Antimatter Rockets," J. Br. btterplanetatT Soc., 35 (9), 1982, pp. 396--404. 20. Forward, R.L., and Davis, J., Mirror Matter: Pio- neering Antimatter Physics, J. Wiley & Sons, NY, NY, 9. Morgan, D.L., "Concepts for the Design of an Anti- 1988. matter Annihilation Rocket," Z Br. blterplanetal 3: Soc., 35 (9), 1982, pp. 396-404. 21. LaPointe, M.R., Antiproton Annihilation Propulsion Using Magnetically Confined Plasma Engines, Disser- 10. Cassenti, B.N., "Antimatter Propulsion for OTV tation, U. New Mexico, Dept. Chemical and Nuclear Applications," J. Propulsion and Power, 1 (2), 1985, Engineering, Albuquerque, NM, 1989. pp. 143-149. 22. LaPointe, M.R., "Antiproton Powered Propulsion 11. Vulpetti, G., "Antimatter Propulsion for Space Ex- with Magnetically Confined Plasma Engines," J. Pro- ploration," J. Br. hzterplanetary Soc., 39 (9), 1986, pulsion and Power, 7 (5), pp. 749-759. pp. 391-409. 23. Callas, J.L., The Application of Monte Carlo Model- 12. Forward, R.L., Advanced Space Propulsion Study: ing to Matter-Antimatter Annihilation Propulsion Con- Antiproton and Beamed Power Propulsion, AFAL-TR- cepts, JPL D-6830, Jet Propulsion Laboratory, Pasa- 87-070, Hughes Research Laboratories, Malibu, CA, dena, CA, Oct 1989. Oct 1987.

NASA/CR--2001-211116 10 24.Huber,F., Antimatterie-Annihilationsantriebe fur 32. Haloulakos, V., and Ayotte, A., "The Prospects for Interplanetare Raumfahrtmissionen, Ph.D. Dissertation, Space-Based Antimatter Production," AIAA Paper 91- Universitat Stuttgart, Institute fur Raumfahrtsysteme, 1987, presented at the 27th Joint Propulsion Confer- 1994. ence, Sacramento, CA, Jun 24-26, 1991.

25. Lewis, R.A., Newton, R., Smith, G.A., Toothacker, 33. Dirac, P.A.M., Directions in Physics, John Wiley & W.S., and Kanzleiter, R.J., "An Antiproton Catalyst for Sons, New York, NY, 1978, pp. 1-37, 55-70. Inertial Confinement Fusion Propulsion," AIAA Paper No. 90-2760, presented at the 26th Joint Propulsion 34. Greiner, W., Relativistic : Conference, Orlando, FL, Jul 16-18, 1990. Wave Equations, Springer-Verlag, Inc., Berlin, 1994, pp. 261-267. 26. Lewis, R.A., Smith, G.A., Toothacker, W.S., Kan- zleiter, R.J., Surratt, M.S., Higman, K.I., and Newton, 35. Mostepanenko, V.M. and N.N. Trunov, The R.J., "An Antiproton Driver for Inertial Confinement Casimir Effect and its Applications, Oxford Science Fusion Propulsion," AIAA Paper No. 91-3618, pre- Publications, Clarendon Press, Oxford, 1997. sented at AIAA/NASA/OAI Conf. on Advanced SEI Technologies, Cleveland, OH, Sep 4--6, 1991. 36. Weinberg, S., The Quantum Theory of Fields, Voi. 1, Cambridge University Press, 1995, pp. 578-593. 27. Schmidt, G. R., Gerrish, H. P., Martin, J. J., Smith, G. A., and Meyer, K. J., "Antimatter Requirements and 37. Forward, R.L., Mass Modification Experiment Energy Costs for Near-Term Propulsion Applications," Definition Study, PL-TR-96-3004, Forward Unlimited, J. Propulsion and Power, 16 (5), Sep-Oct 2000, Malibu, CA, Feb 1996. pp. 923-928. 38. Boyer, T.H., "The Classical Vacuum," Sci. Ant., 253 28. Chapline, G. "Antimatter Breeders," J. Br. bzter- (3), Aug 1985, pp. 70-78. planetary Soc., 35 (9), pp. 423-424, 1982. 39. Milonni, P.W., _uantum Vacuum: An Intro- 29. Cassenti, B.N., "Concepts for the Efficient Produc- duction to Quantum Electronics, Academic Press, New tion and Storage of Antimatter," AIAA-93-2031, pre- York, NY, 1994. sented at the 29th Joint Propulsion Conference, Mon- terey, CA, Jun 28-30, 1993. 40. LaPointe, M. R., Antimatter Production at a Poten- tial Boundary, NASA SBIR Phase I Final Report, Con- 30. Hora, H., "Estimates of the Efficient Production of tract NAS8-98109, prepared for the NASA Marshall Antihydrogen by Lasers of Very High Intensities," Op- Space Flight Center, Huntsville, AL, Nov 1998. toElectronics, 5, 1973, pp. 491-501.

31. Crowe, E.G., "Laser Induced Pair Production as a Matter-Antimatter Source," J. Br. btterplanetary Soc., 36, 1983, pp. 507-508.

I"

NASA/CR--2001-211116 11 Form Approved REPORT DOCUMENTATION PAGE OMB No. 0704-0188 , ,,,, Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite t204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503. 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE August 2001 3. REPORT TYPE ANDFinalDATESContractorCOVEREDReport 4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Antimatter Production at a Potential Boundar3'

WU-755-B4--07-00 6. AUTHOR(S) NCC3-860 NAS8-98109 SBIR Michael R. LaPointe

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER

Ohio Aerospace Institute 22800 Cedar Point Road E-12962 Brook Park, Ohio 44142

' 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORINC-dMONITORING AGENCY REPORTNUMBER

National Aeronautics and Space Administration Washington, DC 20546- 0001 NASA CR--2001-211116 AIAA-2001-3361

11. SUPPLEMENTARY NOTES

Prepared for the 37th Joint Propulsion Conference and Exhibit cosponsored by the AIAA, ASME, SAE, and ASEE, Salt Lake City, Utah, July 8-11, 2001. Project Manager, Dhanireddy Reddy, Power and On-Board Propulsion Technology Division, NASA Glenn Research Center, organization code 5430, 216-433-8133.

12b. DISTRIBUTION CODE r 12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited Subject Category: 73 Distribution: Nonstandard

Available electronically at htto://_ltrs._rc.nasa._ov/GLTRS This publication is available from the NASA Center for AeroSpace Information, 301--621--0390. 13. ABSTRACT (Maximum 200 words)

Current antiproton production techniques rely on high-energy collisions between beam particles and target nuclei to produce particle and antiparticle pairs, but inherently low production and capture efficiencies render these techniques impractical for the cost-effective production of antimatter for space propulsion and other commercial applications. Based on Dirac's theory of the vacuum field, a new antimatter production concept is proposed in which particle- antiparticle pairs are created at the boundary of a steep potential step formed by the suppression of the local vacuum fields. Current antimatter production techniques are reviewed, followed by a description of Dirac's relativistic quantum theory of the vacuum state and corresponding solutions for particle tunneling and reflection from a potential barrier. The use of the Casimir effect to suppress local vacuum fields is presented as a possible technique for generating the sharp potential gradients required for particle-antiparticle pair creation.

14. SUBJECT TERMS 15. NUMBER OF PAGES !7 Antimatter; ; Antiprotons; Propulsion; Matter-antimatter propulsion 16. PRICE CODE

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITYCLASSIFICATION 20. LIMITATION OF ABSTRACT OF REPORT OF THIS PAGE OF ABSTRACT Unclassified Unclassified Unclassified Standard Form 298 (Rev. 2-89) NSN 7540-01-280-5500 Prescribedby ANSI Std. Z3g-18 298-102