Rabinovich, M S

Tsytovich, V N

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Particle Accelerators1973, Vol. 5, pp. 99-103© Gordon and Breach, Science Publishers Ltd.Printed in Glasgow, ScotlandPROSPECTS FOR THE DEVELOPMENT OFNEW COLLECTIVE METHODS OF ACCELERATION tM. S. RABINOVICH and V. N. TSYTOVICHLebedev Physical Institute, Moscow, USSRThe future of new collective methods of acceleration is discussed. For beam coherent acceleration the possibilityis emphasized of longitudinal ring stabilization by using the transitional radiation. For impact accelerationa transient compressor is proposed. Acceleration by nonlinear waves and solitonst in relativistic electron beamsis considered in more detail.t Paper presented at the Symposium on Collective Methodsof Acceleration, Dubna, USSR, September 1972.t EDITORS' NOTE. Although a familiar term to plasmaphysicists, the term 'soliton' may not be familiar to all ofour readers. It is an abbreviation for 'solitary-wave pulsespropagating in non-linear dispersive media'; it has come torefer to any propagating pulse-like excitation (in a plasma)which resists dispersion or break-up.1) Traditional methods:electric field E = 10-100 MV/mmagnetic field H = 2-20 kOe2) New methods (collective methods and super-conducting accelerators)E = 100-1000 MV/mH = 20-200 kOeDuring the past few days we have listened toreviews of various acceleration methods underdifferent stages of development, from models anddesigns of particular installations to hypothesesand sketchy ideas."To clarify the situation we propose a classifica-tion. In general, new methods of accelerationinvolve methods of creating superhigh fields;intentionally we do not specify the kind of field,whether it be magnetic or electric. Using methodsof circular acceleration we can always equal theefficiency of one field in terms of the other. In theGaussian system the condition of equivalence canbe written as follows:H= 2rcEorH (kOe) = (E/5) (MV/m)Thus the following classification is obvious(1)3) Future methodsE = 1000-10,000.MV/mH = 20-200 kOe and higherIt should be noted that in all three divisions theaccelerators can have different energies rangingfrom low to superhigh. This is why a classification"according to attainable energy is not appropriate.At present we witness the completion of theevolution of new methods in the 100-1000 MV/mrange (having in mind the relativistic ring acceler-ator) and in the 20-200 kOe range (having in mindsuperconducting accelerators). Perhaps the timehas come to analyze in greater detail futuremethods; these involve superhigh electric fields incollective methods of acceleration and in laserbeams, and also superhigh magnetic fields. Leav-ing aside the discussion of possibilities in themegagauss range of magnetic fields (this problemwould require special consideration) we shall payour attention to future collective methods.Of course, our considerations will be far frombeing as rigorous as is characteristic of traditionalmethods and from what is required for the relativis-tic electron ring method.Although we cannot suggest a fully worked outscheme for future collective methods, we shall tryto make our considerations concrete.Let us assume, as has already been done in thepapers ofYa. B. Feinberg and A. A. Kolomensky,that plasma and stabilized relativistic electron ringsare used as the media for collective acceleration.Actually, it is well known that it is relatively easyto produce fields of 10,000 MV/m and higher inplasmas and also in laser beams. In particular,such fields retard electron beams very effectively.100 M. S. RABINOVICH AND V. N. TSYTOVICHK max = 4n2( VR)2y1.21 1n-:-1 (2)v YIIwhere vR and VC are Budker factors for the ring andfor the beam.of coherence and simultaneous electron and ionacceleration.Actually, if the electron fl?w accelerates the ring,the maximum electric field is determined, not bythe electron flow, but by the number of particles inthe ring, as in the electron ring accelerator, and theelectron beam acts as a power source. With suchan interpretation it is clear that this method issuitable (if it is valid) for the 1-100 GeV range, andapparently it is not suitable for the 1000-GeV range.For this reason primary attention should be givento the effective use of electron beam power.The maximum coefficient for utilization of powerisAlthough the formula is valid only for vR ~ 1,it is evident that, for N e ;5 1014, the power efficiencyis sufficiently high; but this cannot be said aboutthe energy efficiency.In the previous considerations it was assumedthat the problem of bunch stability has beensolved. But it is far from being solved and it isnecessary to consider possible methods of longi-tudinal bunch size stabilization. This has not beendone rigorously as yet.Other mechanisms than Cerenkov radiation canbe used in collective flow acceleration. The use oftransitional radiation in a modulated flow israther an interesting possibility. In contrast toCerenkov emission, transitional radiation givessuccessive longitudinal focusing and defocusingeffects (like strong focusing in ordinary acceler-ators).If the modulation period is chosen to be(R/2)~YII / vC, then the transitional emission exceedsthe Cerenkov emission when vCYIi ~ 1.Another forgotten acceleration process proposedby V. I. Veksler is known as 'impact acceleration'.Veksler has always associated this method withthe attainment of superhigh particle energiesalthough with low beam intensity. In this connec-It is much more difficult, if at all possible, toutilize such fields in plasma, as well as in lasers,for acceleration.But, if it is possible, high pulse powers willinevitably be required. For example, when 1011ions are accelerated in 10 GV1m fields, the ionsabsorb power at a rate of 5 x 1012 watts; conse-quently the total power required is at least one ortwo orders of magnitude higher. Thus the prob-lems of collective acceleration must be solved inparallel with the problem of creating a pulsed powersource, taking into account the efficiency problem.The utilization of all kinds of superhigh frequencypulse power becomes involved with the difficultproblems of supercondu~tivity. Apparently elec-tron and laser beams are good pulsed power sources.Apart from external souces of pulsed power, itis rather attractive to use accumulated beamenergies. This is the case, for instance, in thewell-known method of utilizing the accumulatedtransverse energy of relativistic rings by trans-forming it into longitudinal energy. The problemof pulsed power does not arise here, of course, butthere remains the problem of the duration of theaction. Usually it is not possible to make it long.In summary, these methods are rather convenient,but not for superhigh energies (that is, in the1-GeV range).Let us return to the first problem of the use ofplasma fields. The problem is closely connectedwith the physics of collective processes in plasmaand will be discussed further especially from thispoint of view.To be specific, these problems will be consideredfor the cases of beam and impact collective accelera-tion mechanisms and also relativistic solitons andnonlinear waves.V. I. Veksler assumed that high electric fieldscould be produced by an impact mechanism. Inthis case the forces arise during short time intervalsand only at the position of the accelerated particles;this greatly reduces the possibility of instabilities.Let us first consider a simpler problem-anelectron ring immersed in an electron beam. Asusual we shall consider the behavior of the ringin the system where the beam is at rest and the ringis moving. Coherent Cerenkov acceleration willplay an important role. To determine the para-meters, it is necessary to write down the condition10- 13NR I"V eV Y1. = 2R (3)COLLECTIVE METHODS OF ACCELERATION 101(8)(7)(9)is a rapid one. Then radiation losses and radiationinstability may prevent the functioning of thecoherent impact mechanism of acceleration.But radiatjon effects can be neglected ifM {('}'II H)2H>M L (y II H)3j[20vL In (8Rja)]The figures mentioned above have been chosen soas to satisfy these conditions. However, we canspeak of the impact mechanism as an establishedone only when the collision mechanism has beenstudied in detail and when the actual value of/hasbeen precisely determined. The result seems to bediscouraging at first sight but we should take intoconsideration the following items.In the calculations we used static values of thebunch parameters corresponding to the valuesbefore the collision, assuming that there is littlechange during the collision. At this moment,the arriving heavy bunch can produce an increasingfield in the neighborhood of the light one, and thelatter will be compressed. However, as yet the self-consistent problem of collisions has not even beendefined. It is not necessary to decrease the minorradius of the heavy bunch. Perhaps the heavybunch could be less like a ring and more like theE-Iayer in Christofilos' 'Astron'. Finally, weabandoned Veksler's principles in the collisionmechanism. We required the bunch form to bepreserved during the collision and the deformationto be small. Thus the acceleration of a largenumber of particles was achieved (on paper). Butthe collision mechanism should be thought of as alarge acceleration of a relatively small group ofparticles.The main drawback of the collective methods ofacceleration just described is the necessity for thecreation of charge bunches by some externalforces. Of course, the procedure is reasonable ifthe electric fields used to produce bunches areconsiderably weaker than those in the bunch, or ifmagnetic fields are used for this purpose.This approach has been consistently maintainedin the density wave accelerator, proposed byFeinberg early in 1956. Perhaps the plasmaaccelerator will be the main collectiv'e accelerator inthe future. A great deal of work remains to bedone in this direction; progress during the past(4)This is rather an attractive formula; using it in astraightforward fashion we obtain very high energyvalues. But a number of difficult conditions mustbe fulfilled for an elastic collision, first, the condi-tion for simultaneous motion of ions and electronsand, second, the condition for elastic reflection.The collision distance can be written formally inthe following formtion we should recall Lawrence's well-known butyet unproved prediction made at the first Conferenceon Accelerators in 1951, that with increasingparticle energy the intensity of accelerated beamswill decrease and, at the high energy limit, willtend to zero.Let us consider the impact acceleration methodusing as an example the collision between twoelectron rings. One light ring (L) is at rest andcontains a small number of ions, which should beaccelerated in the collision process.It is known that in the process of direct elasticcollisiond =f~ (5)'}'1Iwhere'}' II C is the factor corresponding to the transferfrom the center-of-mass system to the laboratorysystem, and / is the parameter determined by thecollision dynamics; f actually depends on all beamparameters. If the collision occurs over a distanced, then the effective acceleration field is2m c2 '\J L(", H)3E - __e _ I -t I II (6)eft" - eR f'L m i 2na( H)3V >-- '}'IImeRfM H ~ 2ML '}'II HThese formulae also are attractive, but, if oneinserts realistic figures, their straightforward useleads to values that are too high.If it is assumed that N eL = 5 X 1015 , N eH =3 X 1016, 'Y-tL = 15, '}'-tH = 50, R = 5 cm, aiR =10- 3 , '}'II =10, then the relations above lead to theconclusion that the collision length should be 50 mand the energy achieved should be 200 GeV.Even if acceleration with f > 105 can possibly beattained, it cannot be assumed that the collision102 M. S. RABINOVICH AND V. N. TSYTOVICHHere n 1 represents beam density and no is plasmadensity.The conditions for optimal excitation areachieved whensixteen years has been very slow, but alwayspositive.The modern state of the problem has beensufficiently discussed in Feinberg's paper. In thispaper we shall concentrate on future possibilitiesof this method using relativistic solitons and non-linear waves of large amplitude.The creation of bunches in a plasma is connectedwith the development of several types of instabi-lities. Stimulated emission is one such instability.It is this emission that amplifies the initially weakeffects. The beam particles in the beam-plasmainteraction can generate oscillations and wavesand, since the presence of the beam is equivalentto an inverse population of energy levels, a masereffect is created. As was mentioned, we areinterested in density waves. Such waves can beexcited by the bunch if slow waves can exist in thesystem with phase velocities equal to or close to thebunch velocity. But the usual case is one in whichthe density oscillations are excited with a widespectrum of wavelengths. Then superpo~ition ofthese waves creates a pattern of rapidly changingoscillating fields which vary randomly from pointto point. Enormous electric fields exist in suchoscillations but it is impossible to use them foracceleration.Ya. B. Feinberg has proposed an effective methodof synchronization of oscillations by forcedsuperposition of oscillations having frequenciescorresponding to the maximum growth rate. Inthis case the induced emission is effectively stimu-lated.We shall consider the conditions under which the,bunch excites a single wave in the plasma. Externalweak fields also can be used, if necessary, tosuppress the effects of spectrum broadening.A necessary, but not sU,fficient, condition for theexcitation of a single wave is a small energy spreadin the beam:(12)(14)(13)2e1Jmax(l---- 2mevlj>where w;e = 4nno e2 jme and no is the plasmadensity. In our system the distance betweenbunches is xojyo and the electric field isand the density of excited energy is approximatelyn1 me e2y; for a current density of 5 x 105 A/cm2and a '}' of 100, the field strength produced is of theorder of tens of gigavoltsjmeter. Apparentlysimilar fields can be produced when the beaminteracts with a retarding wave structure (of thetype of corrugated or spiral waveguide).The amplitude of a nonlinear wave can bedescribed conveniently by the relative amplitudeof the potential difference in the system where thewave profile is stationary.where vlj> is the phase velocity of the wave. Themaximum value of (l for which unstable oscillationand multi-velocity flow do not set in is 4'}'</J2. Thisresult is rather important; we note that in thenonrelativistic case (lmax ~ 1.A nonlinear wave can be either a soliton or aperiodic configuration. Solitons are not producedin a cold plasma in the absence of magnetic field,or in propagation of waves along a magnetic field.For (l ~ 1, the wave splits into a number of quasi-independent bunches. As (l increases, the spacebetween the bunches in the system with the frontat rest also increases.The full average wave energy is W = (E2 j8n)(l +4).In this formula the fact has been taken intoaccount that the kinetic energy density of particlestaking part in the wave build-up is higher by afactor of four than the average field energy.Numerical calculations indicate that the beam givestwo thirds of its energy to the wave. This meansthat the amplitude(l = (3/5)y2 n1 /nO (15)cannot reach its maximum value of 4}'</J2 forntjno ~ 1. It is true that this estimate must beused with care since it has been derived using onlyqualitative energy conservation arguments.(11)(10)COLLECTIVE METHODS OF ACCELERATION 103Evidently the nonlinear wave is rather strong.However, before it is used for acceleration anumber of problems should be completely solved.We have mentioned the fact that it seems quitepossible to satisfy the condition for excitation of asingle wave. However there is no straightforwardevidence supporting this conclusion. The stabilityof such waves has not been studied completely.But it has been shown that, as y is increased, thetime interval during which local perturbations ofthe wave appear also increases. Also, if multi-velocity flows do occur, the difference in y-factorsis rather small. This leads to insignificant re-distribution ofparticle velocities and to insignificantchanges in the structure and shape of the relativisticwave. Parametric instabilities also cannot affectthe shape of the wave, and electron-ion instabilitiesdo not develop ifn1/nO < (l/y3)(rnJrne)2/3 (16)The possibility of using nonlinear waves dependsalso on the ability to control their velocities. It ispossible, in principle, to regulate these velocitiesby profiling plasma density and by use of varyingmagnetic fields. It is also necessary to evolvemethods of ion injection into a nonlinear wave.Of course the situation would be simplified if itwere possible to use stochastic acceleration, butthis is effective only for multicharged ions (the rateof acceleration is proportional to Z2).Thus, if we are to use nonlinear waves in a plasmaa great deal of work must be done. Nevertheless,it may be that this will be the trend of the futureand, in the future, plasma accelerators will competewith laser accelerators and with megagaussmagnetic field accelerators.Our main conclusions are1) The development of new collective methodsrequires further intensive work.2) The time has come to pay more attention tothe study of nonlinear waves in plasma,using high energy relativistic electron beams.Received 9 May 1973

Prospects For The Development Of New Collective Methods Of acceleration

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