Journal of the British Interplanetary Society, Vol. 39, pp. 391-409, 1986.

ANTIMATTER PROPULSION FOR SPACE EXPLORATION

GIOVANNI VULPETTI ·-..Telespazio SpA per le Comunicazioni Spaziali, Via A. Bergamini 50, 00159 Rome, Italy.

''·"

This is chiefly a review paper with additional considerations and suggestions about aspects of matter-antimatter propulsion for space exploration. The paper is divided into six main sections. In the first section the fundamentals of the low-energy antiproton-nucleon annihilation physics are presented. In the second section geocentric, interplanetary and interstellar flights possible by means of antimatter engines are reviewed. In the third section the big problems related to the antimatter handling (production, storage, control) are discussed. In the fourth section proposed matter-antimatter thruster design concepts for Earth-space, interplanetary and out-of-Solar-System missions are examined and some results from computer simulations are discussed. In the fifth section a comparative cost between antimatter-based engines and conventional engines is made. Finally, aspects of a world-wide cooperation to try to make antimatter propulsion a reality are pointed out.

1. INTRODUCTION

In this paper the author is concerned with both a critical review of the past research and some suggestions for future research about the so-called Antimatter Propulsion. This is not a math­ematical paper; nevertheless we will also discuss results of computer simulations of complex mathematics.

Let us begin our dissertation by explaining the concept of antimatter propulsion. Any propulsion system utilises some source of energy to be controlled, in particular to be directed. The ultimate release of energy lies in microstructures such as molecules, atoms, atomic nuclei; subnuclear particles. These last ones display two states: particle and antiparticle; in the known Universe it is believed that matter overwhelms anti­matter. When a particle and its corresponding antiparticle "collide" at a sufficiently low energy, the annihilation proba­bility is high and their interactions results in a high conversion of their rest masses into kinetic energy of other massive particles, photons and neutrinos, the remaining fraction of the initial mass being found in the form of the produced particle's rest mass (the types of products depend upon the type of inter·a-ction responsible for the annihilation). Only the first two energies (i.e. kinetic energy and photons) could be utilised by means of some control process or device. A matter-antimatter annihila­tion propulsion system is conceived as a device which would exploit those energies.

Only really stable or long-life particles-antiparticles could, in principle, be considered for a technological system. This entails that electron-positron and nucleon-antinucleon annihil­ations are the only elements of our set of admissible annihil­ations for potential space propulsion application. As is well­known, the former pair annihilates only into two gamma pho­tons which cannot be effectively controlled and directed as such. The latter pair annihilates by strong interaction and produces a lot of particles, the great part of which are massive, charged, relativistic and short-lived. Before they decay, such particles and their energy can in principle be controlled. As we shall hint in the sequel, even the gammas produced in some decay stage of this annihilation process may be partially con­trolled in energy, namely, if converted. The other advantages of the nucleon-antinucleon annihilation at-rest with respect to the electron-positron annihilation is the much bigger amount of energy released, as it is apparent. Because we ultimately need neutral antimatter in order to be better handled, positrons are to be produced in the same number of antiprotons. Free antineutrons cannot be controlled.

Therefore the high-energy process of interest consists of the antiproton-nucleon annihilation at-rest, the electron-positron

annihilation being a secondary process from a propulsion view­point.

Our paper is then structured as follows: the next section is devoted to a general survey of the antiproton-proton and antiproton-neutron annihilation-at-rest reactions. Successively, we will switch to the discussion of the requirements of missions in the space of the Earth, Solar System and nearby stars. From this basis we will go back to the problems of antimatter production, storage and annihilation c~ntrol. We will then describe some possible antimatter-matter engine design con­cepts. Comparative cost estimates between antimatter propul­sion systems and conventional thruster systems will be men­tioned on a parametric basis. Finally, we will stress a need of an international cooperation in the near future for pursuing effective research on antimatter propulsion.

The interested· reader .cean find a number of references to introduce himself more. deeply into the fields dealt with here (notice in particular th~t Ref. 57 rec .. eived approval for public release in September 1985; therefore Ref. 57 and this paper represent two quite independent efforts about antimatter pro­pulsion).

2. THE ANTIPROTON-NUCLEON ANNIHILATION AT REST

In Refs. 1-18 the reader can find a lot of details about the antiproton-nucleon annihilation (pN) at rest. Because we are chiefly interested in the "global" properties of this annihilation process for a potential space application, we make a synthesis of Ref. 19 whic.h updated old experimental data. We first describe the antiproton-proton (pp) annihilation and, successi­vely, the antiproton-neutron (pn) annihilation. Before doing this, we must outline. some considerations common to the two types of processes with a special emphasis on the annihilation environment. - ·

For possible space propulsion applications the pN annihila­tion must occur at rest. The initial p's momentum (relative to N assumed at rest in the ship frame) should be, say, below 5 MeV /c, essentially for transportation problems on-board (see Section 4.2). Anyway, the antiprotons must' pass through a certain amount of matter, 'generally lose·· their energy and thereafter annihilate. The last step is not a simple thing.

Most of the present-day understanding of the antiproton­nucleon dynamics comes from analyses of photographs from bubble chambers filled with liquid hydrogen or deuterium.

391

/

rrl1 2 3 4 29 E ( KeV)

30fm-- : = ==··== .. ·-4 ii 3

II IC -my

3.2

9.4-t.E,s

t2.5

2 A N N I H I l A T I 0 N

L Hz

1· --

Fig. 1. Energy levels of the protonium (p·p atom). In a liquid molecular target such as the bubble chamber H2, the collisional Stark mixing effect populates the S-levels with high principal quantum number. These levels decay chiefly via annihilation. P-wave annihilations are very rare.

When an antiproton is stopped there, an H atom captures it by its Coulomb field. Stopping and capturing means that the p has been slowed-down to a few eVs in energy and its impact parameter with respect to the H-atom's proton is about the classical radius of the K~shell. The system (p,e-,p) is unstable and partially de-excites by emitting the electron. The remnant system is called antiprotonic hydrogen or protonium. The protonium's energy levels correspond to the ordinary H levels with the Rydberg constant scaled up by about 918 (Fig. 1). The anti proton capture occurs in high-n (n = principal quantum number) orbitals, typically n = 30. In states lower than that of capture, the nuclear strong potential adds to the Coulomb potential and causes a shift and broadening of the protonium energy levels. The excited protonium decays from a high-n. In vacuum this entails a high angular momentum by electric dipole transition; in real environments the Stark effect mixes the degenerate states and, in particular, provides the S-state for a non-negligible probability to be populated. All this ultimately results in a large population in the S-states before annihilation - lSO and 3Sl - for which the principal quantum number is still . rather high. The next step consists of the annihilation which, therefore, takes place largely in high-n S-wave states. The probability of annihilation in such conditions is rather high because the S-orbital wave function exhibits a non-negligible value at the origin. The S-wave annihilation should be many orders of magnitude more probable than the P-wave's for n­values down to ten [ 13].

The above discussion is substantially what is meant by annihilation at rest in a bubble chamber. Annihilation is in reality an environment-dependent process.

Appropriately analogous considerations can be made for pd atoms.

For purposes of space propulsion we are interested in the mean number and the mean energy of the particles following the pN annihilation. Some particles are directly produced, other particles represent the observable products of inter­mediate very-short-life resonance decay. We will not mention such resonances in the next subsections. A discussion about them can be found in Refs. 10, 17 and 19.

2.1 The Antiproton-Proton Annihilation at Rest

Keeping in mind what has been said previously, the mean pp

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G. Vulpetti

annihilation at rest (in liquid hydrogen) can be quantitatively written as follows [19] (a tilde above a particle symbol denotes the corresponding antip~rticle t

p + p => 1.527 ?r+ + 1.527 'Ir- + 1.96 11"0 +

0.012 K+ + 0.012K- + 0.013 KO+ 0.013 KO (1)

Therefore the pp annihilation generates pions and kaons, the latter particles being about 1 per cent of the former ones. This quantity can be neglected from the jet power viewpoint; however, it is not negligible from other points relevant to an antimatter-matter engine design [ 19].

The average energy spectra of the pions and kaons in Eq. (1) are the following [ 19]:

E(?r+) = E(?r-) = 374 MeV E(?rO) = 358.5 MeV - (2)

E(K+) = E(K-) = 633 MeV E(KO) = E(KO) = 633 MeV

Equation (2) regard the pion and kaon total energy. This can be evaluated from measurements either directly or through a , complex procedure of estimate of partial-rate tables of extensive experiments. However, for evaluating the performance of a potential annihilation engine, we must consider the following mass-energy quantities:

M the rest mass of massive particles

KE the kinetic energy of massive particles

GE the energy of gamma rays

NE the energy of neutrinos

Neutrinos are considered zero-mass particles here. They do not contribute to thrust in any case.

Equation (1), which represents the first step after the annihil­ation (apart from the resonances), is characterised by the following values of the above set:

ME= 715.6 MeV KE= 1161 MeV GE= 0 NE= 0(3)

Such values correspond to the energy sharing just after the eta­boson decay [19]. Unfortunately, these parameters undergo a time evolution after 100 attoseconds since the annihilation time. We describe and plot such variations because they are of prime importance for space propulsion. Details can be found in Ref. 19.

Pions and Kaons decay. Their meanlife-at-rest is significantly dilated by their own energy (Eq. (2)) in the LAB-frame. The decay modes of the charged pions are different from the neutral pions. Pionic decay, in turn, greatly differs7(rom kaonic decay [20]. In the latter, in particular, the neutral kaon presents different decays according to the two states which it can be thought of: that is, KOS and KOL (where 'S' and 'L' stand for 'short-life' and 'long-life' respectively). Kaons decay also into pions; pions decay into gamma rays, muons and neutrinos; muons, in turn, decay into electrons and neutrinos. As time since annihilation goes by, there are great changes in the mean number and energy of each type of the mentioned particles. This complex "cascade" is described in detail in Ref. 19. Here we limit ourselves to report a final sequence with the related values of M, KE, GE and NE. Such values together with the matter-on-antimatter ratio and the environment-dependent interaction mode determine the physical efficiency of an anti­matter engine (we will return on such subject in Section 5.). We have:

at eta-meson decay (1 attosecond after annihilation)

M=715.6 MeV KE=l 161 MeV GE=O MeV NE=O MeV (4)

Antimatter Propulsion for Space Exploration

at 11"0 decay (220 attoseconds)

M=451.0 MeV KE=722.9 MeV MeV

at KOS decay (0.11 nanoseconds)

M=445.2 MeV KE=726.l MeV MeV

at K± decay (16 nanoseconds)

GE=702.7 MeV NE=O (5)

GE=705.3 MeV NE=O (6)

M=436.l MeV KE=727.8 MeV GE=707.2 MeV NE=5.5

MeV (7)

at KOL decay (66 nanoseconds)

M=431.6 MeV KE=728.3 MeV GE=709.4 MeV NE=7.3 MeV (8)

at 11" ± decay (110 nanoseconds: any charged pion, primary or produced by a kaon decay, is decayed)

M=326.4 MeV KE=586.3 Mev GE=709.4 Mev NE=254.5 MeV (9)

atµ± decay (10 microseconds)

M=l.6 MeV KE=317.9 MeV GE=709.4 MeV NE=847.7 MeV (10)

(The decimals in (4) through (10) are to be intended as round figures for the energy balance in the mean annihilation process considered. The experimental errors propagated in our calcu­lations are greater than a fraction of MeV.)

Now we have the necessary elements to plot the energy sharing versus time for the products of the antiproton-proton annihilation at rest. Figure 2 displays also the particle meanpath in vacuum. The annihilation energy sharing parameters are reported in terms of fraction of the initial energy available (two proton masses) as well.

2.2 The Antiproton-Neutron Annihilation at Rest

This subsection will follow the same guidelines of Section 2.1, even though the statistics in experiments of antiproton-neutron (pn) annihilation are at present much lower than that of pp. The results of pn annihilation are somewhat different from those relevant to the pp process. This could be suspected in advance by considering the initial pn conditions. First, the total charge is -1; second, the pn state is a pure isopin state (equal to one) in contrast to the pp system which contains a mix of isopin 0 and 1. Furthermore, the pn annihilations can occur only in nuclei heavier than H. The lightest target in a bubble chamber is then liquid deuterium. The pd annihilation proceeds through the formation of the antiprotonic deuterium. Because the deuteron's binding energy is small (2.2 MeV) the first reasonable assumption is that the antiproton annihilates on a substantially free neutron, while the proton acts as a "spectator" (this represents the "impulse approximation" whereupon the proton carries away its Fermi momentum only). Naturally, in a pd reaction pp annihilations occur as well. The pn process is distinguished from pp by its odd number of prongs in a bubble chamber photograph. The pn annihilation is assumed to take place in S-wave (only the Rydberg constant scaled up by 4/3 represents the difference between antiprotonic deuterium and protonium). A great advantage in analysing pd annihilations consists of determining the relative pp and pn annihilation cross sections. From Ref. 15 we report

u(pn) / u(pp) = 0.76 ± 0.02 (11)

! ... , W(AN PA TH

I I i11,. I '" , .. 11111111 -11 • ·• rl I ' ~ .. ,, 1·· 1 · I { ..

I ..... ______ : ______ l---1 '1-0UAI

: IHCf-z 1---------- I '

I t ! -.-,:-oi"-1 >

I ! I 1/ :::

' ' 0 •• . , I ... ., ; 1--------1 I I i '.so;

"

;.. ' 1 I 1~-· ~ :; I I .. -_, __ ._o.!·-·-1"' ~ a u . . , - -·- ,_ - -·- - - ' ., ";, .. !- --,,- -------- ; I II ! ... -.. ·-··-··1 ~ w ' ! I " ~

I . I " -

.. I M ; 'i-'1 M .. ~ I I ----•• ---·1 I I -~~1-1 ~.!!,. I , • I

" -· l •t [ I;,,, ( llC) I

Fig. 2. Proton-antiproton primary and secondary product mean energy as function of time since the annihilation. M=massive particle rest mass, KE=kinetic energy, GE=gamma energy, NE=neutrino energy. Fractional energy and meanpath are also indicated.

a very important figure when one conceives an antimatter engine where the "annihilation chamber" contains atoms with A>l.

From Ref. 19 we write the analog of Eq. (1) for the anti pro­ton-neutron annihilation at rest.

p + n = > 1.067 11"+ + 2.046 11"- + 0.024 KO + 0.024 KO (12)

+ 0.029 K- + 0.020 K+ + x 11"0

The conservation of charge is within the experimental errors in determining the frequencies of the pions and kaons. The "x" in the neutral pion term means that it has not been possible for us to determine the number of such pions starting from the references at our disposal. However the total energy of (x11"0) can be estimated.

We have obtained the following mean energy figures:

E (11"+) = 366.4 MeV E (11"-) = 379.3 MeV

E (K+K) = 1220 MeV E (X11"0) = 652 MeV (13)

Let us note that the averaged energy of the charged pions is 37 5 Me V and the value of E (x11"0) is well within the uncertainty of the 11"0's energy in the pp annihilation. Only the kaon contribution appears outside the corresponding errors, but not excessively.

2.3 The Antiproton Annihilation on Heavy Nuclei

Antimatter propulsion systems should exhibit a very broad range of thrust, probably larger than chemical systems. High thrust stages may in principle be obtained by annihilating a certain amount of antimatter on a much more massive quantity of matter (different modes of operations will be examined in Section 5). This matter cannot be forced to consist of hydrogen or deuterium. Depending upon the type of engine, the reacting mass may consist of elements heavier than D2, probably high-A elements. These nuclei provide a dense target for an antiproton beam.

An incident antiproton eventually produces annihilation on one of the surface nucleons because of its low energy. In fact, at kinetic energies less than 20 MeV the annihilation cross section would be so high that the penetration depth is a small fraction of the nucleon's diameter. However the cross section cannot increase beyond a certain value on account of the

393

relative momentum between the p and any nucleon due to the internal nucleus motion. Some of the mesons produced in the annihilation, as symmetrically emitted in space, can transfer a significant part of their energy to the spectator nucleons. This might result in the explosion of the nucleus, the fragments of which can, in turn, interact significantly with the other nuclei provided the target's density is sufficiently high. The relative frequency of such "fireballs" is estimated about 1-2 per cent of all annihilations on a nucleus [21). In any case these rare events contribute to sharing the (pN) mass among the atoms of a dense flow which is ejected from a spaceship.

When antiprotons are stopped in a dense high-A material, antiprotonic atoms are formed. They de-excite by Auger elec­trons and hard X-rays. Such energy is probably not wasted for either the propulsion system or other ship's systems. This field may be one of the several aspects to be investigated to fully exploit the annihilation energy and/or to avoid dangerous side effects.

2.4 Low-Energy Annihilation Cross Section

We have seen that an annihilation at-rest passes through the formation of antiprotonic atoms. In particular, as soon as the antiproton's wave function overlaps the nucleus appreciably in an antiprotonic atom, one of the consequences of the strong interaction might be a non-negligible deviation of the inverse­velocity law in the annihilation cross section. Needless to say, this would impact upon the design of the "annihilation chamber" in an antimatter engine. The current state of the experimental pp annihilation cross section can be summarised as follows (the p's momentum in LAB is the independent variable):

1. the annihilation cross section (uan) is rather large, greater than the elastic cross section (uel): uan/ uel = 1.8;

2. uan, uel and the total pp cross section ut sometimes display resonances;

3. the expression uan = ut(pp) - ut(pp), where ut(pp) denotes the total elastic pp cross section, furnishes in reality only a crude estimation of uan;

4. in general, at p momenta lower than 3 GeV /c but higher than the pion production threshold, the annihilation cross section is estimated by subtrac­tion: uan = ut - uel - uinel where uinel denotes the inelastic pp cross section;

5. no measurements of any cross section are currently available below 300 MeV /c.

Other details about the NN cross sections can be found in Refs. 6, 7 and 20. The initial states of antiprotonic atoms are strongly affected by the surrounding ambient field. This fact is of particular importance in an antimatter engine concept.

2.S Annihilation Energy Parameters for Space Application

In this subsection we re-arrange the major data so far obtained. We focus our attention on the quantitative aspects of the annihilation energetics. In order to render the related figures a ready input for antimatter propulsion research, we normalise the annihilation mass-energy history displayed in Fig. 2. We define two sets of parameters. These sets are equivalent to each other as far as the information content is concerned. The mission analyst and/or the engine designer can select the most

394

G. Vulpetti

appropriate one case by case. We will use such sets in the next sections.

First set of parameters [ 19):

€ is the fraction of the initial energy (two proton masses if referred to one annihilation) which encom­passes both the massive particle kinetic energy and the photon energy. Such a value is relevant to the chain decay stage (CDS), following the annihilation, which is being considered for a certain propulsion system;

f'Y is the fraction of the initial energy appearing as photons. It depends upon the CDS considered;

fm represents the fraction of the initial energy resulting in rest mass (of the massive particles). It pertains to the CDS considered;

fk denotes the fraction of the initial energy going to massive particle kinetic energy. It is relevant to the CDS considered;

s is the fraction of (1-€) quantity lost into space at zero total momentum (ZTM) in the ship frame (SF);

s'Y is the actual fraction of f'Y lost into space at ZTM in SF;

u is the fraction of (1-s'Y)f'Y re-converted into control­lable massive particles. It represents the rest mass of these (charged) particles. Such re-conversion (if suitable for the considered engine) makes available the energy (l-u) (1-s'Y)f'Y as kinetic energy to be added to fk. Note that u = 0 is equivalent to s'Y = 1, that is the gamma energy is completely lost.

Second or alternative set of parameters [19):

ft

Ee

s'

u'

O"sp

is the total yield of the reaction releasing the energy to be utilised. It equals one for an annihilation reaction;

is the c1 fraction in terms of the effective total energy of the non-negligible-interaction particles. fe equals Et only if no negligible-interaction particles are prod­uced;

is the fraction of ( 1-Ee) lost into space at ZTM in SF;

is the Ee fraction in terms of rest mass (of massive particles). In general, it is composed of two quanti­ties we call u,p and O"ind. where the subscripts 'sp' and 'ind' stand for 'spontaneous' and 'induced' respec­tively;

is the Ee fraction which is by reaction in form of rest mass of massive particles;

O"ind is the Ee fraction which is re-converted into rest mass of massive particles (generally different from those ones of u,p).

No further parameter such as s'Y has been introduced in the latter set. Were re-conversion considered, Ee would equal Em +Ek+( 1-s'Y)f'Y, namely the total energy of the massive particles plus the gamma energy exploited. Note that for any antimatter engine's is either zero or one, independently of the re-conversion process (if any). It can be shown [22) with arguments that go beyond the scope of this paper that the following relationships

Antimatter Propulsion for Space Exploration

TABLE 1.

Particle Decaying

Parameter T/ 'II' 0 it; Jc± kt ~ ~

e 0.619 0.760 0.763 0.76S 0.766 0.690 0.S47

ek 0.619 0.38S 0.387 0.388 0.388 0.312 0.169 0 0 0 0.012 o.oi 1 0.438 0.998

em 0.381 0.240 0.237 0.232 0.230 0.174 0.0009

ee 1 0.626 0.624 0.620 0.618 0.486 0.170 s' 0 1 1 1 1 1 1

Osp 0.381 0.384 0.380 0.37S 0.372 0.358 0.005 -~ 0.626 0.624 0.620 o.618 0.486 0.170

Values of the energy parameters at the successive chain decay stages of the proton-anti proton annihilation at rest. The parameter sets are defined in Section 2. No gamma conversion is considered here. The energy efficiency is found in the last row.

TABLE 2. ---Particle decaying

Parameter 0 ko k± ko w± ~ 17 'II' s L

e o.619 0.760 0.763 0.765 0.766 0.690 0.547

!'I< 0.619 0.385 0.387 0.388 0.388 0.312 0.169

c 0 0 0.012 0.017 0.438 0.998

_fm 0.381 0.240 0.237 0.232 0.230 0.174 0.0009

0 0 0.0029N°

ee I 0.813 0.812 0.809 0.807 0.675 0.359

s . 0 I I

Osp 0.381 0.296 0.292 0.287 0.285 0.258 0.0024

Oind 0 0.0007N° 0.0008N° 0.0015N° -~ 0.813 0.812 0.809 0.807 0.675 0.359

The equivalent of Table I for a 50 per cent conversion of the photon energy. It is supposed that gammas are converted in relativistic electron-positron pairs. The undefined N* in the table stands for the mean effective number of pairs (per one annihilation) which may be generated by conversion.

between the two sets of parameters just defined is of particular importance:

1 -Ek- 2(1-s)(i-E) - (1-s'Y)(l +u)E'Y = s' - Ee(u'+s') (14)

The common value of the two sides of Eq. (14) has a profound impact on the optimal control for the maximum final velocity of a relativistic rocket [22, 23].

A very useful index of engine performance is represented by the ideal energy efficiency, denoted by X. It is defined as follows. If certain energy-carrier particles are to be ejected and, optionally, their energy is shared with an amount of inert mass, then X is the ratio between the ejection energy and the total energy of the exothermic reactions generating such particles. In the case of antimatter propulsion it is fundamental to realise that X is a value dependent on both the considered CDS and those particular environments where the annihilation products give energy to inert matter. No similar behaviour has been seen or foreseen in other propulsion types.

Tables 1 and 2 give the evolution of the pp annihilation energetics in terms of the two sets of parameters defined above. The efficiency X is also calculated.

3. MATTER-ANTIMATTER PROPULSION SPACE MISSION FEATURES

This section is devoted to showing the major characteristics and requirements of a space flight accomplished by a matter-

antimatter annihilation propulsion system. We divide such discussion into three subsections where some particular missions in the Earth space, Solar System and to nearby stars are of interest in the current studies. The degree of approximation in describing major or general features depends upon the class of missions dealt with.

3.1 Missions Around the Earth

Space projects for missions around the Earth continue to grow in importance and number: space station, free-flying multi­payload platforms at various orbital inclination and altitude, very large and massive satellites for telecommunications and future geostationary platforms are possible objectives for the end of this century.

If we consider a one-way low-Earth-orbit (LEO) to geosta­tionary-Earth-orbit (GEO) transfer with a characteristic value of 4 km/s (baseline), we can compute how much antimatter is called for a certain payload (P /L) mass as function of the spacecraft (S/C) mass in LEO. Figure 3 shows such behaviour, the (gross) payload mass being the curve parameter. In these examples the P /L mass ranges from 5 to 19 tonnes. The propulsion system would consist of a high-thrust low-specific­impulse matter-antimatter engine where a small amount of antimatter reacts with a much greater quantity of ordinary matter. In this way, both a large fraction of the gamma energy is transformed in beam energy and charged muons are strongly absorbed by heavy nuclei before they decay. The assumed energy efficiency amounts to 0.67. Figure 3 shows the presence of broad minima for the antimatter; at the minimum the initial S / C mass is five times the P /L mass, independently of the S / C mass. This striking feature was first stressed in 1952 [24] and then pointed out again in 1975 [25]. Figure 3 displays two important results: 0.5 milligrammes of antimatter would allow users to deliver payloads (to GEO) more massive than the future European Ariane-S's, whereas 1.5 milligrammes would do more than the best Centaur stage modified for the US Space Transportation System. In addition, a spacecraft with an integrated antimatter propulsion system could reach its station longitude in less than six hours by using two finite-burn manoeu­vres: prefixing the total thrusting time, for instance 2000 seconds, all cases would imply a specific impulse equal to 179 s and an initial acceleration of 0. l g. This last value would rise up to 0.5 g at the end of thrusting, that is in the GEO burning. Because at GEO altitude the gravitational acceleration is about 0.023 g, thrust would be by far the major field controlling the S/C motion. This feature is emphasised as the propulsion time decreases. Note that the curves of Fig. 3 grow rapidly on the Fig. 3. Antimatter amount versus the initial S/C mass for delta-V = 4 km/s.

c J, .

• P/L I tons] as. a curvt paramtter dtl ta-V = 4 Kr111

a n

4.

t 3.

m a t -, .. e

energ~ fractlon = 0.675

.~ .. 19 . .. . . ~ . . . . . . ;. ; . .. .•.. . . ...... :. .. ,, . • ... : . . . . . . ·. . . . . '

~ .. •. •. l , .• ... ' t .... • • , ~ .':. •. ~ ~ ~ ... ~- ~ .':. •. : :~ .... •. ~ 15 .......... . 1. I_ • .·:·~;~ ..................... ~!~~.·:·.'·~~~.·.·.':10

[mgl . ····-~--.. ··•oot•,"!•.·-~·.•·.~~·~·. 5 ..

0. --~~~~~~~~~~~~~~~~~~~--' 0 20 40 60 00 100 120 140 160 180 20e

!NIT JAL S/C MASS [ t onsl

395

G. Vulpetti

P/L l ti:1nsJ as a. cu1·..,,.e parameter lJ.S PcLJt;~~~i;---=---delta-\i. = 0.1 t~.ffl/S

energ~ fractlon = 0.675 .4

a •• t •. · .. ·, ...

n .;. + t •. • t + • .j •• t •.• t •• ~ . . . t + •• t 5

t .3 l

m ... ': .. • ... •. •. ~ .. • ........ ; .... ' ... ·• . ' .. . . 4 . a t 1 . ·~

t e 1·

•.•• · .. ~ ... ~· .. · ... .;. ••• ~ ........... + ....... + ··-~ ~ ~ .... . ·3

·•· . '•.. . .... ·~·~••+t++t++1++t••······~····~·.;.•t '1 L...

0.1

----i. . . . . . . . [µ.g] .........

2 26 50 INITIAL S/C MASS [tons]

Fig. 4. Antimatter amount versus the initial S/C mass for delta-V = 0.1 km/s.

left of the minima; this rising weakens as the P /L mass increases.

Figure 4 has been constructed similarly to Fig. 3. The differences consist of a delta-V equal to 0.1 km/sand a payload mass ranging from 1 to 5 tonnes. Such delta-V is practically the velocity increment of the ascent phase of the European Retrievable Carrier (Eureca) the mass of which is 3800 kg. Eureca will spend about 185 kg to pass from 300 km to 500 km in altitude. Let us notice the antimatter scale in Fig. 4: a fraction of microgrammes. We shall recall such figures after having dealt with the problems of antimatter production and storage in Section 4 and the antimatter rocket design concepts in Section 5.

3.2 Fast Interplanetary Flight and Precursor Stellar Mission

Interplanetary missions based on chemical propulsion are char­acterised by low-mass payloads and long transfer times. Com­plex trajectories to reach planets and go beyond are governed by the gravitational fields of the Sun and planets; manoeuvres alter the elements of the spacecraft pseudo-conics. Nuclear­Electric Propulsion (NEP) or Solar-Electric Propulsion (SEP) could reduce flight times and significantly increase payloads. However, the vehicle's trajectory is still strongly affected by the Sun's gravitational field. All this is well-known.

In order to discuss the degree of the potential effects of the antimatter propulsion in an interplanetary and out-of-Solar­System mission, let us briefly examine a very extended flight. An interplanetary /precursor interstellar mission has been proposed some years ago [26). The major mission goals would be to explore the interstellar medium in the direction of the incoming interstellar wind, to observe the Solar System as a whole at distances greater than 100-200 AU and to measure the Solar System mass. A significant option may be to fly-by Pluto. Jet Propulsion Laboratory have indicated that NEP is the most suitable propulsion among those ones examined [26). A generic hint was made about antimatter propulsion at that time.

Figure 5 shows .the approximate positions of the planets at

396

the end of March in 2011. In this configuration the Earth velocity is practically parallel to the ecliptic projection of the line Earth-Pluto. To within a few months the Pluto position can be considered unchanged for our purposes. The solid line in Fig. 5 represents the direction of the incoming interstellar wind. Without entering mission opportunity alternatives and so on, we have envisaged the following flight: a three-stage spaceprobe escapes from the Earth, flies-by Pluto and directs itself along the interstellar wind direction. The first stage burns for one day allowing the vehicle to achieve a velocity as high as 500 km/s. The ensuing trajectory is a branch of a hyperbola, the asymptotic deviation angle of which is about eight arcse­conds. The first stage is jettisoned some time after its cut-off. The inclination of this rectilinear trajectory over the ecliptic amounts to 4.5 degrees. The remaining vehicle approaches Pluto after three months. At a distance from Pluto of 43 million kilometres the second stage is activated. The thrust is programmed to follow a profile always orthogonal to the ship velocity. Trajectories of such a type have been studied extensi­vely in Refs. 27-28. They have significant features:

1. the magnitude of the ship velocity is not changed;

2. the powered arc can lie in a plane passing through the initial and final vector velocities;

3. any arbitrary small distance of fly-by is possible, so compensating for the high survey velocity.

(It is plain that no planetary gravitational influence is appreci­able for so high an energy spacecraft. Pluto's mass could not be measured.)

At a certain distance from the Sun the third stage can either stop the spacecraft with respect to a heliocentric frame or accelerate it up to 1000 km/s to pursue towards deeper space. What we are going to discuss is independent of these mission options and related objectives. A computer code has been prepared to deal with aspects of such a flight. Following the theory in Ref. 27, the optimal profile which maximises the final payload has been carried out with the assumption that a matter-

Antimatter Propulsion for Space Exploration

p

~y

J: .s t/'io···············"l······························) x

I

\ \ I

~,._.,2s• t.!i

t I

fl

Fig. 5. Approximate positions of the planets (marked by their order number) on March 30, 2011. The solid line indicates the direction of the incoming interstellar wind.

antimatter engine (no charged pions decayed) controls the spaceprobe trajectory. Figure 6 presents the major behaviours of interest here as function of the propulsion system specific mass (a). At the present-day knowledge we have no technology indication of how heavy an antimatter propulsion system may be.

Therefore, the first information we gain from Fig. 6 is that no flight of this type is practically possible if a> 0.2 kg/MW. This value is very low indeed. However, the order of magnitude (kg/MW) should be ascribed essentially to the very high energy released by annihilation; the real range of values should be due to the propulsion system technology.

Payload values can be very high as well as the antimatter (AM) quantity very small with respect to the inert reaction mass (M). If Mo denotes the initial ship mass and Isp the jet speed, in the case of a = 0.1 kg/MW we see M/ AM = 2.5 x 10s, AM = 2.0 x l0-6*Mo, P/L = 0.07*Mo and Isp = 950 km/s. The spaceship proposed in Ref. 26 could transport a payload of O.Ol3*Mo at a cruise speed equal to 150 km/s.

In Fig. 6 one can select a in a small range about that value for which the inert mass equals the optimal payload mass. Table 3 shows the optimal mass breakdown (for maximum payload) stage by stage. Optimal jet speed, stage initial acceler­ation and total flight time are also indicated. Note that for a = 0.0245 kg/MW P /L = Minert :::;,;: Mprop.syst. (33% and 31 % of Mo respectively). If Mo were equal to 10 tonnes, then the necessary antimatter would amount to about 80 grammes. The payload mass would be as high as 3.3 tonnes. The maximum acceleration level would be 0.6 g. Five hundred AU could be achieved in less than 4.8 years.

Finally, we point out that proper interplanetary flights such as multiple fly-bys of the outer planets are possible with much lower requirements of antimatter. From Fig. 5 we see, for instance, that (choosing a launch window) a mission involving fly-bys of Jupiter, Uranus and Neptune may be favourable by selecting an appropriate cruise speed which would allow some minor orbiters to be left at Jupiter and Uranus. Neptune would be reached by the main vehicle.

3.3 Relativistic Interstellar Flights

It is very well known to the Interstellar Studies scientific

community what are the ranges of flight time, cruise speed and on-board acceleration currently deemed the most appropriate for the first mission to some nearby star, say up to 10-12 ly. In this subsection we briefly discuss the potential capabilities of an antimatter-based starprobe. We focus our attention on the acceleration phase only. As a baseline, we consider exploiting the proton-anti proton annihilation energy in the stage preceding the charged pion decay. The gamma energy is assumed to be lost. From Table I we see that the maximum kinetic energy exploitable is tk = 0.388 (about 100 times the fusion energy). This value strictly holds for highly relativistic jets composed essentially of charged pions. If one mixes the annihilation products with an additional amount of ordinary matter, the cross sections of interaction with nuclei must be considered. The absorption of pions in heavy nuclei is rare at the annihila­tion pion momenta. In an antimatter engine producing relativ­istic jet speeds there will be several jet components at different speeds: high energy pions (emerging from a cloud of atoms), low energy protons and nuclei with a lower energy (what is calculated in computer simulations is the weighted jet speed). Hence, the annihilation energy fraction effectively used to form relativistic beams would be close to tk because the pion component should be dominant. The beam total energy fraction is obtained by adding the beam rest mass fraction. The perform­ance of a flight is determined by the annihilation energy sharing between beam rest mass and beam kinetic energy.

Figure 7 shows three meaningful examples, two of which represent ways the antiproton-nucleon annihilation might be used for achieving relativistic velocities. These are labelled Al and A2. The third one, labelled F, refers to a fusion-based vehicle for comparison. In Table 4 the major data of input are reported. The units system takes on c= 1 and light year= 1; the ship's initial mass is set to unity. Al and F represent multiple propulsion mode cases [29, 30] the "equivalent" jet speed of which has been fixed to 0.95 c. Every mass flow rate is independent of time; in contrast, the matter beam jet speed and the light source (a microwave or laser system in the Solar System) power are time-varying: the related programmes are shown in Fig. 7. A2 represents the pure-rocket maximum terminal velocity behaviour at criticality [22]. The propulsion mass ratio is equally fixed in all cases. From Table 4 and Fig. 7 we note the following:

l. a rocket exploiting antimatter-matter annihilation can achieve a cruise speed as high as 0.38 c with a propulsion ratio as low as 2. The jet speed is strictly constant [22];

2. the multiple propulsion mode (external photon beam + ramjet + rocket) could extend the cruise speed up to 0.58 c even though the rocket-mode were based on thermonuclear fusion. Fusion would require an external photon power slightly greater than the corresponding one for annihilation;

3. the multiple propulsion mode based on the antipro­ton-nucleon annihilation would entail an antimatter consumption much less than the pure-rocket minimum amount of antimatter calculated in Refs 31 and 32 with the same propulsion mass ratio and final speed. This is due to the primary component of thrust in these cases, namely, the radiation pressure. Augmenting the antimatter entails a lower power of the photons source. The decrease in antimatter requirement is in competition with the more complex technology of the multiple propulsion mode and also with the multiple mode based on fusion because of the required amount of the tritium, very rare on the Earth.

Missions to more than one star, either "in parallel" [27] or

397

Table 3 ---------------------------------- I N P U T -----------------------------------

initial speed cruise speed accel. time decel.-L time swing-by angle K-ENERGY YIELD

3.000000E+01 S.OOOOOOE+02 1.000000E+OO 2.000000E+OO O.OOOOOOE+OO 6.180000E-01

[km/sl [km/sl rdaysl [daysl [deg.]

final speed specific mass swing-by time decel.-T time final dev angle

O.OOOOOOE+OO [km/sl 2.4SOOOOE-02 [kg/l'IWl 2.000000E+OO [days] O.OOOOOOE+OO [daysl O.OOOOOOE+OO [deg.l

tankage factor S.OOOOOOE-02 departure planet * * * swing-by planets * * * target EARTH PLUTO 500 A.U.

--------------------------------- 0 U T P U T ----------------------------------

--------------------------------------------------------------------------------STAGE1 STAGE2 S T A G E3

------------------------------------------------------------------------------~ STAGE MASS : 4.1777E+01 : 8.7330E+OO I 4.9490E+01 ACTIVE MASS : 8.7620E-04 : 2.4984E-04 : 4.5840E-04 INERT MASS : 1.8549E+01 : 5.2889E+OO : 9.7041E+OO INERT MASS ON ACTIVE MASS : 2.1169E+04 : 2.1169E+04 : 2.1169E+04 ACTIVE MASS RATE : 5. 1075E-02 : 7.2818E-03 : 1.3361E-02 POWERPLANT MASS : 2.2300E+01 : 3.1793E+OO : S.8334E+OO TANK MASS : 9.2743E-01 : 2.644SE-01 : 4.8S21E-01 T'AN~::+PLANT MASS' : 2.3228E+01 : 3.4438E+OO I 6.3186E+OO p a y 1 o a d : 5.8223E+01 : 4.9490E+01 : 3.3467E+01

PROPULSION MASS RATIO : 1.2277E+OO : 1.0999E+OO : 1.2439E+OO G-FACTOR : 7.1483E-01 : 9.3494E-01 : 8.4118E-01 optimal JET SPEED [km/sl : 2.2907E+03 : 2.2907E+03 : 2.2907E+03 initial acceleration [g] : S.0285E-01 : 1.2313E-01 : 2.6579E-01 flighttime [daysl : 1.7397E+03 SPACECRAFT MASS : 100 ******************************************************************************** total amount of ANTIMATTER: matter on antimatter ratio:

7.9222E-04 4.2340E+04

=====================================================================·========== The extra planetary mission described in Section 3.1: optimal ship's mass breakdown (max payload) for that propulsion system specific mass value causing payload and inert propellant mass to be equal to each other.

--------------------------------------------------------------------------------

G. Vulpetti

Table 4. : ~\I NET I c ENERG~I : EQUIVALENT : ACT I VE f"1ASS : I NERT 11ASS : SCOOPED Case Label : IN ROCKET f"10DE : JET SPEED : FLOW RATE : FLOW RATE : MASS RATE

F 0.004 0.95 0.251 0 0.02

Al 0.388 0.95 0.001 0.250 0.02

A2 0.388 0.58 0.251 0.038 0

Multiple propulsion Mode (cases F and Al) and pure-rocket (case A2) comparison: parameter specification for Fig. 7. A propulsion mass ratio equal to 2 pertains to every case.

Fig. 6. Optimal behaviour of payload mass, antimatter mass, matter on antimatter ratio and jet speed versus the propulsion system specific mass for the extraplanetary mission described in Section 3.2.

"sequentially" [28], are conceptually possible by using an initial boosting phase based on the multiple propulsion made and successive powered phases (after booster jettisoning) based on pure-rocket systems. Antimatter engines appear quite superior, especially with regard to manoeuvres at high speed, but they require extremely low specific mass values [28] .

100 . . . . .

P,L 50 I~

Pa~Load [ % M0J Jet Speed [V-Ear~hl . Ar]tLMiltter [% M0l

. . :-10•Lo;1<~

:•·:· ::~. :: ;::.:.·.:: •:: :-·:·: :·i:-.: :~.; ;:; : :~.: .. :.:.:; ;; ;;;; '.:::::~:·. ~::::.: . il'"oglrvAM> :-. . . - ..... VJErci

0 ·- - .. - ..• - ..•..•...

.005 SPECIFIC MASS lKg/f'UJ .205

398

3.4 Special Targets for Starflight

Literature about realistic interstellar flights has been largely concerned with nearby stars as possible targets for the first starflight. Stars farther than 10-12 ly are not realistically considered by investigators for essentially limits of energy and time, as far as our current knowledge of the physical law is concerned. Anyway, the Centauri system and Barnard's Star are usually reference targets when a new concept of propulsion is proposed. Are there other physical targets outside the Solar

Antimatter Propulsion for Space Exploration

[1] 1.0

II v E

F Al L 0 c

A2 t I T I.) I

0.0

cc • .J._I TPUE JET ~3PEED . 95 i 0. 0

1

L p A D ,. .. ;::_, td E E R R

F\ ~1 t

[3] I 0.25

[ 2)

F.Al

-82 .. ·. ·.,

SH IP 1'1AS~:;

'I 'I

'I 'I

';

Alft

[ 4]

'I "/ '/

· . ... ·. •., ·· ... ·· ..

:; , ., ., :;

··.:::::,

o;;""" .,-:;..· ...

1

Fig. 7. Multiple Propulsion Mode (curves F and Al) and pure rocket (curves A2) comparison. See Section 3.3 and Table 4 for an explanation.

System, hopefully closer to us than the nearby stars? To try to get some answer to this question let us discuss very briefly about two recent results: a theoretical one in astrophysics and an observational one in astronomy.

One of the goals of current star evolution physics is to determine the mass transition point between stars and planets. A star has sufficient mass to prime the hydrogen nuclear fusion in its core; a planet does not. New recent results [33, 34] have shifted the previous star-limit downward, namely, to about 0.08 Me (Me = 1 solar mass). Celestial objects (under a gravitational contraction) with a mass between 0.07 Me and 0.075 Me may eventually achieve a state of "quasi-stars" because their thermonuclear energy, though primed, is not sufficient to make themselves energetically stable (as occurs in the Main Sequence) and they go on cooling. Such objects are called "transition masses." Their luminosity would range from 1.0 x 10·5 to 4.0 x 10-5 Le (Le = Sun's luminosity = 4 x 1017

GW) whereas their surface temperature would vary from 1000 to 1500 K. Therefore it is very hard to observe them.

In December 1984 astronomers of the Steward Observatory of the University of Arizona (USA) announced the discovery of an extrasolar "planet" (the first one ever observed) now named VB-8B [35]. VB-8 is a small star of about 0.1 Me. VB-8B should be a dark companion of VB-8 in the class of the transition masses or, more generally, of the brown dwarfs. A brown dwarf is an object for which the gravitational contraction is ultimately halted by electron degeneration. Such a structure is not able to prime the hydrogen fusion. A brown dwarf has a mass lower than 0.08 Me. The above mentioned quasi-stars would represent the "link region" between proper stars and proper brown dwarfs. Observations are to be refined to possibly eliminate the great uncertainty in the VB-8B mass, in par­ticular.

The discovery of VB-8B is important also from a galaxy physics point of view. Very shortly, the brown dwarfs might be so numerous to account for the "galactic disc missing mass" problem. As a consequence, it is not unreasonable to think

that their distribution in the galactic disc would be almost "uniform." Astrophysicists estimate that in a sphere centred on the Sun with a radius of 0.5 parsec there might be 10 faint brown dwarfs detectable only in the infrared region. Therefore, six of them may be found in a spherical shell between 1.2 and 1.6 ly apart from the Sun; these objects would naturally be outside of the gravitational field of the Sun. Were such circumstances confirmed by observations, then a nearer celestial body of astrophysical and galaxy physics importance may become a serious candidate as the target of the first interstellar mission, thus probably lasting 10 years at most.

4. ANTIMATTER MANAGEMENT

No factory of antimatter exists today. Three big laboratories - CERN in Switzerland, Fermilab in USA and IHEP in USSR - produce fluxes of antiprotons for advanced research in Particles Physics. Although the antimatter amounts managed are still too low for starting even a low-energy space mission project, nevertheless methods and techniques, either developed or in progress, are of basic importance for an assessment about a future antimatter production line. New ideas are rapidly evolving. Current aims regard the major aspects about anti­matter: how to produce and control great amounts of anti­matter. There is no pretension of completion by the author here, but rather the intent is to briefly discuss some key problems. This section is divided into three subsections where the different blocks of Fig. 8 are explained. Figure 8 shows a possible sequence of antimatter management from production to space utilisation.

4.1 Antimatter Production

The only antimatter element we can hope to make, stockpile and successively use is antihydrogen. Therefore we should

399

G. Vulpetti

COLLI DER: ANTI PROTON ANTI PROTON LOW-ENERGY anti proton ANTI PROTON source COLLECTOR ACCUMULATOR SOURCE

t POSl i:ron POSli:ron POSl i:ron ANT I HYDROGEN

- ATOM source collector accumu I at 01 FORM. SVSTEM

.

ANTI HYDROGEN ANTI HYDROGEN Neutral-Atom 1, Storage and t'IOLECULE Control 1 Extraction FORM. SYSTEM System

/. ANNIHILATION ANT I MATTER

UTILIZATION CONTROL LOAD [engines]

Fig. 8. A scheme of antimatter management for space utilisation.

interest ourselves in the production of anti protons and positrons in sufficiently high quantities. By means of them atoms and molecules of anti-H should be made, controlled and stored. Unfortunately no atoms of antihydrogen have been produced hitherto. We first consider current antiproton and positron production systems separately, then we mention a possible upgrading and promising techniques to form and control anti­hydrogen atoms.

Let us start our discussion by considering the first block of Fig. 8: the collider. This is a device which provides an intense flux of protons with kinetic energy much higher than their rest mass. W ~ can identify such a machine for a modern Proton Synchroton (PS) where, however, the target that protons i_mpinge is at rest in the laboratory-frame (LAB). Protons -like any hadron - lose energy in interacting with material by two mechanisms: inelastic collision with no particle production and inelastic collision with particle production. At sufficiently high energy the latter mechanism is dominant. Protons are the most readily available hadrons; particle production can take place also by colliding two counter-circling proton beams: the centre-of-mass energy - on which the particle production probability depends - is at its maximum in these conditions. (However, for a number of reasons it is not possible to exploit such a configuration for producing a high flow of antiprotons, which are among the particles produced in the high-energy proton-nucleon strong-interactions. The proton-proton (pp) data are more extensive than the proton-nucleus (p-nucleus) data. What is done in particles physics laboratories consists of extrapolating the p-nucleus information to the energy region of interest by the ailof the pp's.)

The proton current strikes a fixed target. Many types of particles are generated: some are antiprotons. The antiprotons just produced must be pre-focused and collected effectively. The nuclear target is a high-density material with a suitable geometry. In selecting the atomic weight A of the target one must consider that a high-A increases the cross section of interaction between proton and nucleus, but - at the same time - augments the antiproton absorption in the target itself. The overall antiproton yield - the number of antiprotons produced per length unit in the target - can be expressed as follows [36]:

Y=dN/dx =Io exp(-x/A.abs) exp[-(L-x)/A.'abs] (AO/A.abs) (15)

(.::ip/p) W(p,8) (p3/E)

400

where

Io = initial proton intensity

x = depth in the target

L = length of the target

A.abs = proton absorption length

A.'abs = antiproton absorption length

AO =solid angle acceptance at LAB antiproton emission angle(} measured with respect to the incident protons

E,p = antiproton's energy and momentum

.::ip/p = antiproton momentum acceptance

W = invariant production density [36]

Equation (15) is sufficiently correct for our purposes. It is clear that Y represents the input to the second block of Fig. 8: the Antiproton Collector (AC) device. Y depends also on the target's properties and the acceptance angle. In principle, Y is proportional to Lip and 82max, where 8max is the maximum production angle for which the AC can collect antiprotons. Mechanical and thermal properties of the chemical elements are essential for the target choice. In fact, one should consider that proton beams impinging the target material are very intense (- 1013 protons/s) and highly energetic (26 GeV), to cite typical values currently at CERN [37]. Protons arrive in bunches at the target, lose a high fraction of their initial energy and induce mesonic cascade in the material; in addition, all particles produced lose energy in traversing the target at different angles; antiprotons, in particular, can be reabsorbed. Therefore temperature rises and drops significantly with every proton bunch. This means that thermal shocks could fracture the target, this determining the target lifetime. Furthermore, the target material must be enclosed in a low-density container surrounded by a power dissipator, typically fin-shaped. Strong tests performed at CERN have indicated that a very good target consists of copper contained in a graphite core surrounded by an aluminium dissipator. The copper target is cylindrical in shape, 3 mm in diameter and 10 mm long for each cylinder; 11 rods are used. Operational life is beyond several thousands of hours [37). The choice of the target material is also affected by the device immediately downstream: a magnetic lense foc­using antiprotons (and other particles emerging from the

Antimatter Propulsion for Space Exploration

target). A device shaped as a long narrow horn is generally used [37]. Recently, however, CERN have re-designed the target station. A system composed of a pre-focusing lithium lens, a conducting target to keep antiprotons near the longi­tudinal axis and a downstream focusing lithium lens should augment the antiproton yield by a factor of 16. (Lithium lenses have been developed by a Novosibirsk-Fermilab cooperation.) Such a system should then allow much more antiprotons in a momentum spread of ± 6 per cent to match the space-phase 200 mm.mrad acceptance of the upgraded beam transport system (BTS). A hard copper alloy would replace the previous target. Y should achieve 10-5 per incident proton.

The BTS is a quadrupole-magnet line which transports the produced and focused particles to the proper AC. In this line negative particles are selected. Electrons lose energy by synchroton radiation whereas negative pions and muons decay. So a "clean" beam of antiprotons can be obtained. The AC is a dipole/quadrupole magnet ring where a sufficiently high vacuum is created to allow antiprotons to circulate enough to "adjust" the beam characteristics-to the Antiproion Accumu­lator (AA). In fact, antiproton momentum spread and accept­ance are lower at the AA entrance (factors of four and two respectively for the CERN machine). Antiprotons must there­fore be "cooled." In an AC the cooling is in reality a pre­cooling because in the AA the antiprotons will undergo a further strong reduction of their energy dispersion. Electron cooling and stochastic cooling are two techniques to cool a beam of charged particles. Let us very briefly describe the basic principles of these methods.

In general, the beam cooling has the purpose of decreasing the size and the energy spread of the beam particles circulating in a storage ring. Such "compression" should be achieved with no loss of particles.

An important performance index consists of the beam phase­s pace density. A cooling system acting on a "hot" beam improves this figure of merit. As a consequence, the resulting beam is made suitable for preserving its "quality," for having quasi-monoenergetic particles and for special particles such as antiprotons being accumulated. A low-mass particle beam undergoes a self-cooling by curved trajectory radiation loss; in contrast, massive particles (such as antiprotons) require an external cooling.

The technqiue of cooling by electrons consists essentially of injecting a mono-energetic beam of electrons into the ring where the antiprotons circulate. The dynamical coupling between the two beams causes initially-slow antiprotons to be accelerated and initially-fast antiprotons to be slowed down.

Figure 9 shows a scheme of stochastic cooling. Stochastic cooling is a feedback system. It is essentially composed of a "pick-up" subsystem, an amplifier subsystem and a "kicker" subsystem. The pick-up device senses the displacement of the centre-of-mass of beam samples with respect to the ideal trajectory in a ring. There are two contributions to the pick­up signal: the betatron oscillation component (space-transverse

Fig. 9. A very simplified scheme of stochastic cooling: pick-up signal of a test particle and the related kicker pulse. Cooling can be dealt with in terms of the centre-of-mass motion of samples of particles "connected" to the test particle.

Beam----

J:I Pick-up

I I I I

I Motion of ;-- centre of

mass of sample

\ I I

I '-- <,- -... ~/ ~ ...... __ .,,

Kicker

year machine Laboratory particles cooled

197S-77 ISR CERN I.ES

1978 ICE CERN I.ES - l.E6

1982 AA CERN l.E6 - l.E7

198S-86 ACOL CERN l.E7 - I.ES

1990? 20-TEV S.E8 - l.E9

Table 5. Stochastic cooling rate development. The number of cooled particles are referred to as a time constant of I second.

contribution) and the off-momentum contribution. This signal is suitably amplified and delayed by the amplifier. The kicker transforms the amplified signal in a pulse which partially corrects the sample's centre-of-mass displacement just when such sample passes through the kicker. Cooling is a slow process and generally is accomplished into two steps: betatron cooling and momentum cooling. The former uses beam sample rando­mised by the uncooled momentum. These steps take place after a "phase-space manoeuvre" called debunching [37]. We omit details about stochastic cooling here. References 36 and 37 are appropriate for further information.

A beam transfer line transports the antiprotons from AC to AA. Because a pre-cooling has been performed in AC, the AA is ready to accumulate higher fluxes of antiprotons and to accomplish the stack cooling more effectively. Table 5 shows stochastic cooling values. In practice, developments about this cooling technqiue have produced a gain of one-order-of-magni­tude every four years. One realises that the higher the number of particles cooled, the higher the number of antiprotons circu­lating in an accumulation ring. European current goals for the AA stacking system at CERN are to achieve an accumulation rate of 1.8 x 1012 p/day. One order of magnitude gain may be expected for the next generation of antiproton management systems. In the sequel we will therefore refer ourselves to as a figure of 1.5 x 1013 p/day in considering some near-future consequence on a potential space application.

The energy of the antiprotons circulating in the AA ring is generally high (3.5 GeV for the CERN Antiproton Accumu­lator). To (try to) make antihydrogen it is mandatory to decrease the antiproton energy more and more. Downstream of the AA is therefore necessary a further device which works as a low-energy antiproton source. A system like this exists at CERN, namely, the Low-Energy Antiproton Ring (LEAR) [38], designed and built up for Particles Physics experiments involving antiprotons of sufficiently low energy. During 1984 LEAR has produced antiprotons with energy down to 20 MeV. It is not excluded to achieve energy levels below 1 Me V, thus allowing the annihilation cross sections to be studied experimentally in this extremely low energy region.

In Ref. 39 a way is suggested to have a sort of antiprotons breeder based on TeV level ion-heavy collider. On the other hand, looking at the current development of the accelerator technology, we should note that if an accumulation rate of 1.5 x 1013 p/day were able to be transformed into 1.0 x 1013 anti­H atoms/day (supposing an effective storage) 16 years would be necessary to prepare 0.1 microgrammes of antf-f[A further factor of 3 to 4 in the l 990's would allow us to have the smallest amount of antimatter meaningful for the first experimental engine in LEO (see Sections 3.1 and 5.1) in the first decade of the next century.

Some con.siderations are in order about the antiproton prod­uction power efficiency. Once again, because no antiproton factory has yet been designed to aim at antimatter mass­production, we must refer ourselves to the current technology for particles physics laboratories. To estimate the power effi­ciency for antiproton production, we should largely consider the energy rate dissipation in the first three blocks of Fig. 8. The

401

ratio between the relativistic power of anti protons circulating in AA and the power necessary to supply the collider. AC and AA is today about 3.0 x 10-9• If we consider a device like LEAR which requires some megawatt$ to generate antiprotons of very low kinetic energy, the above figure goes down to 1.0 x 10·10•

Let us consider an example. Were an antiproton production device built in LEO and utilised the solar energy, then the amount of antiprotons for antihydrogen formation would be 4.76x108 microgrammes/km2year *I.Ox 10-10• 15 km2* 0.15 = 0.1 microgrammes/year, provided the current antiproton efficiency and 15 km2 of solar cells with efficiency 0.15 are used. We recall that 0.1 microgrammes of antimatter (plus 0.1 microgrammes of matter) develop 18 MJ of energy of which 10 to 14 MJ may be exploited in a good engine.

So far we have not yet talked about the energetically minor component of the antihydrogen: the positron. Positrons and electrons are produced together in an electromagnetic shower induced by high energy electrons or gamma rays. A point to keep in mind is that, even though the antiprotons were available at a few MeV, at such energies or less the positrons are relativistic particles whereas antiprotons are not. Because the energy of e+ in the p frame must ultimately be less than 13.6 eV in an anti-H formation device, positrons (once extracted from their store) are to be slowed down drastically to match the p's velocity and a capture-stimulated process should be exploited to make anti-H at a high rate. In Refs. 40 and 41 a concept is suggested for enhancing the pe+ capture cross section by two orders of magnitude by means of suitable laser light. Figure 10 shows a possible scheme [ 41].

Going back, then, to the electro-magnetic shower, using gammas of 1 GeV striking 3.7 radiation lengths of tungsten, 4 to 5 positrons would emerge per one gamma [20]. Therefore about 2.0 x 1016 gammas would be necessary to neutralise 0.1 microgrammes of antiprotons. One should collect and confine positrons within an accumulation ring by continuously sup­plying the energy they lose by synchroton radiation. An inter­esting concept to get high amounts of positrons is found in Ref. 42. The technique would utilise ultra-high power laser pulses: some tens of attoseconds and a couple of megajoules per pulse substantially because the pair production induced by light in the presence of a nucleus is a process requiring a high threshold. It is not excluded that a laser like this may be available early next century, largely for thermonuclear fusion.

The above concepts are to be related to the three blocks of Fig. 8 regarding positrons.

4.2 Antimatter Storage and Control

The problem of confining antimatter for a long time before being appropriately extracted and utilised can be coped with from two general viewpoints: storing antiprotons and positrons as such or storing neutral systems (atoms and molecules). To deal realistically with storage schemes one should consider the associated control on annihilation (not to be confused with the annihilation control in an engine); in fact, to be able to keep the annihilation rate as low as possible means that the time interval of storage is controllable. The antimatter storage con­cepts so far proposed are not general, namely, their effectiveness depends strongly on the antiparticle state (charged or neutral) and their quantities. In Ref. 43 it is proposed to use magnetic and electric fields - both external to the antiparticles - to confine pico-moles of antiprotons or positrons. The magnetic field constrains charged antiparticles to spiral around its lines while an electrostatic field forbids annihilation between antipar­ticles and the field source atoms. The device suggested in Ref. 43 would be able to capture positrons up to 1 MeV for an accumulation feasibility experiment. If the positrons were chilled to 1 eV then the confinement would be total. Fuel may be depleted by regulating the energy barrier produced by the applied fields. The very small, but not negligible, limit of

402

G. Vulpetti

antimatter strorable is to be ascribed to the space charge effect. In about the same range is the interesting concept proposed

in Refs. 44 and 45. The key points of this confinement technique could be briefly expressed as follows. Let us first consider a p approaching a H-atom in its ground state; the result is known: if the relative energy is less than 13.6 eV and the impact parameter sufficiently small, a protonium is formed and the annihilation occurs with a very high probability (Section 2). Were the H-atom in its 2P state with no external field, the related wavefunction would have spherical symmetry and no perturbation would result for the Hp system (if the antiproton is far enough from H). However, if the level degeneration is split - for instance by an external magnetic field - the 2PO wavefunction is no longer spherical and the p senses a net repulsive force or energy barrier. In contrast, the two 2P( ± 1) wavefunctions do not offer an energy barrier to the p. Therefore, if one desires to build up a controlled confinement of anti protons (an annihilation pile) not only the hydrogen atoms are to be pumped by photons to produce a population inversion from the ground state to 2PO, but also the system temperature must be somewhat inferior to 0.77 Kin order to effectively prevent the 2PO -> 2P(± 1) transitions. The pile's power may be varied by controlling the temperature. There are, however, a number of problems and alternatives [45] to be examined by careful and accurate computer simulations. Other techniques have been proposed to trap and cool antiprotons at very low temperatures (some Kelvin degrees) by means of Penning traps [46, 47].

To store charged antiparticles as such has the great advantage of avoiding forming antiatoms and antimolecules. The disad­vantage is that the antimatter amount is very low. If antiproton and positron rates were to increase to the'levels desirable for a space propulsion system, the antihydrogen_ formation step appears unavoidable, as shown in Fig. 8 and already mentioned for Fig. 10. Once anti-H atoms are obtained, they must be slowed down, suitably cooled and trapped. In the last years a number of techniques to control and trap neutral atoms have been demonstrated [48-50]. Such methods largely use a combi­nation of laser light, magnetic and electric fields. Some tech­niques are effective on certain atoms, some on other atoms. In fact, one must utilise the physical properties of the considered atoms in an external field. Also, gravitational effects in particle traps have been pointed out [50].

In trapping antihydrogen one should consider that free anti­H atoms have a probability to be photo-ionised. Perhaps, to convert atomic anti-H into molecular anti-H2 and trap mole­cules might be more advantageous. If antihydrogen is arranged as a ball at very low temperature, then a magnetic bottle provides a potential well for it because anti-Hice is diamagnetic [51]. However, a device set up at the Jet Propulsion Laboratory [52] may result in a longer storage time with respect to magnetic levitation. In fact, spheres simulating antihydrogen have been levitated by means of a position controller com­manding an electric field inside which the balls are floating because slightly charged. As shown schematically in Fig. 8, the anti-H ice state though at extremely low temperature nevertheless lends itself to an important function: the extraction of positrons and antiprotons separately. It should be possible to first drive positrons off by ultraviolet light and then to extract antiprotons by electric field emission. Thus the two fluxes of antiparticles can be transported on-board (ending with a stage of self-adjusting plasma if necessary) and delivered to the antimatter utilisation load (Fig. 8), namely, the space propul­sion system.

This system will be the subject of Section. 5.

5. MATTER-ANTIMATTER ROCKET ENGINE DESIGN CONCEPTS

In Section 3 we discussed the dynamical performance of an antimatter-based propulsion system for different levels of space

Antimatter Propulsion for Space Exploration

flight energy. In Section 4 we mentioned a few of the formidable problems in antimatter production, storage, extraction, annihil­ation control. Once sufficient antimatter and adequate tank systems are available, the problem is to arrange a device in order to gain thrust for a space vehicle. The major difficulty in designing a matter-antimatter annihilation engine will per­haps be to effiCieniTy. combine just matter allcf antimatter in order to achieve controllable thrust and specific impulse. In the Section 5.1 we will focus our attention on these aspects. It will be apparent that both the problems are far from simple and the related concepts suggested are only theoretical hints.

Although in principle annihilation systems admit no limits on thrust and jet speed, in practice we are forced to divide the engine concepts in classes:

(I) energy-limited engines,

(2) acceleration-limited engines,

(3) power-limited engines.

The meaning of this terminology, although a classical one, will appear clearer through the context of the next paragraphs.

5.1 Energy-Limited Annihilation Engine Concepts

We have seen in Section 3.1 that the optimal flight and payload conditions for missions around the Earth were to mix a few mi/ligrammes (at most) of antimatter with tens of tonnes of matter. The reaction matter-antimatter cannot take place by "spraying" them into a chamber similar to the fuel and the oxidiser of a liquid chemical engine. There are, in fact, several causes:

1. neutral antimatter must be ionised before being annihilated in a controlled manner with matter;

2. high vacuum must be produced upstream of the annihilation volume;

3. were antiprotons at the energy of a few KeV or less to be stopped in the outer surface thickness of a dense target, at least half of the energy released would be catastrophically deposited into the engine structures;

4. the annihilation reactions represent very intense localised flashes of energy transported by particles much different from atoms (in contrast to the comb­ustion reactions); such sub-nuclear particles must traverse a sufficient quantity of matter to lose energy by interacting with the atomic components.

In Fig. 11 we suggest a design concept which would account for the previous considerations. A Liquid state ordinary matter is arranged inside the reaction chamber followed by a conver­gent-divergent nozzle just like a solid chemical engine. A neutral current of plasma of antiprotons neutralised by posi­trons enters the reaction chamber through a longitudinal orifice. A magnetic field defocuses antiprotons to increase the annihila­tion volume in the inner zone filled with a high-pressure gaseous target injected transversally through a hole. The annihilations produce isotropic fluxes of charged pions, gamma rays and K­mesons. Because of the almost-closed geometry of the annihila­tion zone, the released energy is received by the liquid propellant practically over the whole solid angle. A cylindrical-symmetry massive shell is then heated and vaporised. Slightly spinning the engine would avoid sloshing problems during the propulsion phase.

When the vaporisation just begins the gaseous transversal flux is interrupted and its hole closed. The nozzle shutter is

AHTIPllOTON RING

INTERACTION REGION PHOTON - -·· p......_.._ ••

FOCUSED LASER KAM

l'OSITRON RING --· MIRROR' ~E~ ,.__.

LASlR RING

LENS

I MIRROR

Fig. 10. Laser-aided anti-hydrogen formation scheme (from Ref. 41).

anti protons ----> Jt.=~~~:~~~:11(-,--

' . ir--"-'"""'---- >--__ meter

: target gas

Fig. 11. A matter-antimatter annihilation engine concept for energy­limited manoeuvres in the Earth-space (see Section 5.1 for details).

momentarily open to cause the target gas pressure to decreas·e. The antiproton flow is stopped, but a micropellet of antihyd­rogen is launched into the annihilation zone. The orifice is then rapidly closed. The sphere of anti-H "evaporates" by progressive annihilation with the residual gas. This adds more energy to the propellant which augments its vaporisation; this, in turn, increases the annihilation rate of the pellet as it moves along the chamber and so on.

All this takes place instantaneously, in practice, that is rapidly with respect to gasdynamics times. Liquid propellant and pellet's vaporisation interact (non-linearly) resulting in a high stagnation pressure; the propellant can be exhausted producing high thrust. Because of the current mechanism to heat the inert matter rapidly, pressure, mass flow rate and thrust decay with time. The whole cycle can be repeated until the desired propulsion mass ratio is achieved by using either a large engine or by means of single-shot modules (to examine these options is out of the current context). Note that during the pre-vaporisation phase the heat accumulation in the propellant could be stopped at any time if appropriate monitoring sensors "alert" the control system. This engine can be restarted for multiple finite-burn manoeuvres similarly to a liquid chemical thruster. Table 6 shows values of some parameters in a simple engine configuration - using gaseous helium and liquid oxygen - and neglecting a number of effects which are out of the current aims. No strict optimisation has been made to arrange the above configuration. The variables which chiefly "com­mand" the whole engine configurations are the antimatter pellet mass, the chamber sizes, the range of charged pions at 0.35 GeV /c and the number of radiation lengths for the gamma rays of about 0.2 GeV. A real engine should be strongly dependent on the pion's momentum spread around the above mean value because just there the range versus momentum curve is rather steep [20]. We should notice that such an engine concept would exhibit an energy efficiency value sufficiently high to possibly render the final cost on-orbit significantly low. We shall discuss this consequence in Section 6.

In the energy-limited class of engines a continuous-mode thruster concept is detailed in Ref. 53. The annihilation chamber is cylindrical in shape and a convergent-divergent Da Laval nozzle is considered. The antihydrogen enters the chamber longitudinally; the propellant is inserted simultane­ously. In order to achieve a steady-state thrust level, gaseous

403

Table 6.

antiproton beam kinetic energy antiproton beam cross section gaseous target target pressure PROPELLANT chamber length chamber radius antihydrogen pellet mass annihilation energy efficiency init1al chamber temperature throat area

1.000000E+Ol 2.000000E-01 HELIUM 4.000000E+Ol LOX 1.300000E+02 1.230000E+02 1.000000E+Ol 6.000000E-01 6.000000E+Ol 3.600000E+01

G. Vulpetti

: KeV I cm**2

I atm.

I cm I cm I micrograms

I K I cm•*2

e:<pansion ratio 3.SOOOOOE+Ol I

antiprotons beam absorption 9.999836E-01 heating phase time heating phase antimatter stagnation pressure <•> exit Mach number MASS FLOW RATE <•> SPECIFIC IMPULSE THRUST <•> F·ROPULS ION TI ME thrusting/annihilation energy ratio

2.118063E-01 I seconds 9.812497E-01 : microgram• S.6SS22SE+02 : atm. S.426344E+OO I

3.429S97E+02 I Kg/s 1.02743SE+02 : seconds 3.S39422E+OS : Newtons 2.2S8606E+01 I seconds 9.243S32E-01 I

A possible configuration for an energy-limited annihilation engine. Starred values correspond to I /e of the chamber pressure at time=O. The total impulse per cycle equals 2.17 x I 06 Ns. Thrusting time equals ten times the decay constant.

inert mass must be used. This would entail too low a macro­scopic cross section of heating. In fact, the high energy sub­nuclear particles would "see" a negligible matter if their trajec­tories were rectlinear. A magnetic field surrounding the annihil­ation chamber is then necessary to trap. pions, muons and electrons in order to increase their path in the gas and to allow propellant heating. The magnetic field - configured as a (magnetic) bottle - would be very high at the chamber ends according to Ref. 53. Only type-2 superconductors can support the related current density. In Ref. 53 an annihilation energy efficiency equal to 0.35 is evaluated. The chamber volume is of the order of a couple of cubic metres. The reference mission studied consists of a LEO-GEO-LEO transfer flight.

We mentioned two energy-limited annihilation engine design concepts which seem quite different. The main drawback of the pulsed-mode engine would be the use of several and more modules to achieve the desired propulsion ratio. The continuous­mode engine would exhibit the disadvantages of requiring very high magnetic fields.

A possible compromise between the two concepts may be a pulsed-mode engine with liquid/solid inert mass inside the annihilation chamber with a magnetic field produced by usual coils. Confining pions, muons and electrons would be no longer

Table 7.

Principal characteristics of the engine concept of Fig. 12A (from Ref. 54).

ANTIPROTON FLOW RATE (average)

INJECTED MATTER ATOMIC MASS NO.

INJECTED MATTER FLOW RATE (average)

FULL CYCLE

CONFINEMENT TIME

PLASMA DENSITY IN CONFINEMENT

MAXIMUM TEMPERATURE

MEAN DISTANCE TRAVELLED BY NUCLIDE

EXHAUST KINETIC ENERGY

EXHAUST VELOCITY

THRUST

FRACTION OF P-P MASS ENERGY CONVERTED INTO DIRECT EXHAUST ENERGY

404

2.E+20 particles/sec

240 (approx.)

9.E+24 atoms or ions/sec

17 millisec

millisec

l.5E+l6 atoms or ions/cm3

2. 6E+08 K

500 Km

100 eV/atomic mass unit

140 Km/s

550000 N

50%

necessary, inasmuch as they are going to be stopped inside the non-gaseous inert mass. This may be an area of future investigation.

5.2 Acceleration-Limited Annihilation Engine Concepts

In an interplanetary flight the ratio between the ordinary matter and antimatter components is much less than the geocentric mission's (see Table 3 for an example), although it remains quite high. This entails that the pulses in an engine like that of Section 5.1 would be so high in number and intense in energy that the thruster structures would not withstand the ensuing stresses. In addition, the specific impulse is too low for a mission in the Solar System. In Ref. 34 an engine concept is proposed, the major characteristic of which would be an energy coupling between annihilation products and ordinary matter in order to get thrust and jet speed appropriate for an interplanetary flight booster (or an intermediate stage in a multi-stage arrange­ment). The scheme of such an engine and some key parameters are reported in Fig. 12A from Ref. 54. The central point of this concept is to longitudinally inject antiprotons, whereas ordinary matter of high atomic number flows transversally into an annihilation volume immersed in a magnetic bottle. If the confinement time is sufficiently long, the annihilation charged pions would interact with the nuclei of a high density plasma; this would result in nucleon evaporation, pion absorption, nucleus-nucleus and nucleus-atom collisions which ultimately would distribute the initial annihilation energy throughout a great amount of matter. If uranium or plutonium were used, charge-exchange in nucleon-pion interactions may cause fission, the fragments of which would contribute to and share their energy with the ionised atoms. The magnetic barrier at the throat is weakened to allow the energetic plasma to exhaust. The ejection time plus the confinment time in practice represents the duty cycle time. In contrast to the previous energy-limited engine concepts, the gamma energy can be considered lost. On the other hand, the current concept would permit achieving a high specific impulse and controlling it by means of the matter pulse. Optimal specific impulse, necessary for interplanetary or precursor interstellar missions as discussed in Section 3.2, would be allowed in this engine design class (Table 7).

Antimatter Propulsion for Space Exploration

, .... ., ,___..,

PULSED _-::-: :-: :_ : : : ~ "- - - - -_:_::..:...:. DIRECTED BEAM ANTIPROTON ~ _Pl_A~M~ ::-:: ::: .::_ -- -- -- - '\ CW HIGH ATOMIC BEAM -~,;;:;/-~--;=-::.-------------- MASSNO.AND

" ... ~ - - - - __ :-:-:-::- OTHER SPECIES

ANNIHILATtON, IONIZATION, ANO COLLISION COUPLING REGION

PULSED, NEUTRAL, HIGH ATOMIC MASS NO. ATOM BEAM

DIRECTOR

Fig. 12A. Matter-antimatter annihilation engine concept for acceler­ation-limited manoeuvres (from Ref. 54).

TRANSFERRAL ANNIHLATION

SYSTEM I ENGi€ I 1 meter

ANTIPROTONS=0~~~~ - -_::...:

H ATOMS

PATH OF A

PARTK:ULAR POSITIVE OR NEGATIVE PION

Fig. 128. Matter-antimatter annihilation engine concept for power­limited manoeuvres (from Ref. 54).

5.3 Power-limited Annihilation Engine Concepts

Interstellar missions based on pure-rocket vehicles claim mat­ter-antimatter ratios very low compared with the missions in the Solar System. Only by using a multiple propulsion mode can such values increase, but still decidely lower than the values relevant to the energy-limited and acceleration-limited thrusters.

If we limit ourselves to discuss pure-rocket propulsion system concepts, the key point to get relativistic jet speeds is to directly exhaust the annihilation products. Figure 12B is reported from Ref. 54. It represents a continuous mode engine concept based on the annihilation of antiprotons and hydrogen nuclei at a very low energy of the order of 0.1 e V. Charged pions are directed by a magnetic nozzle which would allow the true jet speed to achieve 0.9 c and more. However, it is mentioned in Ref. 54 that such a low antiproton energy seems much too difficult to obtain, especially onboard, starting from an extrac­tion energy orders of magnitude higher. This is essentially because a high antiproton current is at the same time necessary to obtain a not too low thrust. In any case annihilation in a gaseous target of hydrogen would cause a sure loss of the high energy gammas from the neutral pion decay.

Besides, if one augments the geometric cross sections of the colliding fluxes, the transversal one would sense more and more the high magnetic gradient near the magnetic mirror; as a consequence, the residual hydrogen may become more difficult to be retrieved and re-inserted into the annihilation volume. Such losses would decrease the effective jet speed significantly. Although continuous thrusting is highly desirable, the previous comments would suggest that other arrangements should be considered as well.

Reference 55 presents a number of design considerations about certain aspects of another possible way of obtaining relativistic exhaust speeds and appreciable levels of thrust. Figures 13 and 14 and Table 8 are reported from Ref. 55. Figure 13 shows the overall scheme of this thruster conce'pt.

The engine operates in pulsed mode. A bunch of antiprotons enter the nozzle region along the magnetic axis of the nozzle. Anti protons interact with the nuclei of a target sphere launched by a magnetic injector along a curved trajectory transversal to the antimatter incident beam. The annihilation zone inside the matter pellet is located at a suitable-distance from the magnetic barrier which reflects the charged products gushing out from the pellet. Such products are essentially charged pions, electrons and positrons to be directed and exhausted away by the mag­netic nozzle. What takes place inside the pellet represents the central point of the analysis performed in Ref. 55. Here we summarise it very briefly. The matter target consists of a solid state sphere composed of a core and a shell. The core is of light/intermediate elements, the shell is of heavy elements. The type of elements, their amounts and geometrical arrangement depend upon the following requirements: (1) to get a high probability of annihilation, (2) to obtain a relativistic jet speed, (3) to retain only a small fraction of the annihilation energy left by the charged particles traversing the sphere, ( 4) to (partially) induce gamma ray conversion into energetic elec­trons and positrons. Every pellet is retrieved through a suitable duct facing the injector and re-cycled. This increases the burn­up efficiency and allows the vehicle to exploit the heat each sphere carries. A pellet must have a heavy shell if a fraction of the gamma energy is to be converted into thrust. Engine/ configurations and performances are reported in Table 8. Tl}e model to compute them is rather complex (even though in a first analysis) and is detailed in Ref. 55. Here, we repeat some major considerations and conclusions. Main variables are the antiproton flux (which commands the level of thrust), the antiproton's kinetic energy (upon which the annihilation cross section largely depends), the pulse duration (which affects the pellet configuration and the injector requirements). Essentially, the input to the engine consists of a narrow current-neutralised beam of 1 KeV and not less than 1.0 x 1020 p/s. It impinges on a pellet, the core of which is of beryllium oxide (BeO).

Let us first briefly discuss examples of total gamma energy loss. The p absorption is fairly high. The pellet energy is about two per cent of the retrievable energy. Each massive pellet can be used several times before depletion effects become appreciable. The launch frequency is 1 to 2 kHz. The magnetic nozzle profile is not conic. The magnetic field at the throat is in the 10 to 20 Tesla range. As the antiproton flux increases, the nozzle transversal size strongly decreases whereas the nozzle length can be kept fixed. This results in an increase of the thrust density. The true jet speed is about 0.9 c, whereas the effective speed is 0.5 c.

Different figures arise when one tries to retain a fraction of the gamma energy. A tungsten shell 3.5 mm deep surrounds

Fig. 13. A power-limited matter-antimatter engine concept: Nozzle configuration to direct the high energy particles produced by antipro­ton-proton annihilations inside a pellet.

BEAM OF ANTIPROTONS

\

',

PARTICLE GUIDING -...----- CENTER TRAJECTORY

---- - - - - - - - --·-MAGNETIC FIELD LINES

',,_ -------~ MATTER PELlET

---- MAGNETIC INJECTOR

405

G. Vulpetti TABLE 8

~ antlprolon nux ... l.EZO 5.EZO l.EZI l.EZO 5.EZO l.EZI < puh• duration ,.. 100 50 50 50 zo zo W antlproton ener1y KeV I I I I I I ~ beam cro•• 1ectlon cmZ 0.13 o.u o. u 0.13 0.13 O.IJ

IQ. beam denelty cm·J t ... E13 9. EU 1.9£14 I.BEU 9. EU ... IE14 core material BeO BeO BeO BeO BeO BeO Initial temperature K Z73 Z73 Z73 Z7l Z7l Z7l llnal temperature K Z540 2540 2540 Z040 1110 1110 radlu1 em 0,95 1.5 Z.I 0,76 1.15 l.6J ma11 I 10.1 4Z,5 IZO,J 5,5 19.Z 54.J

,.._ antlproton ab1orptlon ~ 99.1 99.9 99.9 99.4 99.9 99.9 W 1hell matertal w .. w ~ final temperature K JJ&O JJZO J510 < depth cm no sllell 0,)5 O.J5 O.J5 ... ma11 I 75 150 Z77

antloroton ab1orptlon ~ 11 4 11.4 17,4 total aD1orptlon 7o ,,,. 99.9 99,9 ''"' '19.9 99.9 pellet ma11 K1 0.011 0.04Z 0,120 0,0I 0,169 o. ,,. recoverable entrlf KJ 24. T 97,I 276 fZ.4 95 ZIS

LI duty cycle mo I 0,5 o.s o.s o.z o.z ..i pellet .. ioelly m/1 100 zoo JOO 150 JOO 450 ~pellet ener11 KJ 0,055 0,14 5.4 0,9 7,6 JJ. 5 u launch frequency Kffa I z z z 5 5

noaala throat area m• 0,o5 o.z 0,14 o.• 0,10 0.10 annth. re1lon dlltanc1 m 0,75 0,75. 0.75 0,75 0.75 0,75

111 noaale ellft area mZ 1,4 Z.6 I.I '·' z.o l.JJ .:i area pronla lan1th m o.zs o.zs o.zs o.zs o.zs o.zs N noaale len1th m I.II 1,11 I.II l.IZ 1.11 1.11 N Inlet ma1netlc neld KO 94 170 zos .. 190 ZJ7 ~ renecdon coefRclent ~ 9l 9Z 9l 9l 9Z 9Z

outlat mopellc lleld KO ,_, IJ 15,I '·' 14,T 11.J noaat1-r1aldent en1r1y MJ J,I J.t J.I J.I J, I J. I •ln1l•·puh1 lhru•t N 51.1 259 511 •Z JIO uo eyel1 meaa thru1t N 5.11 ZS.9 51.1 6.z JI, u.

i- cycle thnot denolty N/mZ 0.61 10.0 Zl,9 O.IO IS.I 46,6 w mean exh•u•t opeod c 0,905 0.905 0.905 0.911· 0,917 0,917 "" effeetlve exh•u•t 1p11d c 0.511 0.519 0,919 0,6Zt 0,6ZZ 0,6ZZ

total enor11 efficiency " 57.4 ST.4 ST.4 "·' 67,I "·' Jet kinetic power OW 10.6 5J 106 IJ.T 61.5 IJ7

Sizes and performance computed for the power-limited annihilation pulsed-engine concept schemed in Fig. 13 and 14. See Section 5.3 for a discussion of the results.

the BeO core. The charged mesons lose energy in traversing this W-shell, but the core diameter is decreased. The pellet mass becomes serious at high p fluxes, although the injector energy per pellet is still a fraction of the recovered energy. The nozzle magnetic field is higher than the bare-core solution's because the kinetic energy density includes the electron-posi­tron component. The nozzle cross area is further decreased. The re-conversion mode augments the thrust of 20 per cent. The true jet spee\} is slightly increased (one per cent) but, more important, the etf ective exhaust speed receives a benefit of +20 per cent. There are some penalties to be paid for such advantages. First, the duty-cycle duration is constrained to the 200 to 500 microsecond range; second, the pellet's mass and shell-core temperature gradient may add complexity .{o the injector and re-cycling subsystem; third, the overall mass of the number of pellets necessary to assure repetitive pulses may offset the thrust gain at very high antiproton fluxes.

This engine type cannot undergo a scaling up. A number of parallel thruster modules is necessary to achieve the flight

Fig. 14. Ordinary matter pellet configuration for the engine concept of Fig. 13: a heavy element shell should be added to light or intermediate element core in order to convert gamma photons.

PELLET! MOTION

ANTI PROTON BEAM

~ -----f-'.t,----

406

acceleration. If engine reliability is increased, on-board trans­portation of the antiproton and positron beams should become more complex.

Considerable research is called in solving the big problem of efficiently combining matter and antimatter to make a good engine.

6. ANTIMATTER ENGINE FLIGHT COST

This section is substantially based on Ref. 56 where a cost comparison between conventional and antihydrogen propulsion systems is made. We divide our discussion into two parts. In the former we briefly report the results of Ref. 56 which shows quantitative reliable values about the cost problem. In the latter we extend the conclusions of Ref. 56 by considering again an engine concept such as the one proposed in Section 5 .1.

6.1 Cost Comparison of Conventional and Antimatter Propulsion Missions

Reference 56 presents a comparative study of fuel cost between a number of significant conventional propulsion systems and antimatter systems. The former ones consist of storable chemical, cryogenic chemical and nuclear thermal propulsion systems. Electric, laser, solar-sail etc. propulsion have not been included because of the assumption to perform manoeuvres in short times. Mission delta-V values up to 50 km/shave been considered in order to show that manoeuvres hardly realistic for conventional propulsion are possible with antimatter engines, for which propulsion mass ratios should not exceed the limit of five. Because manoeuvres are quasi-impulsive in the assumptions of Ref. 56, the cost equations for chemical-like and antimatter propulsion systems are based upon the usual one-dimensional rocket equation; for the latter systems the explicit conversion energy equation has been added. The overall cost taken into consideration in Ref. 56 consists of: ( 1) the cost to transport a certain amount of propellant (or reaction mass to be ejected during a mission starting from LEO) from ground

Antimatter Propulsion for Space Exploration

100

... 80 ~ u ..... !: 60 ... ... i?: 40 ~ ..... ... • 20

0 5 10 15 20

MISSION DELTA-V, km/1

Fig. 15. Relative cost as function of mission delta-V for conventional and antimatter propulsion systems. A sufficiently extended range of high-energy missions shows where antimatter engines begin to be less expensive than chemical-like propulsion systems (from Ref. 56). The overall propulsion efficiency of the antimatter-matter annihilation device has been assumed 0.30.

to LEO, the related specific cost being fixed at 5000 $/kg (the current price value); (2) the cost to produce the necessary amount of antihydrogen for an antimatter propulsion system; this value ranges over a large interval because today it is not yet possible to well estimate the specific cost of antimatter production. Let us notice that the unit of such price is M$/mg. The analysis performed in Ref. 56 is centred on two key aspects: the ratio between the two specific costs and the adjustable specific impulse of an antimatter engine.

Figure 15 presents the results of fuel cost comparison between liquid bi-propellant, LH2/LOX, Nuclear-thermal engines and an antimatter (energy-limited) thruster the overall energy effi­ciency of which has been fixed at 0.30. Figure 15 can furnish the mission fuel cost per tonne of empty vehicle, but - much more important - shows where antimatter propulsion begins to be less expensive than the other propulsion methods. Thus, the major conclusion established in Ref. 56 is that if the specific cost to produce antimatter were as low as 1 M$/mg then antimatter flights would be less expensive than any other considered for mission delta-V greater than 5 km/s.

6.2 Extension of Cost Comparison

We have noted two particular things in Ref. 56: (1) the energy efficiency of the antimatter propulsion system has been kept fixed at 30 per cent; (2) no particular reference to some annihilation engine concept has been made. In the current paper we are in a different situation. In fact, in Section 5 we have considered many types of engine concepts; in particular in Section 5.1 there are concepts to effectively mix some milligrammes of antimatter with tonnes of matter. In one of those concepts the interactions of the gamma rays and charged pions with the inert matter are deep. The matter amount could be regulated in order to achieve 2.5 to 3 radiation lengths for both electromagnetic and hadronic cascades. Leptonic/ electromagnetic secondary cascades follow each charged pion stopped in the matter shell. The annihilation energy sharing history for non-interacting gammas, pions and muons (from annihilation) is very different from that in high - interaction environments. As a consequence, the overall energy efficiency of an engine like that suggested in Section 5.1 may double Ref. 56 assumptions. The explanation of the physical processes which bring forth the mentioned cascades are outside the current context.

We have used the same equations of Ref. 56 to minimise the

antimatter propulsion cost and make the ratio with respect to the cost of conventional propulsion with a specific impulse of 900 s. This ratio has been plotted as a function of the mission delta-V in Fig. 16 for antimatter energy efficiencies of 0.40 and 0.50. One can see that for an efficiency of 40 per cent and a price of 2 M$/mg the antimatter propulsion systems are less expensive than conventional systems for any value of delta-V. An increase of efficiency up to 50 per cent would allow the extention of the range of antimatter production costs up to 3 M$/mg for delta-V greater than 1 km/s.

Thus, missions involving LEO-GEO transfers for platforms and heavy telecommunications satellites or lower-energy transfers for scientific satellites (for instance, transporting heavy instruments for research) may be included in the advan­tage of using antimatter engines.

7. INTERNATIONAL COOPERATION

Astronautics involves a "harmonic processing" of the major results of basic and technological disciplines. Space flight has so far required progresses in Physics, Mathematics, Chemistry, Engineering, Astronomy, Computer Science, Medicine and so forth, and has stimulated new developments in these and other areas. Thus, new disciplines such as Astrodynamics and Space Propulsion are full scientific disciplines which interact success­fully with each other. Antimatter-matter annihilation propul­sion is based on vast fields of Particles Physics and their related technology. Theoretical results in this propulsion area have been obtained by appropriately considering the particle-antiparticle interaction, but much more results are expected especially at the time of passage from ideas to practice. How long for this first desirable goal? We cannot estimate this time interval; ho_w~ver, the scientific community can affect it by promoting an international cooperation as soon as possible. How soon? The answer to this question may be only guessed, in our opinion. In fact, so far most of the studies for potential space applications of the antiproton-nucleon annihilation energy may have been performed with no support but small funds provided by those companies for which the interested researchers usually work. On their own will, researchers have discussed and exchanged information, suggestions and papers with each other. The Journal of the British Interplanetary Society and Astronautica Acta are effective means to spread ideas about antimatter propulsion into the world. Among government institutions, the U.S. Air Force have shown a practical interest in this field [57]. It is true that in the early delicate phase of new research scientists feel themselves free to express their ideas and go up with their scientific skill and imagination. It is also true that in these last five years antimatter propulsion research has been more systematic and effective than in the previous 25 years. This has contributed to the undoubted recognition that- though very big problems are to be solved - there are several and more potential space applications of antimatter propulsion; moreover, in areas such as fast interplanetary missions and interstellar flight antiproton-nucleon propulsion systems may represent a very promising direction.

Very probably this first phase of antimatter propulsion research is not ended; however we think that investigators have their minds clearer for what is necessary (although presumably not sufficient) to make a step forward. The International Academy of Astronautics can promote and organise more advanced studies in the fields already deemed important in antimatter propulsion.

If an international cooperation starts in the near future, the current scientific generation could achieve major objectives within a reasonable time. Naturally, even such studies are to be viewed in the light of complex and different policies which the various space agencies in the world are following.

407

c 0 s T

R A T I 0

c 0 s T

R A T I 0

2

1

0

2

1

0

0

antimatter engine effi.ci enc'=! = 0. 40

·········C[·············•t·•••NI~Ri .• 1."Ls:b~•··· ·····=··········:··········L··~M$1·9·· =

·····<···········:··········:········~···~·········~·~···· ·················••( ................. ·;··········:··········:·········~

........ ·~....... . . ... . . . . . . . . . . . . . . . . . . . . . . . . .. ·:·.. . . . . . . . . . . . . . . . . . . . . . . . . . . ........ .

MISSION 10

DELTA-V CKm/s]

antimatter engine efficienc'=f = 0.50 . . . . . . .

...... j......... . .... NU.CLE.AR ... I SP .. [=:: ... 9.0.0i. .s ...... . . . . . . . . . . . . . . . . ··········:·········· ··········:·········-:·········· . . . . . . . . . . . .

··········

20

1~ ......... ) .......... f·········+····~

0

. , .......... ; .......... : .......... ; . . . . . . . . . . . . . . . . . . ......... ~. . .... .

MISSION 10

DELTA-V CKm/s] 20

Fig. 16. Fuel cost ratio versus mission delta-V. The antimatter engine efficiency has been increased according to the thruster concept of Section 5.1.

8. CONCLUSIONS

G. Vulpetti

In this paper we have - with no pretention of completion -arranged a review of the current major aspects of antimatter­matter annihilation for a possible pacific use in space. Antipro­ton-nucleon annihilation propulsion systems would be unique among all other propulsion devices conceived hitherto for essen­tially two reasons: (1) the annihilation offers the highest yield of conversion of mass into kinetic energy, (2) the antiproton+­nucleon system, in particular, exhibits the highest energy den­sity. The first point would allow the rocket specific impulse to become relativistic. The second point would make possible to leave out very high power external-to-engine sources on-board and, at the same time, would allow spacecraft propulsion systems to be very compact in size. In addition, no significant restriction on thrust and jet speed would occur with antiproton­nucleon annihilation (current annihilation engine concepts should not be considered as a sort of limit for thrust and exhaust speed).

should be undertaken. In parallel to such a research new types of engines where no negligible amount of antimatter is to interact effectively with matter would open quite new frontiers in the physics and egineering of space propulsion. Accurate and careful computer simulations can give precious design information just today. Perhaps, it is the time that personal and almost-isolated research performed in the past years be organised and augmented in power and results. Such previous interest and effort have allowed us to achieve a point: to realise that several future things in space could be made better with, and much more things would be hardly possible without, antimatter propulsion.

Such things appear to be so attractive and promising for space applications that appropriate efforts to solve the big problems such as antihydrogen production, storage and control

408

REFERENCES

Here the following notation is used for brevity: ** = Proceedings of the Symosium on Antinucleon-Nucleon Annihil­ations, Chexbres, 1972.

Antimatter Propulsion for Space Exploration

*** = Proceedings of the Joint CERN-KFK Workshop on Physics with Cooled Low Energetic Antiprotons, Karlsruhe (West Germany), March 1979.

**** = 5th European Symposium on Nucleon-Antinucleon Interac­tions, Bressanone (Italy), June 1980.

1. E. Segre, 'Nuclei and Particles,' The Benjamin/Cummings Publi-shing Company, Reading, Mass., 1977.

2. H. Poth, 'Fundamental Properties of Antinucleons,' *** 3. E. Klempt, 'Antiprotonic Atoms,' *** 4. C. Voci, 'Antineutrons at LEAR,' *** 5. H. Kock, 'Investigations on Baryonium with Stopped Antipro­

tons,' *** 6. H. R. Rubinstein, 'Theory ofNucleon-Antinucleon Annihilation,'

** 7. M.A. Schneegans, 'Anti.N-N Annihilation at LEAR,' *** 8. The ASTERIX Collaboration, 'A Study of anti.p p interactions

at Rest in a H2 Gas Target at LEAR (proposal),' August 1980. 9. College de France Collaboration, 'An Inclusive View on p-anti.p­

> n(pi) at Rest,' ** 10. C. Defoix and P. Espigat, 'Experimental Analysis of the Reaction

p-anti.p-> 2(pi+,p-)+pi0 at Rest (non-OmegaO events). Evi­dence for a roO-roO Effect around 1440 MeV,' **

11. V. Simak, 'High-Energy Interactions of Anti protons,' CERN Note 1975.

12. M. R. Pennington, 'Low Energy Anti.P-P Physics: Why Now? CERN Note 1982.

13. The ASTERIX collaboration, 'Protonium Spectroscopy and Identification of P-wave and S-wave Initial States of p-anti.p annihilation at rest with the ASTERIX Experiment at LEAR, CERN /EP 82-150, Oct. 1982.

14. T. Fields and R. Singer, 'Clusters in anti.p-p Annihilation and in pp Ionization,' **

15. R. Bizzarri, et al., 'Pion and Kaon Production in Antiproton­Neutron Annihilation at Rest,' II Nuovo Cimento, 53A, (1964).

16. A. Bettini, et al., 'Annihilation anti.p n at rest into Final States Containing K-mesons,' II Nuovo Cimento, 62A, 1038 (1969).

17. M. Gaspero, 'pi+ and pi- Inclusive Spectra in anti.p n Annihila­tion at Rest,' Internal Note 527 of Institute of Physics, Rome University, February 1974.

18. Th. Papadopoulou, et al., 'The Inclusive Charged Pion Spectra in anti.p-n Annihilation ar Rest,' Physics Letters, 43B, 401 (1973).

19. G. Vulpetti, 'A Propulsion-Oriented Synthesis of the Antiproton­N ucleon Annihilation Experimental Results,' JBIS, 37, 124-134 (1984).

20. 'Review of Particle Properties: Particle Data Group,' CERN, July 1984.

21. J. Rafelski, et al .. 'Hot Hadronic and Quark Matter in anti.p Annihilation on Nuclei,' ***

22. G. Vulpetti, 'Maximum Terminal Velocity of Relativistic Rocket,' Acta Astronautica, 12, 81-90 (1985).

23. G. Vulpetti, 'An Approach to the Modelling of Matter-Anti­matter Propulsion Systems,' JBIS, 37, 403-409 (1984).

24. L. R. Shepherd, 'Interstellat Flight,' JBIS, 11, 149-167 (1952). 25. D. D. Papailou (Ed.), 'Frontiers in Propulsion Research,' JPL

TM 33-722, 1975. 26. L. D. Jaffe, et al., 'An Interstellar Precursor Mission,' JBIS, 33,

3-26 (1980). 27. G. Vulpetti, 'Relativistic Astrodynamics: Non-Rectilinear Tra­

jectories for Star Exploration Flights,' JBIS. 34, 477-485 (1981). 28. G. Vulpetti, 'Relativistic Astrodynamics: The Problem of Payload

Optimisation in a Two-Star Exploration Flight with an Inter­mediate Powered Swing-by,' JBIS, 37, 515-521 (1984).

29. G. Vulpetti, 'Multiple Propulsion Concept: Theory and Perform­ance,' JBIS, 32, 209-214 (1979).

30. G. Vulpetti, 'The General Theory of the Multiple Propulsion,' unpublished.

31. B. N. Cassenti, 'Design Considerations for Relativistic Anti­matter Rockets,' JBIS, 35, 396-404 (1982).

32. B. N. Cassenti, 'Optimisation of Relativistic Antimatter Rockets,' JBIS. 37, 483-490 (1984).

33. F. D'Antona and I. Mazzitelli, 'Mass-Luminosity Relation and Initial Mass Function of the Faint End of the Main Sequence,' Astronomy and Astrophysics, 127, 149-152 (1983).

34. F. D'Antona and I. Mazzitelli, 'Evolution of Very Low Mass Stars and Brown Dwarfs ... ' Astrophys. J., 296, 502-513 (1985).

35. D. McCarthy Jr., R. Probst and F. Low, 'Infrared Detection of a Close Cool Companion to Van Birsbroeck 8,' Astrophys. J ..

290, L9-Ll3 (1985). 36. 'CAS: Cern Accelerator School, Antiprotons for Colliding Beam

Facilities,' CERN 84-15, December 1984. 37. E. J. N. Wilson (Ed.), 'Design Study of an Antiproton Collector

for the Antiproton Accumulator (ACOL),' CERN 83-10, October 1983.

38. 'Design Study of a Facility for Experiments with Low Energy Antiprotons (LEAR),' CERN/PS/DL 80-7, May 1980.

39. G. Chapline, 'Antimatter Breeders?' JB/S, 35, 423-424 (1982). 40. R. Neumann, H. Poth, A. Winnecken and A. Wolf, 'Laser­

Enhanced Electron-ion Capture and Antihydrogen Formation,' Z. Physics A, 313, 253-262 (1983).

41. R. L. Forward, 'Antiproton Annihilation Propulsion,' AIAA Paper 84-1482.

42. D. G. Crowe, 'Laser Induced Pair Production as a Matter­Antimatter Source,' JBIS, 36, 507-508 (1983).

43. R.R. Zito and D. G. Crowe, 'Confinement of Energetic Antiparti­cles by Electric and Magnetic Fields,' preprint 1984.

44. R.R. Zito, 'The Cryogenic Confinement of Antiprotons for Space Propulsion Systems,' JBIS, 35, 414-421 (1982).

45. R. R. Zito, 'Chain Reactions in a Hydrogen-Antiproton Pile,' JBIS, 36, 308-310 (1983).

46. Torelli, 'A Device for Trapping and Cooling to Low Temperature Antiprotons,' ***

47. N. Beverini, et al., 'A Penning Trap to Store Antiprotons,' Scuola di Erice, Erice, (Trapani, Italy), May 1982.

48. R. W. Cline, 'Magnetic Confinement of Spin-Polarised Atomic Hydrogen,' Phys. Rev. Letters, 45, 2117-2120 (1980).

49. R. Sprik, et al., 'Compression of Spin-polarized Hydrogen to High Density,' Phys. Rev. Letters, 51, 479-482 (1982).

50. W. D. Phillips (Ed.), 'Laser Cooled and Trapped Ions - Work­shop on Spectroscopic Applications of Slow Atomic Beam,' National Bureau of Standard, Gaithersburg, SP-653, 1983.

51. V. S. Letokhov and V. G. Minogin, 'Possibility of Accumulation and Storage of Cold Atoms in Magnetic Traps,' Optics Comm .. 135, 199-202 (1980).

52. W-K Rhim, M. M. Saffren and D. D. Elleman, 'Development of Electrostatic Levitator at JPL,' in Materials Processing in the Reduced Gravity Environment of Space, G. E. Rindone (Ed.), Elsevier, 1982.

53. B. N. Cassenti, 'Antimatter Propulsion for OTV Applications,' Journal of Propulsion and Power, 1, 143-149 (1985).

54. D. L. Morgan, Jr., 'Concepts for the Design of an Antimatter Annihilation Rocket,' JBIS, 35, 405-412 (1982).

55. G. Vulpetti, 'A Concept of Low-Thrust Relativistic-Jet-Speed High-Efficiency Matter-Antimatter Annihilation Propulsfon System,' IAF-83-397.

56. R. L. Forward, B. N. Cassenti and D. Miller, 'Cost Comparison of Chemical and Antihydrogen Propulsion Systems for High Delta-V Missions,' AIAA Paper 85-1455.

57. R. L. Forward, 'Antiproton Annihilation Propulsion,' U.S. Air Force Rocket Propulsion Laboratory, TR-85-034, September 1985.

(This paper was presented at the !AA Interstellar Space Flight Session of the 36th International Astronautical Congress held in Stockholm, October 1985).

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