NASA Contractor Report 185 13 1 

AIAA-89-2334 

Antiproton Powered Propulsion 

With Magnetically Confined 

Plasma Engines 

Michael R. LaPointe 

Sverdrup Technology, Inc. 

NASA LRwis Research Center Group 

Cleveland, Ohio 

August 1989 

Prepared for 

Lewis Research Center 

Under Contract NAS3-25266 

National Aeronautics and 

Space Administration 

(NASA-CR-t85131) AFTIPBOTOB POREBED R89-27700 

PROPULSION YITH HAGNXTICaLLY COXfIBIED PLASMA 

EIGIUES Final Report [Sterdrap Tecb~oloqy) 

26 P CSCL 21ii Uaclas 

G3/20 0224118 
ANTIPROTON POWERED PROPULSION WITH 

MAGNETICALLY CONFINED PLASMA ENGINES 

Michael R. LaPointe' 

Sverdrup Technology, Inc. 

NASA Lewis Research Center Group 

Cleveland, Ohio 44135 

Abstract 

Matter-antimatter annihilation releases more energy per unit mass than any other method of 

energy production, making it an attractive energy source for spacecraf't propulsion. In the magnetically confined plasma engine, antiproton beams are injected axially into a pulsed magnetic mirror 

system, where they annihilate with an initially neutral hydrogen gas. The resulting charged annihilation products transfer energy to the hydrogen propellant, which is then exhausted through one 

end of the pulsed mirror system to provide thrust. The calculated energy transfer efficiencies for a 

low number density ( 1014cm-a) hydrogen propellant are insufficient to warrant operating the engine 

in this mode. Efficiencies are improved using moderate propellant number densities ( 10'ecm-a), but 

the energy transferred to the plasma in a realistic magnetic mirror system is generally limited to 

less than 2% of the initial proton-antiproton annihilation energy. The energy transfer efficiencies are 

highest for high number density (lO'*~m-~) propellants, but plasma temperatures are reduced by 

excessive radiation losses. Low to moderate thrust over a wide range of specific impulse can be generated with moderate propellant number densities, while higher thrust but lower specific impulse may 

be generated using high propellant number densities. Significant mass will be required to shield the 

superconducting magnet coils from the high energy gamma radiation emitted by neutral pion decay. 

The mass of such a radiation shield may dominate the total engine mass, and could severely diminish 

the performance of antiproton powered engines which utilize magnetic confinement. The problem is 

compounded in the antiproton powered plasma engine, where lower energy plasma bremsstrahlung 

radiation may cause shield surface ablation and degradation. 

Introduction 

Over the past few decades, spacecraft propulsion systems based on the combustion of chemical 

fuels have proven a reliable and satisfactory propulsion source. As anibitioiis in space coiitiiirie 

to grow, however, the use of chemical fuels requires nidtiple rocket staging, large and expensive 

propellant-to-payload mass ratios, and increasingly complex orbital dynaiiiics for intoitively simple 

missions. The limited energy available in cheinical conibustion is inadequate for several missions of 

interest, and the continued advancement of space exploration will require a coiiiiiiitiiient to develop 

new, advanced propulsion concepts. 

'Member, AIAA 

1 
Perhaps the most exotic reaction considered for advanced spacecraft propulsion is the annihilation 

of matter and antimatter. The energy released per kilogram sf combined matter and antimatter 

is over 250 times the specific energy released in nuclear fusion, and over 8 orders of magnitude 

greater than the specific energy released in chemical combustion('). Efilciently transferring this 

reaction energy to a propellant could provide high thrust and optimum exhaust velocities without 

the limitations imposed by chemical combustion energy or massive external power supplies. By 

tailoring the amount of annihilation energy required to perform a specific mission, spacecraft mass 

ratiost less than 5:l may be obtained(l). 

Background 

All known elementary particles, with the exception of the photon and the xo and /.io mesons, have 

antiparticle counterparts. An antiparticle has the same mass, spin, and lifetime as its complimentary 

particle, but opposite charge (if any) and opposite alignment between its spin and magnetic moment. 

The photon, xo meson, and /.io meson are their own antiparticles. Stable elementary particles include 

the electron (positron), proton (antiproton), photons, and neutrinos. 

When a particle and antiparticle meet they annihilate, liberating energy equal to twice the rest 

mass of either particle. This energy may be produced immediately as energetic gamma rays, or 

the annihilation process may produce intermediate particles which then decay or undergo further 

annihilation. The need to store the antimatter in a stable form for long duration space flight limits 

possible antimatter fuels to the positron and the antiproton. 

Electron-Positron Annihilation 

Direct annihilation of an electron with a positron proceeds via the reaction 

e- +et + 27 (E7 = 0.511MeV) (1) 

where each of the emitted 7-ray photons has an energy equal to half the sum of the rest mass plus 

kinetic energies of the electron-positron (e-.+) pair. An electron and positron may also undergo 

radiative capture to form a bound state of positronium (Ps) through the process 

e-+e+ -+Ps+hv (2) 

The energetic 7-rays are then released upon subsequent annihilation of the positronium. 

The first serious consideration of antimatter annihilation energy for space travel centered on 

electron-positron annihilation. In 1953 Sanger@) proposed the concept of a "photon rocket", which 

was an attempt to utilize the energetic gamma rays either to provide direct thrust or to heat a 

propellant. However, engine efficiency using a directed 7-ray exhaust is limited by the inability to 

effectively collimate the energetic photons. Althoiigh the ?-ray energy will not couple direct.l,v t.o a 

propellant, it could be absorbed by a refractory iiietal heat exchanger. A propellant is then heated 

as it passes through channels in the heat exchanger, with the hot gas exhausted through a standard 

nozzle to provide thrust. The storage density of positroniuni fuel is so low, however, that the 

required storage facility mass way overwheliii any potential benefit derived using electron-positron 

aniiihilation energy (4). 

'The empty vehicle mass plus the propellant mass, divided by the empty vehicle mass. 

2 
Proton- Antiproton Annihilation 

lo+ ' I I ' ' ' ' ',1 

- 

- 

- 

- 

'. 107 - 

10s - 

104 -\ 

103 - - 

102 - \ '. - 

101 - 

1- (0,) \, 

lo-1 - \ - 

- 

+= 'Ob - \ - 

*\. (4 

\ - 

\ \ '. - 

\ 

\ 

10-2 - ' ItII\lIl 

Antiproton annihilation enjoys several advantages over positron annihilation as an energy source for 

spacecraft propulsion. The higher rest mass energies of the proton and antiproton yield a total of 1877 

MeVt per annihilation event, compared with 1.02 MeV released by electron-positron annihilation. 

As discussed below, a significant fraction of the proton-antiproton (H) annihilation energy appears 

in the kinetic energy of charged particles, which may be collimated for direct thrust or used to heat 

a propellant more effectively than the gamma radiation released in electron-positron annihilation. 

Antiprotons and positrons may be cooled and combined to form antihydrogen('). Although it 

remains a technical challenge, it may be possible to further condense the antihydrogen to form 

antihydrogen crystald4*'). Several schemes have been proposed to confine the antihydrogen "icen 

using magnetic, electrostatic, or electromagnetic traps('*'), yielding a much higher storage density 

for the antiproton fuel. Electromagnetic radiation may be used to detach antihydrogen molecules or 

atoms from the surface of the crystal and ionize the antihydrogen into positrons and antiprotons('). 

The antiprotons may be guided with electric and magnetic fields to a reaction chamber, where they 

annihilate with protons to provide propulsive energy. The positrons, stripped from the antihydrogen 

atoms, could be used to provide additional power for auxiliary spacecraft components('). 

Protons and antiprotons may undergo direct annihilation, or at low energies may form bound 

states of protonium (Pn) leading to subsequent annihilation('). Protonium may be formed as a 

result of radiative capture 

or by rearrangement collisions in a hydrogen gas 

Figure 1: Coolomb corrected crou rcctions for 

proton-antiproton direct .nnihilstion (e.,), radiative capture (e,), and rearrangement mllirionr (e,~). 

normalized to atomic crou section (rr: = 8.7974~ 

Adapted Gam Morgan and Hughatq. 

1 MeV = 10' cV = 16 x lo-'' Joules 

3 
p+ #-+ n*+ + n*- + m*O 

0 1.3x10-'*r * - 27 

*+ - p++v, 

nsul.6, 111252 

ET 2 130-300 MeV 

K-E(x*) 2: 260 MeV 7.0xIO-'r 

7.Qx lo-'# 

u- - p-+V; KE(p*) N 192.3 MeV 

p+ 6'2%-*r e+ + u, + p, zE(e+) N 100 MeV 

p- - e +vp +v; K-E(e-) N 100 MeV 

e- + e+ -+ 27 E, = 0.511 MeV 

6.1~10-~s - 

Table 1: Proton-Antiproton Annihilation Scheme. 

The general proton-antiproton annihilation scheme is presented in Table 1. Each of the three 

charged pions has a rest mass energy of 139.6 MeV, and each of the two neutral pions has a rest 

mass energy of 135.0 MeV; thus a total of 689 MeV is contained in pion rest mass energies. The 

average kinetic energy of the charged pions is 250 MeV/pion(8), thus 750 MeV or about 40% of the 

annihilation energy resides in charged pion kinetic energy. With a kinetic energy of 260 MeV, the 

pion is travelling at 93% the speed of light and relativistic effects extend its lifetime from 26 ns at 

rest to about 70 ns. Unless acted upon, it will travel almost 21 meters before it decays. 

The remainder of the annihilation energy resides in the kinetic energy of the neutral pions, roughly 

220 MeV/pion. At this energy the neutral pion lifetime is extended from 8.4 x seconds to 

about 2.2 x lo-'' seconds, and it will travel 6.6 x lo-' meters before decaying. Upon decay each 

neutral pion produces two energetic gamma rays, each with energies between 130 and 300 MeV/r. 

The decay of the ~r+ or *- meson liberates an amount of energy equal to their rest mass energy 

and kinetic energy combined, or roughly 390 MeV/pion. The T+ decays into a charged muon (p+) 

and a mu neutrino (up). The p+ has a rest mass energy of 105.7 MeV and an average kinetic energy 

of 192.3 MeV/muon('), leaving the neutrino with roughly 90 MeV. The energetics are the same 

for the decay of a 1~- into a p- and an antip-neutrino (o,,). The total kinetic energy of the three 

charged muons created by the decay of the three charged pions is thus 577 MeV, or about 31% of 

the initial pji annihilation energy. 

A charged muon with a kinetic energy of 192.3 MeV is travelling at 94% the speed of light, and 

its lifetime is increased from 2.2 x lo-' seconds to 6.2 x seconds. Unless acted upon, the muon 

will travel almost 1800 meters before it decays. The neutrinos, travelling at the speed of light, will 

carry their energy out of the system. 

The pt decays into a positron, an e neutrino (ve), and an anti-p neutrino (P,,), while the pdecays into an electron, a p neutrino, and an anti-e neutrino (fie). The total energy available from 

tlie charged muon decay is about 300 MeV/muon. Of this energy, 0.511 MeV goes into creating 

the electron or positron, about 100 MeV into the electron or positron kinetic energy('), and tlie 

remainder to the non-interacting neutrinos. Thus the decay of the three charged muons arising in 

the pp annihilation scenario will provide roughly 300 MeV in the form of kinetic energy of the three 

electrons/positrons, corresponding to 16% of the initial proton-antiproton annihilation energy. The 

electrons and positrons are stable against decay, but can annihilate with one another to produce 

0.511 MeV yrays, the ultimate end of the pp annihilation process. 

4 
Antiproton Powered Plasma Engine 

Several antiproton powered rocket designs have been suggested, ranging from the low thrust, 

high specific impulse pion rocket to the high thrust, low specific impulse solid and gas core thermal 

engines('). The former concept is restricted to interstellar or deep space missions which require 

relativistic exhaust velocities, while the latter concepts are limited in performance by thermal constraints on material walls. A design dich minimires material constraints while providing a range 

of operating parameters is the antiproton powered plasma rocket, which utilizes magnetic mirror 

fields to contain both the charged annihilation byproducts and the ionized propellant. Morgan(') 

has sketched a design for a pulsed heavy ion plasma engine, in which antiprotons annihilate with 

nucleons in a heavy atom nucleus to produce energetic charged nuclides and particles. The charged 

byproducts are confined by external magnetic field coils and collisionally transfer their energy to 

the remaining heavy atoms, forming a magnetically confined plasma. The magnetic mirror field is 

then relaxed at one end and the plasma escapes to provide thrust. By tailoring the antiproton and 

propellant injection rates, it is possible to achieve a variety of thrust and specific impulse values 

with a single engine design. 

The efficiency of the pulsed heavy ion plasma engine is limited by the amount of energy residing 

in the kinetic energy of the charged annihilation byproducts, estimated to be less than 20% of the 

initial annihilation energy('); of this amount some fraction less than unity will be transferred to the 

heavy ion propellant. Engine life will be limited by radioactive byproduct decay, neutron radiation 

damage, and neutral fragment sputtering of surrounding material. If instead the charged byproducts 

produced by antiproton annihilation in hydrogen could be contained and their energy coupled to a 

hydrogen plasma, a variable thrust, variable I,, engine could be designed without the disadvantages 

of heavy atom annihilation. With this goal in mind, a computer model was constructed to predict 

the performance of an antiproton powered, magnetically confined hydrogen plasma engine. 

Pulsed 6-H Rocket Model 

The system to be modeled is dynamic and complex. On one time scale, antiprotons annihilate 

with an initially neutral hydrogen gas to produce relativistic, charged pions. The pions traverse the 

hydrogen propellant and transfer some amount of energy before decaying into charged, relativistic 

muons over a time scale of several nanoseconds. The energetic muons interact with the hydrogen 

over microsecond time scales before decaying into extremely relativistic electrons and positrons. The 

electrons and positrons in turn give up energy to the hydrogen over a time scale corresponding to 

the plasma confinement time, typically a few milliseconds. The electrons and positrons are stable, 

although positrons may be lost due to annihilation with plasma electrons. Strong magnetic fields 

are used for confinement and stability, but even so particles will be continually lost from the system. 

Thus at any given time the ensemble will consist of protons, antiprotons, plasma electrons, hydrogen 

atoms, pions(&), muons(&), decay electrons, and positrons, evolving and interacting on time scales 

which may differ over six orders of magnitude. 

To simplify the system modeling, the rf and R- inesons are not distinguished, and are assunied 

to have an initial kinetic energy equal to the average distribution kinetic energv of 2.50 MeV/pion. 

Similarly, no distinction is made between the charged muons, which are assunied to have an initial 

kinetic energy of 192 MeV/niuon. Muon decay produces electrons and positrons, and it is assunied 

that half of the electron/positron number density consists of electrons, the other half of positrons, 

each with an initial kinetic energy of 100 MeV/e*. This separation allows an estiinate to be made of 

positron depletion due to annihilation with plasma electrons. The assumption of indistinguishable 

particles is valid since Couloinb interactions and energy exchange rates are proportional to even 

powers of the particle charge. The possibility of relativistic rfr- or p+p- annihilation occuring in 

5 
low pion or muon number densities over their respective lifetimes is remote and not included in the 

model. The use of initial average kinetic energies is somewhat crude, but a comparison of energy 

loss rates calculated over the range of experimentally observed particle kinetic energies indicates the 

error introduced by this approximation is negligible("). 

Rate equations(") are used to evaluate the antiproton and charged annihilation byproduct number densities at each time step. Both PH rearrangement collision annihilation and pii direct annihilation cross sections are included in the antiproton annihilation rate calculations. Positron annihilation 

with ambient plasma electrons is included in the model. Relativistic forms of the energy loss equations derived by Bethe-Bloch(") and Sivukhin(") are used to estimate the energy transferred by 

the relativistic particles to the hydrogen propellant. Bremsstrahlung and synchrotron radiation may 

be neglected for the energetic pions and muons("), but are important energy loss mechanisms for 

the relativistic electrons and positrons and are included in the simulation. Plasma synchrotron radiation is neglected, but plasma bremsstrahlung radiation, a dominant energy loss mechanism at 

higher temperatures and plasma number densities, is evaluated at each time step and the plasma 

energy adjusted accordingly. Deexcitation and recombination energy losses, which may appear as 

the plasma is heated from an initially neutral to fully ionized state, are small and are not included 

in the model("). 

The simulation treats all similar particles created during a given time step as an identical group; 

thus, all pions created during the nth time step At have the same energy, lose the same amount of 

energy to the hydrogen propellant, and decay at the same time. Similar arguments hold for the muon 

and electron/positron distributions. Hence at any given time there will be [ %] groups of pions in 

the system, [w] groups of muons, and a continually growing number of electron/positron groups 

built up as the muon groups decay. Each group is followed through the system until they decay 

(for pion and muon groups) or until the run is completed (for the electron/positron groups). This 

bookkeeping procedure allows reasonable estimates to be made of the particle-propellant interactions 

without requiring excessive computer time. Details of the code structure are given in reference 10. 

Particle Confinement 

Magnetic fields are used to constrain the charged annihilation byproducts and confine the hydrogen 

plasma away from any material walls. The magnetic mirror system (Figure 2) is assumed to consist 

of solenoidal current coils to produce a longitudinal magnetic field and mirror field coils at each 

end of the system to provide particle containment and overall MHD stability(13). Antiprotons are 

injected axially along magnetic field lines and the neutral hydrogen propellant is injected radially 

across the field lines. Once the plasma is heated, one end of the magnetic mirror system is relaxed, 

forming a magnetic nozzle and allowing the plasma to escape. 

The minimum magnetic field strengths required to contain the system of relativistic particles 

and plasma propellant are calculated by balancing the magnetic field pressure and plasma/particle 

kinetic pressure, 

B' 

where n is the number density and (kT) is the temperature of the it* species, and the summation 

extends over all particle species present in the system. An additional constraint on minimum field 

strengths is imposed by requiring the relativistic particle gyroradii to be much smaller than the 

reaction chamber dimensions, yielding a minimum field strength of about 10 Tesla for typical reaction 

6 
RIRROR 

COIL 

RIRROR COIL a; 

SOLENOID COIL 

Figure 2: Magnetic Mirror System. (a) Field Coils. (b) Field Strength. 

i 

I 

b I I 

! 

hi" 

I 

I 

I 

I 

I 

I 

I 

i 

chamber dimensions("). 

The probability that a charged particle will be lost from the magnetic mirror system is given 

by('4) 

112 P=l-(,-) R, - 1 

where P is the probability of escape and R, is the magnetic mirror ratio, the ratio of the maximiim 

to ininimum magnetic field strengths. For a uniform magnetic field, the mirror ratio is unity and 

no particles are confined. As R, --t 00, the probability of escape goes to zero. Current technology 

restricts maximum magnetic field strengths in the mirror regions to well below 50 Tesla("), hence 

the mirror ratio of the system will be limited to fairly low values. Loss probabilities are used in the 

simulation to modify the relativistic particle number densities at each time step. Plasma diffusion 

and end losses are negligible over millisecond plasma confinement times("), and the propellant 

number density is assumed to remain constant during confinement. 

Engine Performance 

Energy transfer efficiencies for the engine are calculated using 

(Ei + Ee)np 

(1877MeV)n, v= (7) 

where E, and E, are the calculated plasma ion and electron energies, respectively, np is the hydrogen 

propellant number density, np is the initial antiproton number density, and 1877 MeV is the amount 

of energy released in each proton-antiproton annihilation. 

A simple energy balance may be used to estimate the rise in propellant teiiiperatrire due to the 

influx of annihilation energy: 

tplfa,c2 = dl,,c,,AT (8) 

where Ma is the total amount of annihilated mass, Alp is the total amount of propellant mass, c, is the 

specific heat of the propellant at constant voluxne, AT is the change in propellant temperature, and 

q is the efficiency with which the annihilation energy is transferred to the propellant. In the limiting 

7 
cases of low temperature molecular hydrogen and high temperature atomic or ionized hydrogen, the 

specific heat may be calculated using(") 

where Ro is the universal gas constant, M is the molecular (atomic) weight of the propellant, and 

y is the adiabatic index of the gas. For molecular hydrogen, 7=7/5, while for atomic or ionized 

hydrogen, y=5/3. Using the energy balance equation, the plasma ion energies predicted by the code 

are converted. to propellant temperatures via 

T(eV) = &ods(eV) (7 - 1)M' (10) 

where both T and Ecodc are expressed in units of eV, and My is the molecular or atomic weight in 

amu. 

Number densities are used in the simulation to provide flexibility in the choice of total reaction 

chamber volume. Once the chamber volume V, is selected, the hydrogen propellant mass flow rate 

may be calculated from 

where mp is the atomic mass of hydrogen, np is the hydrogen propellant number density, and At 

is the pulse repetition period of the engine. Similarly, the antiproton mass flow rate may be found 

using 

where mp and np are the antiproton rest mass and initial number density, respectively. 

Engine thrust and specific impulse are estimated using the ideal rocket approximations(*'). An 

additional assumption is made that all of the ionized exhaust leaves the chamber axially with the 

same average energy, directed by a 100% efficient magnetic nozzle. The exhaust velocity is then 

given by 

and the estimated specific impulse (I,p) of the engine is 

The equivalent continuous 

and in terms of propellant 

thrust produced during each pulse is given by 

Th = AI,. 

number density may be written 

where Ate is the engine pulse period. 

8 
Results and Discussion 

0 

The model was tested against an antiproton powered orbital-transfer vehicle (OTV) study 

performed by Cassenti("). The predictions of engine thrust and specific impulse('') agree with 

Cassenti's Monte Carlo based simulations to within 5%. In addition, preliminary Monte Carlo 

simulations performed at the Jet Propulsion Laboratory (JPL) of the annihilation energy transfer 

efficiencies in a hydrogen plasma are in good agreement with the energy transfer efficiencies predicted 

by the code("). 

Selected results are presented in the following sections for low, moderate, and high hydrogen 

propellant number densities and a range of antiproton number densities. Cases presented in the first 

part of each section assume no charged particles are lost from the system, and represent an upper 

limit on engine performance. Combinations leading to optimum propellant heating in each case are 

reexamined using finite magnetic mirror ratios to evaluate the effect of particle losses on engine performance. Mirror ratios of 2 and 3 are used in compliance with current technology constraints('e). 

Antiproton and hydrogen injection energies are set at 0.1 eV to allow rapid injection into the reaction 

chamber, yet retain a sufficiently low center-of-mass velocity for efficient annihilation. Maximum 

electron and ion energies, annihilation energy.transfer efficiencies, minimum magnetic field strength 

reqirements, predicted specific impulse, and predicted thrust (normalized to reaction chamber volume and pulse repetition rate) are tabulated in each section, and estimates of engine performance 

are given. 

Low Number Densitv Hvdroeen Plasma 

The lowest hydrogen propellant number density considered in this study is lO'*~m-~. Figures 3(a) 

through 3(d) display antiproton, pion, muon, and relativistic electron/positron number density evolutions for initial antiproton number densities between lO'~m-~ and 1012cm-3, respectively, and 

mirror ratios of infinity. It is seen that antiproton annihilation becomes less efficient as the initial 

antiproton number density is increased, due to the rapid heating of the hydrogen propellant and 

the resulting decrease in proton-antiproton annihilation cross sections. The fraction of antiprotons 

remaining in the system after one millisecond increases from essentially zero at lower antiproton 

number densities to almost 70% for initial antiproton number densities of lO"~m-~. Charged annihilation and decay byproduct evolutions are altered by the prolonged annihilation times. Significant 

amounts of pions and muons remain in the system for longer times, and maximum byproduct number densities are reduced by the prolonged annihilation period. Electron/positron number densities, 

which increase to roughly 3 times the initial antiproton number density in Figure 3(a), are reduced 

to approximately 98% of the initial antiproton number density in Figure 3(d). 

Plasma ion energies are plotted for each of the intial antiproton number densities in Figure 4. 

Comparing the number density evolutions with the temperature curves, it is clear that the electrons 

and positrons are primarily responsible for heating the plasma, with little or no contribution from 

the pions and muons. The continued production of particles during the prolonged annihilation times 

slowed program execution considerably, and computer runs were terminated at 1 iiis confineiiient 

times for economy. Test runs performed out to 5 nis indicate t.hat plasnia teinperat tires increase 

linearly with increasing confinement time. 

Balancing plasma temperature with efficient antiproton annihilation, the optiiiial antiproton 

number density for running the low hydrogen propellant number density engine appears to be around 

1010~n~-3. This case was rerun using magnetic mirror ratios of 2 and 3 to evaluate the effect of 

charged particle losses on the heating process. As seen in Figure 5, the ion energy at 1 nis is reduced 

from approximately 8 eV with no mirror losses to 4.5 eV with a mirror ratio of 3, and 3 eV with a 

9 
lo 1 I _----- 

1 

10-2 

Figure 3: P, I, p, and e* number density evolutions for np = lO"cm-'. (a) np = 108cm-3, (b) np = 

10'0cm-31 (c) nI = 101*cm-', and (d) np = IO"cm-'. No mirror losses. 

10 
- 

c. 

> m 

m 

V u 0 

w 

Figure 4: Ion temperature versus time for various 

initial antiproton number densities; n, = 101'crn-'. 

No mirror lays. 

Figure 6: Ion kmper8ture versus time for nrious 

mirror ratios; n, = IO~~C~-~, n, = W'cm". 

mirror ratio of 2. The continual loss of pions from the system reduces muon production, which in 

turn reduces electron/positron production. The reduced electron/positron production rate, coupled 

with their continual loss from the magnetic mirror system, significantly diminishes the propellant 

temperature and the associated engine performance. 

Table 2 summarizes the results for the low number density hydrogen plasma engine. Maximum 

propellant temperatures are achieved at higher antiproton number densities, but at the expense of 

wasting antiproton fuel. In addition, the plasma electrons are being heated faster than they can 

share their energy with the ions, and the plasma moves away from thermal equilibrium as the initial 

antiproton number density is increased. The optimum antiproton number density is estimated to be 

1010cm-3, and with a mirror ratio of 3 the maximum ion energy is about 4.5 eV after 1 ms, yielding 

a low annihilation energy transfer efficiency of 0.0048%. Assuming a 5 ms confinement time, the 

ion temperature is 22.5 eV, and the efficiency is approximately 0.024%. The calculated magnetic 

field strengths required for confinement are smaller than the 10 Tesla field required to constrain the 

pion gyroradii to reasonable values (x 10 cm), and are primarily due to relativistic particle kinetic 

pressure rather than plasma thermal pressure. 

For the optimum case outlined above, a 1 ms plasma confinement time yields a specific impulse of 

3030 seconds and a normalized thrust of 5.1 x lo-" N-s/cma, where the thrust has been normalized 

to the reaction chamber volume and engine pulse period. Assuming the reaction chamber has a 

radius of 1 meter and a length of 10 meters, and assuming a pulse period of 10 ms, the equivalent 

continuous thrust is only 1.6 N (0.35 Ibf). Increasing the plasma confinement time to 5 ms yields 

a specific impulse of 5530 seconds and an equivalent continuous thrust of 3.6 N (0.80 Ibf). In both 

cases the hydrogen propellant flow rate is 3.1 x 10" H/pulse (525 mg/s), and the antiproton flow 

rate is 3.1 x lOI7 @/pulse (52.5 pg/s), since thrust is normalized to engine repetition rate and not 

plasma Confinement time. 

The low energy transfer efficiencies associated with the low hydrogen propellant number deiisitv 

severely limit the potential performance of the plasnia engine. Increasing the hydrogen number 

density results in higher energy transfer efficiencies and iiiiproves engine performance, as shown in 

the following section. 

11 
np( cm-') 

109 

10'O 

10'0 

10'0 

10" 

10'2 

~ B,i,,(T) I&) Th (N.sec/cm') 

0.35 1430 2.3 x lo-'' 

1.1 4040 6.7 x lo-'' 

0.81 3030 5.1 x lo-'' 

0.65 2475 4.1 x lo-'' 

3.1 11100 1.8 x lo-' 

8.5 19700 3.3 x lo-' 

- Rn 

00 

00 

3 

2 

00 

00 

EL (ev) 

1.0 

8.1 

4.5 

3.0 

66 

370 

-~ 

%a= (ev) 

1.0 

8.1 

4.5 

3.0 

60 

190 

rl 

1.07 x 10-4 

8.5 x lo-' 

4.8 x lo-' 

3.2 x lo-' 

6.71 x lo-' 

3.0 x lo-' 

Table 2: Plasma heating and rocket performance parameters for hydrogen number density of 

1014cm-3. Confinement time = 1 ms; energy and efficiency parameters increase linearly with time 

for longer confinement times. Thrust is normalized to chamber volume and engine pulse period. 

Moderate Number Density Hydrogen Plasma 

A hydrogen propellant number density of 10'scm-a was chosen to model the performance of a 

moderate number density hydrogen plasma engine. Figures 6(a) and 6(b) show the antiproton and 

annihilation byproduct number density evolutions for initial antiproton number densities of lO'~rn-~ 

and 10'acm-3, respectively. Number density evolutions for initial antiproton number densities of 

10'0cm-3 and lO"~m-~ are similar to those shown in Figure 6(a). At the lower antiproton number 

densities, essentially complete antiproton annihilation take place during the 5 ms confinement time. 

Pion number densities reach a maximum slightly in excess of the initial antiproton number densities 

before decaying from the system. Muon number densities climb to nearly 3 times the initial antiproton number densities before decaying, in agreement with the initial assumption of three charged 

mesons produced per annihilation event. The electron/positron number densities grow to 3 times 

the initial antiproton number density as the muons decay, and remain constant at this level. Increasing the initial antiproton number density to 10'2cm-3 heats the hydrogen too rapidly, decreasing the 

annihilation cross sections and prolonging the period of proton-antiproton annihilation. At the end 

of 5 ms, nearly lO'~m-~ antiprotons remain in the system, and will be exhausted with the plasma 

propellant. 

Figure 7 shows the ion energy evolution for each of the initial antiproton number densities. The 

flattening of the energy curve for the case np = 10gcm-3 is due to plasma bremsstrahlung; the 

energy deposited in the plasma by the charged annihilation products is balanced by bremsstrahlung 

losses, with no net gain in plasma energy. Energy deposition rates associated with the higher initial 

antiproton number densities exceed the rate at which bremsstrahlung radiation is lost, resulting in 

steadily increasing propellant temperatures. Also evident is the increased plasma energies caused 

by the relativistic muons and, to a lesser extent, the relativistic pions. At higher initial antiprotoil 

number densities the muons may substantially heat the plasma before decaying froin the system. 

Miniinuni magnetic field profiles for each of the above cases are presented in Figure 8. In each 

case, the minimum calculated field strength is due primarily to the relativistic particle kinetic pressure, which greatly exceeds the plasma thermal pressure. The evolution of the minimum magnetic 

field strength closely follows the production and decay of the annihilation byproducts (Figure 6). 

12 
Figare 6: P, z, p, and e* number density evolutions for 5 = lO*%m-’. (a) nI = 10°cm-s, (b) 9 = IO”cm-’. No nJrror losses. 

TIME (SI 

Figure 7: Ion temperature versus time Tor various 

initial antiproton number densities; np = 10*ecm-J. 

No mirror losses. 

Figure 8: Minimum required magnetic field strength 

versus the for various initial antiproton number 

densities; np = lO“’~rn-~, no mirror losses. 

13 
For initial antiproton number densities of 1012cm-a, the minimum field strength required for 

particle containment is approximately 14 Tesla, larger than the 10 Tesla previously assumed for 

reduced pion gyroradii. Rerunning this case with finite mirror ratios reduced the niinimum required 

field strengths to 12 Tesla for a mirror ratio of 3, and 10 Tesla for a mirror ratio of 2 (Figure 9). 

The decrease in ion energies due to the escape of charged particles from the confinement system is 

shown in Figure 10. Ion energies at 5 ms decrease from nearly 3280 eV with no mirror losses to 1765 

eV with R,,,=3, and 1125 eV with L=2. 

- 

- Ic 

c 

E Lp __..__----- 

flIRROR RATIO: 

NO LOSSES 

R.) - 

HIRROR RATIO: 

NO LOSSES 

Figure 9: Minimum required magnetic field strength 

versus time for various mirror ratios; up = W'cm-a, 

n, = 10'zcm-'. 

Figure IO: Ion temper.ture versus time for nrrious 

mirror ratios; np = 10lecm-*, up = 1012cm-a 

Table 3 lists plasma and engine performance parameters for the moderate number density plasma 

engine. Energy efficiencies are greatly improved over the low number density cases presented previously, and complete antiproton annihilation occurs under most operating conditions. A respectable 

range of thrust and specific impulse values are available for reasonable antiproton mass injection 

rates and magnetic mirror ratios, which may allow some flexibility in mission designs. 

Assuming a reaction chamber radius of 1 meter, length of 10 meters, and engine repetition rate 

of 10 ins yields a hydrogen propellant mass flow rate of 3.14 x loz3 H/pulse (52.5 g/s). For an 

antiproton number density of ~O~~CII~-~, the antiproton mass flow rate is 3.14 x lo" Plpulse (52.5 

pg/s). Using a mirror ratio of 3 yields a maximum ion energy of 10.4 eV over a 5 ms plasma 

confinement time. The predicted specific impulse is 4610 seconds, and the normalized thrust is 

7.6 x N.s/cni3, which for the above parameters yields an equivalent continuoiis thrust of 2.400 

N (535 Ibf) each cycle with an energy transfer efficiency of 1.1%. Increasing the initial antiproton 

number density to lO"~m-~ requires an antiproton mass flow rate of 3.14 :< IO" P/s (5.25 tirg/s), 

and results in a maximum ion energy of 1765 eV with an energy transfer efficiency of 1.9%. The 

specific impulse is raised to an excessive 60,000 seconds, and the normalized thrust is 9.8 x lo-' 

N.s/cm3 for an equivalent continuous thrust of 30,400 N (6800 lbf). The specific impulse niight 

be lowered, and the thrust increased, by mixing cold hydrogen gas with the hot plasma propellant 

before exhausting. 

i 

14 
1 

0.009 

0.023 

0.011 

0.031 

0.016 

0.036 

0.019 

0.012 

E&,,, (ev) 

1.3 

22 

10.4 

295 

152 

3470 

1806 

1140 

kin(") 

0.32 

1.4 

0.75 

4.4 

2.4 

14 

12 

10 

Ep,,, (eV) 

1.3 

22 

10.4 

294 

152 

3280 

1765 

1125 

np(cm-9 

109 

1010 

10'0 

10" 

10" 

10'2 

10'2 

10'2 

R, 

do 

do 

3 

do 

3 

do 

3 

2 

IlP(s) 

1630 

6700 

4610 

24500 

17600 

81800 

60000 

48000 

Table 3: Plasma heating and rocket performance parameters for hydrogen number density of 

101ecm-3. Confinement time = 5 ms. Thrust is normalized to chamber volume and engine pulse 

period. 

Th (N-sec/cm*) 

2.7 x io-' 

1.1 x 10-6 

7.6 x io-' 

4.0 x lob6 

2.9 x 

1.3 x 

9.8 x lo-' 

7.9 x lo-' 

Although plasma bremsstrahlung radiation becomes a concern in terms of shielding requirements, 

the general performance of the antiproton powered plasma engine is dramatically improved using 

a moderate number density hydrogen propellant. The following section discusses predicted engine 

performance when the propellant number density is increased further. 

High Number Density Hydrogen Plasma 

Based on the previous results, it is expected that increasing the hydrogen number density will 

increase both the energy transferred into the plasma by the charged annihilation products and the 

energy lost from the plasma by radiation. The highest hydrogen number density considered in the 

study is lO"~m-~, and Figures ll(a) and ll(b) display charged particle number density evolutions 

corresponding to initial antiproton number densities of 10'0cm-3 and 10'3cm-3, respectively. The 

nearly identical figures bracket the range of antiproton number densities used in the high propellant 

number density simulations. Coniplete antiproton annihilation occurs within 100 nanoseconds in all 

cases, and each of the pion, muon, and electron/positron number densities in turn climb to niaxiiiiuin 

values 3 times higher than the initial antiproton number density. Due to the brief but intense 

antiproton annihilation period, the pions completely decay from the system within microseconds, 

and the muons are depleted within fractions of a millisecond, leaving the electrons and positrons to 

heat the plasma over the remaining confinement times. 

The ion energy evolution (Figure 12) displays several reinarkable features. At low initial anti proton number densities, the ion energy is limited by plasma bremsstrahlung radiation to values slightly 

over I eV. Increasing the initial antiproton number density to 10" c111-~ raises the ion energy only 

slightly to 1.8 eV, again due to plasma radiation losses balancing the annihilation energy deposition. 

Increasing the initial antiproton number density still further results in a substantial heating of the 

plasma, as the energy deposited by the charged annihilation products exceeds the plasma energy 

lost by radiation. The role of the pions and nilions in heating the plasma becomes more evident, 

15 
although it is interesting to note that the net energy deposition from these particles is limited by 

plasma bremsstrahlung to fairly low valres. The bulk of the plasma heating comes from the electrons 

and positrons, which dominate the plasma radiation losses and raise the propellant temperature several orders of riiagnitude in a short period of time. Each of the energy curves are seen to peak at 

a time of 400 ps, after which the plasma energy falls rapidly to below 1 eV. A consideration of the 

energy loss equations shows that at this time the relativistic electrons and positrons have given up 

essentially all of their energy to the plasma, and with no source of heating the plasma rapidly loses 

energy by bremsstrahlung radiation. As the plasma cools it recombines (Figure 13), and conflnement may be lost as the neutral hydrogen escapes through the magnetic fields. Consequently, to 

ruii the engine efficiently at high propellant number densities requires that the injection, heating, 

and exhaust cycle all be performed within 400 ps, or plasma cooling and neutral propellant loss will 

diminish the performance of the engine. 

0: W m 

J 

L 

- .e---- 

I., ', ?ARTICLES: 

-1 I 

Figure 11: P, x, p, and e* number density evolutions for 5 =: 10'%m-'. (a) 9 = 101Ocm-', (b) 

ng = 10L3cm-'. No mirror losses. 

10'- 

I (MTIPROIONS) 

1 1 I I 1 1 

10-8 10-7 .io-6 18 10-4 VI-' 

TIME (SI 

Figure 12: Ion temperature versus time for various 

initial antiproton number densities; np = 10a8crn-'. 

No mirror losses. 

16 

TIME (51 

Figure 13: Fraction of 10'8cm-' hydrogen gas ionized versus time for various initial antiproton number densities. No mirror losses. 
Figure 14 shows the minimum magnetic field strengths required to confine the system of charged 

particles and plasma, where again the field evolutions closely follow the production and decay of 

the relativistic annihilation byproducts. At low antiproton number densities, the field strengths are 

below the 10 Tesla field minimum set by the particle orbit constraints. As the initial antiproton 

number density is increased to 1017cm-5, the minimum field increases to 18 Tesla. The evolution 

of the magnetic field strengths highlights the production and decay of the charged annihilation 

products, as well as the heating and subsequent cooling of the hydrogen plasma. Increasing the 

initial antiproton number density to 10"cm-' requires a minimum confining field strength of nearly 

60 Tesla for the central field coils, clearly beyond the capability of current or projected magnetic 

containment technology. Thus the optimum antiproton number density at which to run the high 

propellant number density plasma engine is around 1012cm-a; higher antiproton number densities 

require unrealistic magnetic field strengths to confine the system, and plasma heating due to lower 

antiproton number densities is severely diminished by plasma bremsstrahlung radiation. Plasma 

and rocket performance parameters are summarized for the high number density propellant engine 

in Table 4 below. 

l.ElO/d 

- Ic 

0 

c 

m 1- 

TIME (J) 

Figure 14: Minimum required magnetic field strength 

versus time for various initial antiproton number 

densities; np = I018cm-', no mirror losses. 

Figure 15: Ion temperature versus time for various 

mirror ratios; n, = 10'8cm-a, n, = I01zcm-3. 

17 
ng( 

10'0 

10" 

1012 

10" 

10'2 

1013 

- R, 

00 

00 

00 

3 

2 

00 

EL,, (ev) 

1.3 

1.8 

81 

28 

12 

1780 

Ep,,, 

1.3 

1.8 

81 

28 

12 

1780 

rl 

0.139 

0.019 

0.086 

0.030 

0.012 

0.189 

' Bmin(T) 

1.8 

6.7 

18 

16.7 

14.6 

57 

12860 

4950 

60300 

Th (N.sec/cm3) 

2.7~ lo-' 

3.1 x lo-' 

2.1 x 10-~ 

1.2~10-' 

9.9~ 10-~ 

8.1 x lo-' 

Table 4: Plasma heating and rocket performance parameters for hydrogen number density of 

10'8cn1-3. Confinement time = 400 ps. Thrust is normalized to chamber volume and engine pulse 

period. 

The maximum ion energy reaches 81 eV for the optimum case with no particle losses. The ion 

energy is reduced to 28 eV for a mirror ratio of 3, and to 12 eV for a mirror ratio of 2 (Figure 

15). The corresponding magnetic field strengths are reduced from 18 Tesla with no mirror losses 

to 16 Tesla when R-=3 and 15 Tesla when %=2, indicating that the relativistic charged particle 

pressure rather than the plasma thermal pressure plays a dominant role in defining the minimum 

magnetic field strengths. Assuming a mirror ratio of 2, the specific impulse is 4950 seconds, and 

the normalized engine thrust is 8.1 x N.s/cnia. Assuming the standard 1 m by 10 m reaction 

chamber and a 10 ms engine repetition rate, and assuming the propellant is exhausted at its peak 

temperature within 400ps, yields an equivalent continuous thrust of 250 kN (56 klbf) with an energy 

transfer efficiency of 1.2%. 

Additional Design Considerations 

There are an abundance of basic technology issues related to the design and operation of an 

antiproton powered vehicle, not the least of which concerns the amount of antiprotons required 

for fuel (current yearly production rates would suffice for only a few engine pulses). Adopting the 

uncertain premise that the antihydrogen fuel will be available, several crucial design elements remain 

to be evaluated. 

Maanetic Field Coils 

The magnetic mirror system used to contain thc charged, relativistic anniliilatioii products and 

the ionized plasiiia is presumed to consist of superconducting soleiioidal field coils for the central 

chamber, bracketed at each end with superconducting magnetic mirror coils for plasiiia stabilitv 

and confinement. One end of the magnetic mirror system is pulsed, allowing the heated propellant 

to escape. The remaining mirror coil and the niain solenoidal field coils would be run steady 

state, and could conceivably be energized using space station facilities before a mission begins. An 

efficient energy storage and transfer system will be required to power the exhaust coil during pulsed 

operation and return the energy to storage when the field is relaxed. One possibility is to store the 

energy inductively using additional superconducting electromagnets. Stacey(*') discusses the use of 

18 
a capacitive shunt transfer circuit to transfer energy between a superconducting storage coil and a 

superconducting fusion device coil. The energy transfer circuit and related pulse forming network 

could be adapted for a pulsed mirror coil with minimal modifications. 

The energy transfer between the pulsed mirror coil and the energy storage coil will undoubtedly 

be less than 100% efficient, and an onboard energy source may be required to replenish lost field 

coil energy. One possible source of auxiliary power is the charged particle flux leaking through the 

magnetic mirrors during each heating cycle. It may be possible to use a direct energy converter 

placed at the end of the mirror system to tap some of the directed charged energy as the pions 

(and other charged particles) escape magnetic confinement. Even a very inefficient converter might 

provide enough energy to resupply the pulsed mirror coil, and the energy of the annihilation products 

escaping through the loss cones would not be entirely wasted. Magnetic field coil power requirements 

and auxiliary power alternatives are discussed in reference 10. 

The mass of the magnetic confinement system is expected to be a major part of the total 

rocket mass. Superconducting coils made of NbaSn/NbTi are currently used in magnetic fusion 

engineering(21), and are used here to provide a preliminary estimate of the total coil mass which 

may be required for an antiproton powered vehicle. The density of NbTi is approximately 6.4 g/cni3, 

and coil dimensions may be scaled from the MARS (Mirror Advanced Reactor Study) tandem mirror 

fusion plant design(21). The central cell of the MARS design consists of 44 identical solenoidalal 

coils spaced 3.16 meters apart. Each coil has an inner radius of 2.44 m, thickness of 0.932 m, and 

width of 0.884 m, and provides a central field strength of roughly 5 T. The antiproton powered 

rocket annihilation chamber has half the radius but requires twice the field, hence the coil thickness 

and width may remain about the same. The coil volume is approximately 7.6 m3, corresponding 

to a inass of about 4.9~10' kg. The assumed length of the antiproton annihilation chamber is 10 

meters; spaced 3 meters apart, the main chamber would require 3 solenoidal coils. Combined with 

the two end coils, the estimated mass of the magnet system is roughly 2.5~10~ kg. In practice, 

the coil structure includes copper stabilizing material, electrical insulation, mechanical support, and 

associated cooling systems, which will substantially increase the mass and may significantly diminish 

low thrust engine performance. 

Antiproton Storage __.___ and Transport 

Several authors have discussed methods of storage and transport for the antihydrogen f~el(~9'). As 

an added complication, storage and transport systems for the magnetically confined plasma engine 

must also contend with charged annihilation products and plasma particles escaping through the 

mirror coil back along the antiproton beam path. It may be beneficial to place the storage chamber 

at an angle with respect to the magnetic mirror axis to keep charged particles from penetrating 

and heating the storage region. Pulsed electric or magnetic guide fields could then be used to direct 

incoming antiproton bunches into the annihilation chamber at the start of each cycle. After injection 

the guide fields are pulsed off as charged particles from the resulting annihilations escape back along 

the axis, perhaps passing through the direct energj converter mentioned above to srrpplv auxiliary 

power. When the reaction chamber is evacuated, the guide fields are prilsccl on and a new hunch 

of antiprotons are diverted into the chamber. Alternativelv, antiprotons iniglit he rrconihiiied with 

positrons, and the neutral antihydrogen atoms injected across the field lines. Efficient antiproton 

fuel transport and injection cycling is critical for the pulsed plasma engine operation. 

19 
Shielding 

Copious amounts of radiation are prodd both by antiproton annihilations and by the confined 

plrsma. Sensitive ship components must be protected, and the additional mass of a radiation 

shield will reduce the amount of psyload the rocket can transport. Casrenti(z2) has performed 

a preliminary numerical rnalyrlr d the crew shielding r+nd for an antiproton powered OTV 

spacecraft(’8~. The crew is assumed to be located 100 metm away fmm the radiation source, and 

a tungsten shadow shield is placed between the crew and the anniWoa chamber. The radiation 

source is assumed to be the 200 MeV (average energy) gamma rays produced by prompt neutral 

pion decay. The simulation models pair creation, ionisation energy lms, and positron annihilation 

production of secondary gamma rays within the shield material, but neglects the production of high 

energy CleCtIOM created by ionisation and Compton scattering of secondary particles. The high 

energy electrons will be a source of secondary gamma radiation due to bremsstrahlung emission, and 

the simulation underestimates the number of lower energy gamma rays produced in the shielding 

material. The sirnulation is one dimensional, hence radiation scattering is also neglected. Assuming 

8 mg of mass are annihilated, the model predicts a minimum lidd thickness of 6.5 cm for adequate 

crew shielding. The estimated mtm of the rhield is thus on the order of 3.9~ Id kg. The 10 tonne 

payload assumed in the OTV study must mw inch& this mass, reducing the ddiverable payload 

by nearly 40%. 

Additional mass will be required to protect the supercducting coils, which are immediately 

outside the reaction chamber. Bd onthe &ore radiation model, and ussuming the coils are placed 

1 meter from the radiation source, an additional 11.8 cm of tmngstea Shielding is required for the 

OTV magnetic field coils. Assuming a blanket shield is used around the entire reaction chamber, 

the required shield mass is 28x lo8 kg, or nearly 3 times greater than the 10 tonne payload assumed 

in the OTV mission study. Shadow shielding of the superconducting coils could reduce the required 

shielding mass, although protecting the coils from scattered radiation may limit amy potential mass 

reduction. 

The problem is exacerbated for the antiproton powered plasma engine operating at high temperatures, since plasma bremsstrahlung radiation must now be included in the total dosage calculations. 

Unlike the penetrating 200 MeV gammas, the lower energy bremsstrahlung photons will deposit 

most of their energy in the surface layers of the shield material, leading to wall ablation and shield 

degradation similar to that seen in magnetic fusion energy devices(”). Presumably, much of the 

research directed toward solving the problem of first wall ablation in fusion plasma reactors can 

be transferred to the problem of shield ablation in the antiproton powered engine. The disparate 

energies of the gamma radiation may require a multilayered shield design, and the optimum design 

of such a shield is clearly an important area for future research. 

A rough estimate of the maximurn radisted energy from an antiproton powered plasma engine 

can be made by assunling an antipraton number density of 1012cm-a, a hydrogen plasma number 

density of 10’8cm-a, and a plasma temperature of 10 eV (corresponding to the high propellant 

number density case with a mirror ratio of 2). Again assuming a chamber radius of 1 in and a length 

of 10 m yields a total chamber volume of 31 m3 (3.1 Y 1O7rm3). The total gamnia radiation prodiicetl 

in each 400 ps pulse by neutral pion decay is approximately 

(1:) 

where it is assumed that 2 neutral pions are created in each annihilation event and each subsequently 

decays into two 200 MeV gamma rays. The plasma radiates an additional 6.6~ lo8 J each pulse, 

for a total radiated energy of 4.7 GJ per pulse. Dividing by the chamber surface area yields a total 

dosage of about 75 MJ/m2 per pulse; an engine repetition rate of 10 msec would thus produce 7.5 

ET io1’. 3.1 x IOf * 2.2 - 200 Mer- o 4.0 CJ 

20 
GW/ml. Assuming the superconducting coil cooling system can remove the equivalent of a few 

Watts/m' requires a shield thickness on the order of 17 em, for a total shield mass of 2.24~10' kg. 

The equivalent continuous thrust produced by the engine is around 250 kN over a 10 ms engine cycle. 

Assuming the shield mass dominates the total mass of the engine yields an average acceleration of 

about 1 ni/sl. To reach a velocity of 6.6 km/s (suitable for an OTV mission) requires a burn time of 

approximately 5500 seconds (1.5 hours). The expended propellant mass is on the order of 2.9~ 10' 

kg, and the required antiproton mass is 28.6 grams. 

The shielding mass would be reduced for shorter reaction chamber lengths or for longer engine 

cycles, although such measures would also reduce the average engine thrust. Alternatively, the 

shield mass might be reduced by using shadow shields to protect the crew, superconducting coils, 

and related support structure. In either instance the shield mass will comprise a major portion of the 

total engine mass, a reality imposed on any antiproton powered engine using magnetic confinement. 

The impact of such severe mass penalties on mission performance underscores the need for refined 

radiation shield analysis. 

Since the radiation shielding absorbs significant power, it must be cooled either actively or by 

passive radiation cooling. The additional mass of the cooling system will further reduce the available 

payload fraction, and design studies should be carried out to determine the optimum means of 

dissipating the energy imparted to the shield. It may be possible to mitigate the mass penalty 

associated with shielding and shield cooling by tapping some of the energy deposited in the shield 

for use in an auxiliary power systern(l2). The increase in shield temperature caused by absorbing an 

amount of energy E is given by F Y AT= - 

Jc,, M 

where cp is the specific heat of the shield material (33 cal/kg°C for tungsten), J is the mechanical 

equivalent of heat (4.186 J/cal), and M is the shield mass. The temperature of a 2.3~ 10' kg tungsten 

shield absorbing roughly 5 GJ/pulse would increase about 160 OC per pulse. Depending on the rate 

at which energy was removed from the shield, the steady state temperature could be much higher, 

providing a useful reservoir of energy for additional power requirements. 

Conclusion 

Matter-antimatter annihilation produces more energy per unit mass than any other method of 

energy production, making it an attractive energy source for spacecraft propulsion. The energetic 

charged particles produced in proton-antiproton annihilation may be exhausted directly to provide 

a low thrust, high specific impulse engine, or used to heat a propellant for higher thrust and lower 

specific impulse. The magnetically confined pulsed plasma engine is designed to minimite thermal 

constraints on material walls while providing a range of operating parameters. In this concept, 

antiproton beams are injec',ed axially into a pulsed magnetic mirror system, where they annihilate 

with an initially neutral hydrogen gas. The resulting charged annihilation products transfer enerRv 

to the hydrogen propellant, which is then exhausted through one end of the pulsed mirror sysfeiii 

to provide thrust. Engine thrust and specific impulse are controlled bv adjusting the iiriiiiber of 

hydrogen atonis and antiprotons injected each pulse. 

Numerical simulations were developed to calculate the annihilation rate of antiprotons in hydrogen and to follow the resulting pion, muon, and clectron/positron number density evolutions. Plasiiia 

heating due to charged particle interactions and cooling due to radiative losses were evaluated for several initial antiproton and hydrogen number densities. Mininiuni magnetic field strengt lis required to 

21 
confine the plasma and charged annihilation products were evaluated as the system evolved. Plasma 

temperatures were used to estimate engine thrust and specific impulse. 

The pulsed hydrogen plasma engine suffers &om extremely low enerrg transfer efficiencies at low 

hydrogen number densities, and from ucusive plasma bremsstrahiung radiation at high hydrogen 

number densities. Optimum performance was obtained with a hydrogen number density of 10'6cm'5 

and antiproton number densities between 1010cm-3 and 1O"cm-'. LOW to moderate thrusts (5 30 

kN) over a wide range of specific impulse values (4600 seconds to 60,000 seconds) were generated 

using this moderate hydrogen number density for 5 ms plasma confinement times and realistic 

magnetic mirror systems. Energy transfer efficiencies were generally las than 2%, with relativistic 

electrons and positrons providing most of the plasma heating. Higher thrust could be produced 

with higher hydrogen number densities, but the plasma will radiatively cool and recombine if it is 

not expelled within a few hundred microseconds after injection. Assuming the plasma can be fully 

exhausted from a realistic magnetic mirror system at its peak temperature, the high number density 

hydrogen propellant can produce a marimum specific impulse of 4950 seconds with an equivalent 

continuous thrust of approximately 250 kN. 

Apart from the formidable problem of generating and storing sufficient antiproton fuel, the key 

engineering issues facing the magnetically confined pulsed plasma engine are the design and construction of the superconducting magnetic field coils, efficient pulsed coil operation, antiproton transport 

into the annihilation region, and radiation shielding. Preliminary analysis indicates that substantial 

mass will be required to shield the superconducting coils from the high energy y-rays emitted in the 

pjj annihilation process. Shielding problems are compounded by plasma bremsstrahlung radiation, 

which will contribute to shield surface ablation and degradation. The mass of the radiation shield 

will dominate the total engine mass and significantly impact engine performance. These initial results underscore the need to include the radiation shield mass in all antiproton powered spacecraft 

designs. 

Acknowledgements 

This report is based on dissertation research performed at the University of New Mexico, Albuquerque, New Mexico. The author is indebted to Dr. Norman Roderick, Department of Cheniical 

and Nuclear Engineering, UNM, for his counseling and guidance during the course of this project. 

Computer simulations were performed at the NASA Lewis Research Center, Cleveland, Ohio. 

References 

1. Massier, P. F., "The Need for Expanded Exploration of Matter-Antimatter Annihilation for 

Propulsion Application", Journal of the British Interplanetary Society (J.B.I.S.), Vol. 35, 1982, pp. 

387-390. 

2. Forward, R. L., B. N. Cassenti, and D. Miller, "C'ost Comparison of C'heniical aid Antihvdrogen 

Propulsion Systems for High AV Missions", AIAA-85-1455, July 1985. 

3. Sanger, E., "Zur theorie der Photoneraketen" ("The Theory of Photon Rockets"), IngeniturArchiv. Vol. 21, 1953, pp. 213-226. 

4. Maj. G. NordIey, USAF, Air Force Astronautics Laboratory, Edwards AFB, CA; personal coiiiniunication. 

22 
6. Forward, R. L., Antiproton Annihilation Propulsron, AFRPL TR-86-034, AFRPL/LKC, Edwards 

AFB, Ca., Sep. 1985. 

8. Morgan, D. L., “Concepts for the Design of an Antimatter Annihilation Rocket”, J.B.I.S., Vol. 

36, 1982, pp. 405-412. 

7. Morgan, D. L. and V. M. Hughes, “Atomic Processes Involved in in Matter-Antimatter Annihilation”, Phys. Rev., Vol. D-2 (8), 1970, pp. 1389-1399. 

6. Agnew, L. E. Jr., T. Elioff, W. G. Fowler, R. L. Lander, W. M. Powell, E. Segre, H. M. Steiner, 

H. S. White, C. Wiegand, and T. Ypsilantis, “Antiproton Interactions in Hydrogen and Carbon 

Below 200 MeV”, Phys. Rev. Vol. 118 (6), 1960, pp. 1371-1391. 

9. Morgan, D. L., Annahilations of Antiprotons an Heavy Nuclei, AFRPL TR-86-011, AFRPL/LKc, 

Edwards AFB, Ca., April 1986. 

10. LaPointe, M. R., “Antiproton Annihilation Propulsion with Magnetically Confined Plasma 

Engines”, Ph.D. Dissertation, The University of New Mexico, Albuquerque, New Mexico, May 1989. 

Sternheimer, R. M., “Fundamental Principles and Methods of Particle Detection”, Methods of 

hperimental Physics: Nuclear Physics, Vol 5(A), L. C. L. Yuan and C.4. Wu (eds.), Academic 

Press, 1961, pp. 1-288. 

11. 

12. Sivukhin, D. V., “Coulomb Collisions in a Fully Ionized Plasma”, Reviews of Plasma Physics, 

Vol. 4, M. A. Leontovich (ed.), Consultants Bureau, New York, 1966, pp. 93-240. 

13. Post, R. F., “Experimental Base of Mirror-Confinement Physics”, Fusion, Vol. l(A): Magnetic 

Confinement, E. Teller (ed.), 1981, pp. 369-402. 

14. Glasstone, S., and R. H. Lovberg, Controlled Thermonuclear Reactions, D. van Nostrand Csmpany, Inc., Princeton, N.J., 1960, pp. 366-400. 

16. Montgomery, D. B. “High Field Magnetic Confinement of Fusion Plasmas”, and Miura, N. and 

F. Herlach, “Pulsed and Ultrastrong Magnetic Fields”, Topics in Applied Physics, Vol. 57: Strong 

and Ultrastrong Magnetic Fields and Their Applications, F. Herlach (ed.), Springer-Verlag, 1985, 

pp. 205-349. 

16. 

17. 

18. 

Jahn, R. G., Physics of Electric Propulsion, McGraw Hill, Inc., 1968. 

Sutton, G. P., Rocket Propulsion Elements, 2nd ed., J. Wiley & Sons, 1958, pp. 45-53. 

Cassenti, B. N., “Antimatter Propulsion for OTV Applications”, J. Propulsion and Power, Vol. 

1 (2), March-April, 1985, pp. 143-149. 

19. Callas, J ., “Modeling Antiproton - Plasma Interactions”, presentation at Antiproton Technology 

Workshop, Brookhaven Nirtional Laboratories, Upton, N.Y., May 1989. 

20. 

21. 

22. 

Stacey, W. M., Fusion, J. Wiley 8 Sons, 1984 

Gross, R. A., Fusion Energy, J. Wiley R: Sons, Pub., 1984. 

Cassenti, B. N., “Radiation Shield Analysis for Antimat.ter Rockets”, United Technologies Rrsearch Center, Silver Lane, East Hartford, Connecticut 06108; Q 198i United Technologies C‘orporation. 

23 
Report Documentation Page 

2. Government Accession No. NASA CR-185131 1. Report No. 3. Recipient's Catalog No. 

AIAA-89-2334 

4. Title and Subtitle 

Antiproton Powered Propulsion With Magnetically 

Confined Plasma Engines 

5. Report Date 

August 1989 

7. Author(@ 8. Performing Organization Report No. 

Michael R. LaPointe 

12. Sponsoring Agency Name and Address 

National Aeronautics and Space Administration 

Lewis Research Center 

Cleveland, Ohio 44135-3191 

None (E-5025) 

10. Work Unit No. 

Contractor Report 

Final 

14. Sponsoring Agency Code 

506-42-41 

9. Performing Organization Name and Address 

11. Contract or Grant No. 

19. Security Classif. (of this report) 

Unclassified 

Sverdrup Technology, Inc. 

NASA Lewis Research Center Group 

Cleveland, Ohio 44135 

20. Security Classif. (of this page) 121. No of y 22. Price' 

Unclassified I A03 

I NAS3-25266 

13. Type of Report and Period Covered 

16. Abstract 

Matter-antimatter annihilation releases more energy per unit mass than any other method of energy production, 

making it an attractive energy source for spacecraft propulsion. In the magnetically confined plasma engine, 

antiproton beams are injected axially into a pulsed magnetic mirror system, where they annihilate with an initially 

neutral hydrogen gas. The resulting charged annihilation products transfer energy to the hydrogen propellant, 

which is then exhausted through one end of the pulsed mirror system to provide thrust. The calculated energy 

transfer efficiencies for a low number density (1014 cmP3) hydrogen propellant are insufficient to warrant operating the engine in this mode. Efficiencies are improved using moderate propellant number densities ( 10l6 ~m-~), 

but the energy transferred to the plasma in a realistic magnetic mirror system is generally limited to less than 2% 

of the initial proton-antiproton annihilation energy. The energy transfer efficiencies are highest for high number 

density (10l8 c~n-~) propellants, but plasma temperatures are reduced by excessive radiation losses. Low to 

moderate thrust over a wide range of specific impulse can be generated with moderate propellant number 

densities, while higher thrust but lower specific impulse may be generated using high propellant number densities. 

Significant mass will be required to shield the superconducting magnet coils from the high energy gamma radiation 

emitted by neutral pion decay. The mass of such a radiation shield may dominate the total engine mass, and 

could severely diminsh the performance of antiproton powered engines which utilize magnetic confinement. The 

problem is compounded in the antiproton powered plasma engine, where lower energy plasma bremsstrahlung 

radiation may cause shield surface ablation and degradation. 

17. Key Words (Suggested by Author@)) 

Antimatter 

Plasma propulsion 

Magnetic confinement 

18. Distribution Statement 

Unclassified -Unlimited 

Subject Category 20 

'For sale by the National Technical Information Service, Springfield, Virginia 221 61 NASA FORM 1626 OCT 86