Matter-Antimatter Propulsion via QFT Effects from Parallel Electric and Magnetic Fields 22 April 2016 Gerald B. Cleaver Head, Early Universe Cosmology & Strings Division Center for Astrophysics, Space Physics, & Engineering Research Baylor University Waco, Texas II. Proposed Method of Spacecraft Propulsion III. Collection & Storage

IV. In Situ Production (QFT-Basis) (i) From Laser Interactions (ii) From Parallel Electric and Magnetic Fields (iii) Enhancement from Pulsed Electric Fields V. Derivation of Parallel E & B Enhancement Particle/anti-particle pair production (PAP PP) from vacuum via strong E-fields investigated for century QM foundation developed by Fritz Sauter

et al. in1930s Placed on sound QED basis by Julian Schwinger in1951 Pair production occurs when electric field strength E0 above critical value E*, Schwinger limit (SL), at which becomes nonlinear with self-interactions 1.3 x 10 V/cm Corresponding SL intensity I* = 2.1 x 1029 W/cm2 As energy density of x-ray lasers approach

SL critical strength, feasibility/functionality of electron-positron pair production gaining interest. Laser intensities within 1 order of magnitude Physical processes for lowering critical energy density below the SL (& enhancing pair production above SL) through additional QM effects being explored. U. of Connecticut/U. of Duisburg-Essen examining pulsation of inhomogeneous E fields within a carrier wave. Or enhancement via QM effects w/

addition of a magnetic field B parallel to the electric field E. Magnetic field enhancement to quark/anti-quark pair production through QCD chiral symmetry breaking effects investigated theoretically by John Preskill at Caltech in1980s Don Page at the U. of Alberta showed in 2007 B fields parallel to E fields also enhance electron/positron pair production via an analogous QED effect, w/ enhancement going predominantly as a linear function of B0/E0,

Particle/antiparticle pair production as a highly efficient fuel source for intra solar system and interstellar propulsion proposed by Devon Crow in 1983 Viability of this method of propulsion reviewed, esp. from the parallel electric and magnetic field method spacetime vacuum. Energy is drawn from the external electric (and magnetic) fields. Process is somewhat analogous to particle production near the event horizon of a black hole, which

reduces the mass of the black hole accordingly. Primary difference is, while both particle and antiparticle are produced from virtual pair by the electric and magnetic fields, only one particle of an initially virtual pair escapes from a black hole (as Hawking radiation) and antiparticle is captured by black hole. Matter/Antimatter & Parity Left-handed

versions (spin in direction opposite of its motion) Right-handed versions (spin in same direction of its motion) = Left-handed Anti-Particle

9 Matter/Antimatter 1928: British physicist P.A.M. Dirac showed that Einstein's relativity implied every particle has corresponding antiparticle, same masses, but opposite electric charges. 1932: Carl Anderson at Caltech recorded positively charged electron (positron) passing through lead plate in cloud chamber (for which he received Nobel prize).

10 1955: Antiproton experimentally confirmed at Berkeley by Emilio Segre and Owen Chamberlain (earning1959 Nobel prize). 1956: Antineutron discovered at the Bevatron at Lawrence Berkeley Nation Lab by Bruce Cork and colleagues. 11 1995: CERN researchers use Low Energy

Antiproton Ring (LEAR) to slow down antiprotons. Managed to pair positrons and antiprotons together, producing nine hydrogen anti-atoms, each lasting a mere 40 nanoseconds. Within 3 years, CERN group producing approx. 2000 anti-hydrogen atoms per hour. Production rates of antimatter at LHC have increased significantly since then (as did past production rates at Fermilab) 12 Matter/Antimatter [MAM] is ideal rocket

fuel because all of mass in MAM collisions is converted into energy. MAM reactions produce 10 million times the energy produced by conventional chemical reactions used to fuel the space shuttle, 1,000 times more powerful than nuclear fission produced at a nuclear power plant & 300 times more powerful than the energy released by nuclear fusion. 13 Should an ample supply of antimatter be produced or collected, a secure means of

storage (i.e., magnetic confinement) would then be devised; the antimatter must be kept separate from matter until a spacecraft needs more power, unless stored as anti-hydrogen (positronium annihilates within minutes) and/or MAM created in situ and immediately emitted as propellant. 14 Then why hasnt MAM spacecraft propulsion systems been developed: Antimatter remains most expensive substance on Earth. In 2000 it cost $62.5

trillion a microgram ($1.75 quadrillion an ounce) of electron/positron pairs. Fermilab was producing about 15 nanograms a year. However, price drops with each advancement in particle accelerator intensity and efficiency, The LHC now produces about 1 microgram ~ 1021 electron/positron pairs per12 days at a cost of $200,000 or 1 milligram in about 12,000 To be commercially viable, this price would need to drop by about a factor of TenThousand. As quoted in Status of Antimatter, NASA Glenn Research Ctr. www.nasa.gov/centers/glenn/technology/

warp/antistat.html (dated 14 July 2015). This goal could be reached within a decade or two. This was the projected time scale expected by some back in the 1980s. 16 Much more antimatter needed for interstellar mission (& for planet reconnaissance/landing mission, will need enough fuel to decelerate into target star system). Starship with a 100-ton payload designed to cruising at 0.40 c estimated to require equivalent of 80 ocean supertankers full of antimatter fuel.

For cruise speed ~ 0.25 c, fuel requirements dramatically lower (news.discovery.com/space/ harvesting-antimatter-in-space-to-fuel-starships120523.html#mkcpgn =rssnws1 ) --R. Obousy, JBIS 64 (2011) 378. 17 Early Papers: R. Forward, Antiproton Annihilation Propulsion, USAF Rocket Propulsion Laboratory Report AFRPL, 1985. Devon Crowe, Laser Induced Pair Production as a Matter-Antimatter Source, JBIS 36 (1983), 507.

G. Schmidt et al., Antimatter Production for Near-tern Propulsion Applications, AIAA 99-2691, NASA Marshall Space Flight Center 18 Early Papers: In 2000 NASA scientists announced early designs for an antimatter engine that might be capable of fueling a spaceship for a trip to Mars using only a milligram of MAM.

19 2012: R. Keane and W.M. Zhang examined magnetic nozzle design for charged pion emission from quark-antiquark collisions. Showed effective exhaust speeds ~ 0.7 c feasible. Efficiency ~ 30% for quark/antiquark emission > 30% for electron/positron emission They optimized geometry and field configuration of nozzle using a magnetic 20

field on order of 10 T. Alternative to MAM Generation: 2011: antiprotons discovered trapped by Earth's magnetic field by the international PAMELA (Payload for Antimatter/Matter Exploration and Light-nuclei Astrophysics) satellite. The Alpha Magnetic Spectrometer on ISS also able to detect, identify, and measure antiparticles in Earth orbit. 21 Alternative to MAM Generation:

Theoretical studies suggest that the magneto- spheres of much larger planets, like Jupiter, should have more antiprotons than Earth. "If feasible, harvesting antimatter in space would completely bypass the obstacle of low energy efficiency when an accelerator is used to produce antimatter, 22 MAM Propulsion Systems:

However, an ideal MAM propelled spacecraft should contain systems for both collecting and generating MAM, with creation especially as an emergency option if stored MAM leaks out of magnetic containment chambers or is annihilated prematurely by matter leaking in. 23 In Situ MAM Generation Schwinger Pair production of spin-1/2 fermions from the vacuum through intense electric field quantum effect

F. Sauter, Z. Phys 69 (1931) 742 W. Heisenberg and H. Euler, Z. Physics 98 (1936) 714. V. Weisskopf and K. Dan Vidensk, Selsk. Mat. Fys. Medd. XIV (1936) #6 J. Schwinger, Phys. Rev. 82 (1951) (putting pair production on sound QED basis) 24 For electron-positron production, the critical value of the electric field strength is above the Schwinger limit defined by E* = m2c3/(e) = 1.3 x 1018 V/m. with m and e the mass and |charge| of the

electron. At this scale the electromagnetic field (vacuum) becomes non-linear. 25 In vacuum, classical Maxwell's equations perfectly linear differential equations. This implies by the superposition principle that the sum of any two solutions to Maxwell's equations is yet another solution to Maxwell's equations. E.g., two beams of light pointed toward each other should simply add together their electric fields and pass right through each other.

In QED, however, non-elastic photon photon scattering becomes possible when the combined energy is large enough to create virtual electronpositron pairs 26 When the average strength of an electric field E0 is above Es = 1018 V/m , the pair production rate of charged particles per unit time and unit crosssection found from QM computation of probability of tunnelling of virtual pairs from Dirac sea (a.k.a., instanton calculations) Strongest lasers produce electric fields ~ 1017 V/m.

27 Matter/Anti-Matter (MAM) Production X-ray free electron lasers from Linac Coherent Light Source at SLAC and TESLA at DESY approaching ES . The Extreme Light Infrastructure (ELI) Ultra-High Field Facility (4th site) planned for Eastern Europe around 2020 should also reach E*. (Ten lasers concentrating 200 petawatts of power into a very narrow beam for around 10-12 s pulses.) 28

Matter/Anti-Matter (MAM) Production Via localized electric fields: S. Kim and D. Page, Phys. Rev. D75 (2007) 103517. Consider a static plane-symmetric z-dependent electric field E(z) in the z-direction of maximum value E0 and of effective length L such that E0L = E(z) dz allows pair production of a particle of mass m and charge q if = m/(qE0L) < 1 equivalently E0 > 29 Matter/Anti-Matter (MAM) Production

Alternately, if we want a time varying field E(t) rather than spatially varying, replace with T , L with T, and dz with dt. In this case, pair production occurs even with T > 1, but is suppressed. 30 Matter/Anti-Matter (MAM) Propulsion Systems: In each process when E0 is above the minimum value, PPR of charged particles per unit time and unit cross-section found from tunnelling of virtual

pairs from the Dirac sea where instantons determine the QM tunnelling probabilities. To leading WKB order: For Sauter electric field E(z) = E0 sech[2(z/L)], the PPR is N = (qE0)5/2L (1-2)5/4 exp[-Z{1-(1-2)1/2}] /(4 3 m) ~ (qE0)5/2L/(4 3 m) as 0 31 Can lower minimum value of E0 significantly by adding constant magnetic field B parallel to E0: PPR of charged particles per unit time and unit cross-section is modified (as derived by Don Page)

to (Note: in natural units [B] = [E], since c = 1 rather than [B] = E/c). In these matching units, B0 > E* realistically possible, NB = (B/E0)(qE0)5/2L (1-2)3/4 exp[-Z{1-(1-2)1/2}] * coth[B/E0(1-2)1/2]/(4 2 m) ~ (B/E0) (qE0)5/2L coth[B/E0]/(4 2 m) (as -> 0) = ( B/E ) coth[B/E ] N In the limit of B -> 0, NB reduces to N. Allows significantly weaker E0. [Idea of B || E first presented in J. Preskill, 1987 lecture

notes; Proposed for Spacecraft Propulsion by Cleaver in 100 YSS Proceedings] 33 Orders of magnitude for Magnetic Fields to Enhance Rates B ~ Es/c = (2 1018 V/M)/(3 108 m/s) = 109 to 10 T Or find from using B-field to reduce effective mass of electron (quark) (2n + 1 g/2) e c2 B + (mc2)2 = 0 With n = 0, get for electron/positron pair production: B = (0.5 106 eV)2/[0.001 x 4 10-15 eV s e (3 108 m/s)2] = 1012 T

for quark/anti-quark pair production: B = (2.4 106 eV)2/[0.4 x 4 10-15 eV s e (3 108 m/s)2] = 1011 T (*Note: Actually pion/anti-pion production rather than quark/antiquark raises to above B for e/p.) So order of magnitude estimates indicate B ~ 10 9 to 12 T ~ magnetic field strength of a magnetar! 34 List of orders of magnitude for magnetic fields Factor (tesla) Value (SI units)Item 15 10 2 fT SQUID magnetometers on Gravity Probe B gyros measure fields 1012 1 pT Human brain magnetic field 109 10 nTMagnetic field strength in the heliosphere

106 24 T Strength of magnetic taoe near tape head 5 10 31 T Strength of Earths magnetic field at equator 3 10 0.5 mT The suggested exposure limit for cardiac pacemakers 5 mT The strength of a typical refrigerator magnet 101 0.15 T The magnetic field strength of a sunspot 0 10 2.4 T Coil gap of a typical loudspeaker magnet 9.4 T Modern high resolution research magnetic resonance imaging

16 T Strength used to levitate a frog 45 T Strongest continuous magnetic field yet produced in a laboratory (FSU) 102 300 TStrongest pulsed non-destructive magnetic field yet produced in a lab, LANL 730 TStrongest pulsed magnetic field yet obtained in a laboratory, destroying the equipment used (Inst. for Solid State Physics, Tokyo) 3 10 2.8 kT Strongest (pulsed) magnetic field ever obtained (w/ explosives) in a lab, 6 10 100 MT Strength of a neutron star 9 to 12 10 0.1-100 GTStrength of a magnetar

53 10 2 1029 YT Planck magnetic field strength 35 PPR can also be enhanced by a factor of orders 10 to 100 or greater if the electric field (laser in general) is pulsed with internal modulation. For the details of this type of PPR enhancement, see for example R. Schutshold, H. Giles, and G. Dunne, Phys. Rev. Lett. 101 (2008) 130404; Ibid.,

Int. J. Mod. Phys. A25 (2010) 2373; C. Schneider and R. Schutzhold, arXiv:1407.3584. S. Kim, H. Lee, and R. 36 Matter/Anti-Matter (MAM) Production Enhancement: PPR could be strongly enhanced by simultaneous combination of a pulsed (laser) electric field E with internal modulation combined with parallel magnetic field B. The enhancement combination may

provide for viable in situ electron/positron and/or quark/antiquark pair production from the vacuum for spacecraft propulsion. As such, it would be made possible by nonlinear quantum field theory effects on the 37 electromagnetic vacuum. Chiral Fermion Pair Production From Parallel Electric and Magnetic Fields While not envisioned as a propulsion source for spacecraft, this basic idea for MAM production via

parallel fields was discussed by John Preskill at Caltech in the late 1980s. The underlying physics behind MAM production from parallel electric and magnetic 38 Chiral Fermion Pair Production From Parallel Electric and Magnetic Fields CSB is an effect that

(1) connects left- and right-handed elementary particles (specifically for quarks) in the strong coupling limit of QCD and/or (2) distinguishes between lh & rh particles via B-field interaction effects in QED Why only the parallel components of the electric and magnetic fields are relevant to this effect will be worked 39

Chirality = Handedness (Left-Handed and Right Handed) ~ Chiral Symmetry = Left-Handed and Right-Handed versions of same particle (equivalently Left-Handed particle and antiparticle) are independent particles (Technically mean the phases of each are independent.) Chiral Symmetry Breaking (CSB) = L-H and R-H particles are not independent (phases are correlated & exactly opposite) 40

At high energies (much above a few GeV), when strong force becomes weak, quarks have Chiral Symmetry ~ At low energies (below a few GeV), when strong force is strong, quarks experience Chiral Symmetry Breaking 41 ~

~ CSB allows an interaction term FF between the field strength tensor F and its ~ dual field strength tensor F= F, where indices range over 0, 1, 2, 3 For Electromagnetic force, the field strength tensor components are F01 = -F10 = Ex, F02 = -F20 = Ey, F03 = -F30 = Ez, 42

~ F12 = -F21= -Bz, F13 = -F31 = Bx, F23 = -F32 = Bx , For electromagnetics, F F = E B + E B Why this term can result in particle/antiparticle pair production is interesting. To start, consider a spin S = fermions of mass m and electric charge e in a constant magnetic field B

aligned along the z-axis, B = Bz. The electromagnetic gauge field producing the physical magnetic field B can be chosen as A = B x y. The square of the Hamiltonian for a fermion in this 43 The g gyromagnetic operator is very close to 2:

H2 = px2 + pz2 + (py e B x)2 + m2 2 e B Sz. py and pz are constants of motion (since they commute with H). Hence these can be ignored (eliminated from the Hamiltonian as constants). Then note that the contribution px2 + (eB)2( x x0)2 , with x0= -py/(eB) has the form of a simple harmonic oscillator (SHO). A QM SHO of this form always has stated quantized energy of the form (2 n + 1) e B, where n is an integer. This yields H2 = pz2 + py2 + (2n + 1 - 2 Sz)e B + m2, 44 So, consider a RH particle (Sz = ) and

the ground state mode (n=0) with no motion in the y direction. Then the Hamiltonian simplifies to: H 2 = p z2 + m 2 In the massless limit, this indicates a zero mode which even very low energy parallel E (not on yet) and B fields can excite, resulting in pair 45 In reality, for massive fermion states (quarks,

electrons), the E field must be stronger. (Note that the Sz = - fermion has an increased effective mass, an indication of CSB. That is, RH Particle & LH antiparticle production rate increases w/ B, But, LH Particle & RH antiparticle production rate decreases w/ B. 46 Turn on an E field in the B direction, slowly

(adiabatically) increasing its strength. E = E z = -dA/dt w/ Az= E t (gauge choice A0 = 0). Then, H2 = (pz E t)2 + m2 Energy levels are discrete and, with increasing t, move along a mass-shell hyperbola. 47 While this process was originally considered by John Preskill at CIT to produce a quark-antiquark pair, used to produce electron-antielectron pair. The latter is more likely since electron mass ~ 1/5 up quark mass

~ 1/270 pi meson mass 48 We can understand what is happening physically by applying the famous Dirac Sea concept of both positive and negative energy states. In the ground state of a fermion system, all negative energy modes are filled and all positive energy modes are empty. Each mode can be assigned a helicity. Let all have Sz = +1/2 (RH). Positive energy modes with positive (negative) momentum are RH (LH). The opposite it true for filled negative energy modes. 49

For an electric field E with sufficient energy density, the negative energy quarks will jump across the 2m (~1 MeV for electrons, ~ 8 MeV for up quarks, ~14 MeV for down quarks) gaps separating the negative and positive energy states. The physical realization of this is chiral particle pair production: RH particle (filled energy state) & LH antiparticle (negative energy statethat is, a hole). 50 A quark/anti-quark pair will either form uncharged pion state or multiple charged or

uncharged pions if pair has sufficient kinetic energy to separate far enough for the potential energy from strong force interaction of the quarks to be greater than the mass of another quark pair. Then another quark/anti-quark pair will pop into existence and a net effect can be a pair of pions of opposite charge. 51 More likely, an electron/positron pair will pop into existence. Thus, parallel electric and magnetic fields could be used as MAM generator (a.k.a., chiral fermion pair production) via low energy effects allowed through chiral symmetry breaking

or (more likely) through E-field spatial/temporal modulation. The charged pion pairs and electron/positron pairs can be directed by external magnetic fields to produce thrust for a manned or unmanned spacecraft. 52 Conclusions: MAM production from strong electric field near or above Schwinger limit nearing feasibility.

Enhancement of MAM PPR via inclusion of magnetic field parallel to electric field possibly in combination with enhancement from pulsed electric field with internal modulation. The latter may provides MAMon-demand propulsion 53 Acknowledgements: Sauter, Heisenberg, Euler, Weisskopf, Dan, and Schwinger of course! R. Schutshold, H. Giles, G. Dunne, C. Schneider, and S. Kim for series of pulsed E field pair production design & engineering papers.

Richard Obousy, VARIES proposal in JBIS 64 (2011) 378. John Preskill for B||E idea and his related notes. Don Page and S. Kim for B||E system pair production rate calculation. 54 References: [1] F. Sauter, Z. Phys 69 (1931) 742; W. Heisenberg and H. Euler, Z. Physics 98 (1936) 714; V. Weisskopf and K. Dan Vidensk, Selsk. Mat. Fys. Medd. XIV (1936) #6.

[2] J. Schwinger, Phys. Rev. 82 (1951) 664. [3] R. Schutshold, H. Giles, and G. Dunne, Phys. Rev. Lett. 101 (2008) 130404; Ibid., Int. J. Mod. Phys. A25 (2010) 2373; C. Schneider and R. Schutzhold, arXiv:1407.3584. S. Kim, H. Lee, and R. Ruffini, arXiv:1207.5213. [4] J. Preskill, 1987 QCD Lecture Notes, www.theory.caltech.edu/~preskill/notes.ht 55 [6] R. Forward, Antiproton Annihilation Propulsion, USAF Rocket Propulsion Laboratory Report AFRPL, 1985; D. Crowe, JBIS 36 (1983) 507; G. Schmidt et al., Antimatter Production for Near-tern

Propulsion Applications, AIAA 99-2691, NASA Marshall Space Flight Center [7] R. Keane and W.M. Zhang, Beamed Core Antimatter Propulsion: Engine Design and Optimization, arXIv:1205.2281v2. 56

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