Download From Parallel Electric and Magnetic Fields

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
Matter-Antimatter:
I. History: Discovery & Generation
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
I. History
🚀 Particle/anti-particle pair production (PAP PP)
from vacuum via strong E-fields investigated for
century
🚀 QM foundation developed by Fritz Sauter et al.
in1930’s
🚀 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 non-linear with self-interactions
🚀 SL when energy w/in Compton wavelength = rest
mass of an electron, E* = m2c3/(eħ) = 1.3 x 1016 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 electronpositron 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 in1980’s
🚀 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
🚀 Note: Particle/anti-particle pair production does
not (and cannot) take energy from the 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
Right-handed
versions
(spin in same
direction of its
motion)
Left-handed
versions
(spin in direction
opposite 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 hasn’t 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 days ~ 30
years at a cost ~ two-hundred-billion dollars.
🚀 To be commercially viable, this price would need to
drop by about a factor of Ten-Thousand.” 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 1980’s.
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 )
17
--R. Obousy, JBIS 64 (2011) 378.
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 quarkantiquark 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 field on order of 10 T.
--R. Keane and W.M. Zhang, “Beamed Core Antimatter
Propulsion: Engine Design and Optimization”,
arXIv:1205.2281v2.
20
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 magnetospheres 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,” – R. Keane and W.M. Zhang
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/(eħ) = 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 electron–
positron pairs spontaneously,
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 = ½ ∫E(z) dz
allows pair production of a particle of mass m and
charge q if
ε = m/(qE0L) < 1 equivalently E0 > m/(qL)
(in natural units of GN = c = ħ = 1).
29
Matter/Anti-Matter (MAM) Production
🚀Alternately, if we want a time varying field E(t)
rather than spatially varying, replace ε with εT , L with
T, and dz with dt. In this case, pair production occurs
even with εT > 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-ε2)5/4 exp[-Z{1-(1-ε2)1/2}] /(4 π3 m )
~ (qE0)5/2L/(4 π3 m) as ε 0
with ε = m/(qE0L) and Z = 2πqE0L2
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-ε2)3/4 exp[-Z{1-(1-ε2)1/2}]
* coth[πB/E0(1-ε2)1/2]/(4 π2 m)
~ (B/E0) (qE0)5/2L coth[πB/E0]/(4 π2 m)
(as ε -> 0)
= (π B/E0) coth[πB/E0] 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) ħ 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 ~ 109 to 12 T ~ magnetic field strength of a magnetar!
34
List of orders of magnitude for magnetic fields
Factor (tesla)
10−15
2 fT
−12
10
1 pT
−9
10
10 nT
−6
10
24 µT
−5
10
31 µT
−3
10
0.5 mT
5 mT
−1
10
0.15 T
0
10
2.4 T
9.4 T
16 T
45 T
2
10
300 T
730 T
103
106
109 to 12
1053
Value (SI units)
Item
SQUID magnetometers on Gravity Probe B gyros measure fields
Human brain magnetic field
Magnetic field strength in the heliosphere
Strength of magnetic taoe near tape head
Strength of Earth’s magnetic field at equator
The suggested exposure limit for cardiac pacemakers
The strength of a typical refrigerator magnet
The magnetic field strength of a sunspot
Coil gap of a typical loudspeaker magnet
Modern high resolution research magnetic resonance imaging
Strength used to levitate a frog
Strongest continuous magnetic field yet produced in a laboratory (FSU)
Strongest pulsed non-destructive magnetic field yet produced in a lab, LANL
Strongest pulsed magnetic field yet obtained in a laboratory, destroying the
equipment used (Inst. for Solid State Physics, Tokyo)
2.8 kT
Strongest (pulsed) magnetic field ever obtained (w/ explosives) in a lab,
100 MT
Strength of a neutron star
0.1-100 GTStrength of a magnetar
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. Ruffini,
arXiv:1207.5213.
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
non-linear quantum field theory effects on the
electromagnetic vacuum.
37
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 1980’s.
🚀 The underlying physics behind MAM
production from parallel electric and magnetic
fields is associated with chiral symmetry
breaking (CSB).
38
Chiral Fermion Pair Production From Parallel Electric
and Magnetic Fields
🚀 CSB is an effect that
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 Bfield interaction effects in QED
Why only the parallel components of the
electric and magnetic fields are relevant to this
effect will be worked out in the Hamiltonian
formalism.
(1)
39
🚀 Chirality = Handedness (Left-Handed and Right
Handed)
~
🚀 Chiral Symmetry = Left-Handed and Right-Handed
versions of same particle (equivalently Left-Handed
particle and anti-particle) 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 FμνFμν between the
field strength
tensor F and its dual field strength
~
tensor Fμν= εμνρσ Fρσ, 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,
F12 = -F21= -Bz, F13 = -F31 = Bx, F23 = -F32 = Bx,
~
🚀 For electromagnetics, FμνFμν = ExBx + EyBy + EzBz
= EB.
(The dot product “ indicates that only the parallel
components of E and B interact).
🚀 Why this term can result in particle/antiparticle
pair production is interesting.
To start, consider a spin S = ½ 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
field is
H2 = (p – eA)2 + m2 – g e BS
= px2 + pz2 + (py – e B x)2 + m2 – geB Sz
w/ p the fermion’s momentum (operator), and g its
gyromagnetic operator.
⌃
⌃
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,
with Sz = +1/2 or -1/2.
44
🚀 So, consider a RH particle (Sz = ½) and the
ground state mode (n=0) with no motion in the y
direction. Then the Hamiltonian simplifies to:
H2 = pz2 + m2
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 production.
45
🚀 In reality, for massive fermion states (quarks,
electrons), the E field must be stronger. (Note that
the Sz = -½ 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 state—that 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.html
[5] S. Pyo Kim and D. Page, Phys. Rev. D78 (2008)
103517.
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