Electron cooling and new possibilities in elementary particlephysics

G. I. Budker1» and A. N. Skrinskii

Nuclear Physics Institute, Siberian Division, USSR Academy of Sciences, NovosibirskUsp. Fiz. Nauk 124, 561-595 (April 1978)

This review is devoted to a new method in experimental physics—electron cooling, which opens the

possibility of storing intense and highly monochromatic beams of heavy particles and carrying out a wide

range of experiments with high luminosity and resolution. The method is based on the cooling of beams by

an accompanying electron flux as the result of Coulomb collisions of the particles. In the first part of the

review the theoretical basis of the method is briefly considered. The apparatus ΝΛΡ-Μ is described with

its electron cooling, and the results of successful experiments on cooling a proton beam are presented. In

the second part the new possibilities opened by the use of electron cooling are discussed: storage of

intense beams of antiprotons and achievement of proton-antiproton colliding beams, performance of

experiments at the ultimate in low energies (with participation of antiparticles), storage of polarized

antiprotons and other particles, production of antiatoms, storage of antideuterons, and experiments with

ion beams.

PACS numbers: 29.25.Fb, 29.2O.Dh

CONTENTSIntroduction 277

1. General Description of Electron Cooling 279

2. Kinetics of Electron Cooling (Single Traversal by the Electron Beam) 280

3. Experimental Study of Electron Cooling Process 283

4. Storage of Intense Antiproton Beams 287

5. New Possibilities in Elementary Particle Physics 288

a. Experiments with super-thin internal targets 288

b. Acceleration of stored antiprotons 289

c. Continuously cooled colliding beams 289

d. The ultimate in low energies 290

e. Antiatoms 291

f. Polarization experiments. 291

g. Antideuterons 291

h. Experiments with ion beams 292

i. Colliding proton-antiproton beams at the ultimate in high energies 293

Conclusion 294

References 295

INTRODUCTION make it so complex that the effective phase density de-creases. However, to increase the density it is essen-

In carrying out almost any experiments with use of tial to introduce forces of a dissipative nature,

beams of charged particles, it is of fundamental im- L o g i c a i l y the simplest procedure is to use for thisportance to be able to compress the beams, to decrease e d i s s i t i v e f o r c e s a n a l o g o u s t 0 o r d i n a r y f r i c .their size and the momentum spread of the particles (in U o n a n d d i r e c t e d t ^ ^ v e Q f e a c h

magnitude and direction), in other words, to be able to U c l e H ^ e x t e r n a l e g o u r c e i n ^ c a s e a c _cool" the flux of fast charged particles, lowering their , ,. . r .. , , . >

6 F ' & celerating system of the accelerator or storage ring)effective temperature in the accompanying system. ,, . ,, . . . r ,. , .,

f v~ J & " ' adds energy to all particles of the beam, exactly com-pensating the energy loss of the equilibrium particle,

However, this cannot be achieved by use of any speci- ^ d e v i a t i o n s o f t h e p a r t i c l e s f r o m t h e equilibrium mo-fied external electromagnetic fields, i.e., fields which f Q p & c o r r e c t c h o i c e Q f ^ s t _ r i structure,do not depend on the motion of the individual particles of w m d e c r e a s e w i t h t h e o f u L t h e b e t a .the beam. The principle which applies in this c a s e - a t r Q n ^ s y n c h r o t r o n o s c i l l a t i o n s w i l l b e d a m p e d .special case of Liouville s theorem—is that the densityof the particles of a beam in six-dimensional phase The characteristic damping time in this case is thespace (the space of generalized coordinates and con- ratio of the particle energy to the rate of energy lossjugate momenta) is a quantity which is constant and and is equal to the time of complete stopping of a par-determined by the initial conditions. By means of focus- t ide for an energy loss which does not depend on theing and acceleration in any combination one can only particle energy. Damping of the deviations of the par-change the shape of the phase space occupied by the t ide energy from the equilibrium value is due to the de-beam particles but cannot change its magnitude or in- pendence of the rate of energy loss on the particle en-crease the phase density. Aberrations of any kind can, ergy. In the simplest case these deviations are dampedof course, greatly distort the shape of the volume and if the rate of energy loss increases with increasing par-

ticle energy; in the opposite case the deviations fromthe equilibrium energy will increase with time. In more

u Dr. Budker died July 4, 1977. complex cases, for example, in the presence of acceler-277 Sov. Phys. Usp. 21(4), April 1978 0038-5670/78/040277-20$01.10 © 1979 American Institute of Physics 277

ator-related coupling between the degrees of freedom ofa particle, the damping decrements in individual de-grees of freedom can change. However, the sum of thedamping decrements of the phase volumes in all threeindependent degrees of freedom of the particles, i.e.,the increment of increase of the phase density, does notdepend here on the focusing structure of the storage ringand is determined by the sum of the ratio of twice therate of energy loss to the particle energy and the par-tial derivative of this rate with respect to energy.

The beam will be compressed to dimensions deter-mined by the equality of the frictional power (rate of en-ergy loss) and the power of the diffusion processes.

The best known and most effectively used example ofthis type is the use of radiation damping (the forces ofthe reaction of radiation) for cooling electron and posi-tron beams, which is of crucial importance for storageof large positron currents and for achievement of exper-iments with colliding electron-electron beams and, inparticular, electron-positron beams. Such experiments,begun in 1967 with experiments at Novosibirsk, now pro-vide a significant part of all fundamental information onelementary-particle physics.

In radiation cooling the diffusion effectwhichis in prin-ciple present andwhich at high energies is dominant isthe quantization of the energy radiated by charged parti-cles, which leads to an increase of the energy spreadand a buildup of the transverse oscillations. Radiativefriction turns out to be important only for the lightestcharged particles—electrons and positrons—and only ata sufficiently high energy. For all other particles it isnecessary to seek other methods of cooling.

For this purpose it is possible to use energy loss byionization, placing in the storage ring or accelerator atarget of the required thickness. For nonrelativistic en-ergies the friction thus introduced turns out to be sub-

, stantially reduced as the result of the large negative de-rivative of the rate of energy loss with respect to ener-gy. And for all energies an unpleasant aspect of thismethod is the rapid diffusion due to multiple scatteringof the particles by the nuclei and electrons of the target.The steady-state phase volume of the beam cannot bemade particularly small even when the target is installedat an azimuth with a beam size specially reduced as theresult of choice of the focusing structure of the storagering (at a sharp minimum of the β-functions) and withuse of the lightest possible materials.

For protons and antiprotons at high energies the situa-tion is considerably less favorable because of the in-crease in the relative role of nuclear interactions ofthese particles, as a result of which the lifetime be-comes less than the cooling time.

The most reasonable field of application of ionizationcooling is the cooling of high-energy muons, whichhave no nuclear interaction. Cooled beams of muons (incyclic installations) can be used, for example, to gen-erate very narrowly directed and intense fluxes of neu-trinos of all four types, either allowing the muons to de-cay directly at the cooling energy, or accelerating themuons in linear accelerators or short-pulse cyclic ac-

celerators, thereby increasing the neutrino energy. Ofparticular interest is the construction of apparatus withcolliding muon beams at ultrahigh energies, utilizing in-tense cooled muon beams of the necessary energy, guidemagnets with very high fields (to increase the number ofcollisions during the muon lifetime), and special com-pression of the beams at the point of collision.

For protons, antiprotons, and ions a qualitatively newmethod of cooling beams of charged particles has turnedout to be very effective, a method which does not involveenergy loss of the equilibrium (central) particles of thebeam. This method—electron cooling—was proposed byone of the authors at the beginning of the 1960s and waspublished in 1966.1 At the present time at our Institutein Novosibirsk the method has been studied in detail the-oretically2"7 and experimentally.8"29 The present re-view is devoted to a discussion of the physical and tech-nical problems of electron cooling and of a wide rangeof applications of the technique which are apparent atthis time. The review is based mainly on the work ofG. I. Budker, Ya. S. Derbenev, N. S. Dikanskii, I. N.Meshkov, V. V. Parkhomchuk, D. V. Pestrikov, R. A.Salimov, A. N. Skrinskii, and B. N. Sukhina.

In its simplest form the idea of the method is as fol-lows. In one of the straight sections of a storage ringin which a beam of heavy particles, for example, pro-tons, is circulating, an intense beam of electrons withthe same average velocity and a small momentumspread is passed parallel to the proton beam. Then at acommon region of the trajectory in the rest system ofthe beams the "hot" proton gas is within the "cold" elec-tron gas and is cooled as the result of Coulomb colli-sions. The cooling time corresponds to the relaxationtime of the proton-gas temperature (taking into accountthe relativistic time dilation and the duty cycle of eachproton in the electron beam). As a result the phasespace of the proton beam decreases in all degrees offreedom and the beam is compressed.

This compression continues in principle until the pro-ton temperature in the center-of-mass system becomesequal to the electron temperature. Hence it follows thatthe steady-state angular spread θρ in the proton beam isless than the electron angular spread by a factor

Since the value of <j, can be made of the order of 10~3,the steady-state angular spread for protons or antipro-tons can be reduced to 10~5.

A completely different method which also may turn outto be applicable to compression of beams of heavy par-ticles is the method of stochastic cooling.30"40 The ideais that a very fast negative-feedback system is intro-duced in the storage ring, which quenches the local(azimuthal) fluctuations in the location of the center ofgravity of the beam; the remaining degrees of freedomof the beam, which as a rule consists of a very largenumber of particles (107-1014) must be cooled as the re-sult of transfer of the momentum spread of the particlesinto oscillations of the center of gravity of the beam re-sulting from the spread in energy and, correspondingly

278 Sov. Phys. Usp. 21(4), April 1978 G. I. Budker and A. N. Skrinskii 278

in frequency of revolution. The efficiency of cooling fallsoff with increase of the number of particles, but at thesame time it falls off comparatively weakly with increaseof the energy and with increase of the phase space ofthe beam. The limit for cooling depends on the level towhich it is possible to reduce the noise in the negative-feedback system; obtaining very low noise in such awideband electronic system with high gain is not a sim-ple problem. At CERN, encouraging initial experimentalresults have been obtained in thelSRproton storage ringand at the present time detailed experiments are plan-ned. If they are successful this method will become animportant supplement to the electron-cooling method.

1. GENERAL DESCRIPTION OF ELECTRON COOLING

The characteristic features of the electron-coolingprocess and the problems which arise in putting it intopractice depend strongly on the energy region at whichthe cooling is carried out.

a) At comparatively low energies corresponding to elec-tron energiesup to 2-3 MeV (proton or antiproton energyup to 4-6 GeV), the most natural arrangement is use of di-rect electrostatic acceleration of the electrons to thenecessary energy and with subsequent inflection into thecooling region and collection on a collector after ex-traction. In this case, while at very low energies (elec-tron energies up to several keV) the problem of the pow-er drawn from the high-voltage source and dissipated inthe collector is practically nonexistent, on the otherhand for electron energies of hundreds of keV and abovethis problem becomes one of the principal technicalproblems. A natural solution for this energy region isthe use of energy recovery, i.e., slowing the electronsdown to the lowest possible energy before they hit thecollector, which is connected to the accelerating voltagesource Uo through a rectifier with a small positive biasvoltage Uc. The voltage Uc must be sufficient for col-lection of the entire cooling electron current Je on thecollector (sufficient to overcome space-charge limita-tion). The product VJe in practice is what determinesthe power drawn from the supply and dissipated in thecollector. The voltage Uc can be reduced to a level ofthe order of a kilovolt and correspondingly the ratio ofthe power dissipation to the reactive power U,yJe can bereduced to a level of 1% or even lower.

The current requirement from the main accelerating-voltage source is determined by the loss of electrons dueto scattering in the residual gas, by the ionization in theaccelerating and decelerating sections (and without spe-cial measures being taken also in the cooling section),by the defects in the electron optics, and by the loss atthe collector. This requirement can be reduced to alevel of 10"4. Such a low load on the main power sourceis very convenient, since the requirements on voltagestability and absence of fluctuations for the source areextremely high.

In cooling a bunched beam of heavy particles, in orderto reduce the average electron current it is possible toswitch off the electron gun during the entire time whenthere are no particles being cooled in the cooling section,

with a corresponding advantage in average electron cur-rent. It is only necessary to ensure that the modulationof the electron current does not lead to modulation of theelectron energy and an increase of the electron tempera-ture.

b) An important problem is to assure transport of theintense electron beam over large distances (long coolingregions) while retaining a low effective electron tem-perature. Compensation of the transverse repulsion ofthe electrons requires introduction of focusing which isadequately distributed and of short focal length. In prin-ciple it is possible to introduce external fields of variousconfigurations. However, any axial focusing can pre-vent the appearance of additional transverse velocitiesonly for a given value of electron current; on change ofthe current it is necessary to readjust the focusing.Moreover, external axial focusing in a straight coolingsection cannot be uniform over the length—the use ofquadrupole lenses is unavoidable. The alternating signof the focusing obtained leads to appearance of addition-al angles in the electron beam. But the use of ions ac-cumulated in the beam for automatic space-charge com-pensation of the electron beam can lead to appearanceof various types of plasma instabilities.

It is much more reasonable to use a longitudinal mag-netic field, uniform except for the places of inflectionand extraction, accompanying the electron beam fromthe cathode to its exit from the cooling region; the ac-tion of the longitudinal field on the protons must be takeninto account, of course, in the focusing structure andcorrections of the storage ring. Here the transverseelectron velocities arising as the result of the action ofspace charge of the electron beam are smaller, thelarger is the longitudinal magnetic field, and it is com-paratively easy to make them less than the temperaturevelocities. Here the longitudinal field Hn must satisfythe condition

where e is the electronic charge, ne is the electron-beam density, r 0 is the radius of its cross section, βequals the ratio of the particle velocity to the velocity oflight, andy = (l-/S

2)-V2.

If the accompanying magnetic field is sufficientlylarge, the transverse velocities of the electrons aredetermined mainly by the cathode temperature and theimperfections in the beam optics; we note that the trans-verse velocities in the moving system are preserved inelectrostatic acceleration.

In regard to the spread of longitudinal velocities of theelectrons in the moving system, the contribution of theinitial electron temperature (of the order of the cathodetemperature Tc) drops sharply on acceleration by a po-tential, since the conserved quantity is the energyspread23 :

(1.1)"- kin

The transverse velocities of the electrons make a con-tribution of the same order to their longitudinal temper-

279 Sov. Phys. Usp. 21(4), April 1978 G. I. Budkerand A. N. Skrinskii 279

ature. If the transverse temperature turns out to be forany reason higher than the cathode temperature, its con-tribution to the longitudinal temperature increases cor-respondingly. For not too low energies, other sourcesof longitudinal velocity spread become dominant: fluctu-ations of the accelerating voltage, coherent instabilitiesin the intense electron beam, and for very long coolingsections—collisions of the electrons with each other withtransfer of a part of the transverse momenta to longitu-dinal momenta (the manifestation of a tendency to equal-ization of the longitudinal and transverse temperatures).

A separate question is the appearance in the case oflarge electron currents of a quite substantial potentialdifference inside the beam and accordingly a dependenceof the electron energy on the distance from the center ofthe beam. This circumstance affects the cooling effi-ciency and may require, for example, compensation ofthe electron charge by light positive ions.

c) For proton energies of the order 4-6 GeV andabove (electron energy 2-3 MeV and above) the use ofthe arrangement described above to produce the electronbeam already becomes unreasonable and it is necessaryto go over to a closed orbit in which an electron beamwith the necessary value of instantaneous current anddensity is injected from an external source. The mag-netic-field configuration must provide the possibility ofcyclic motion of the electrons and sufficiently strongtransverse focusing. At low energies it is perhaps rea-sonable to use again for focusing an accompanying longi-tudinal magnetic field, making it closed and toroidal. Anintense cyclic beam will rather rapidly be heated, pri-marily as the result of coherent instabilities. To avoidan excessive increase of temperature at electron ener-gies of about 10 MeV and below, the only available meth-od is to replace the beam by a new batch of cold elec-trons. Here the average power consumed by the systemwill be reduced in proportion to the ratio of the electronrevolution time in the toroid to the heating time of theelectron beam.

At still higher energies it becomes possible to use ra-diative cooling of the electrons. It is possible to choosethe electron-storage-ring structure such that at least the"single-particle" electron temperature will be sufficient-ly low.

If the proton beam being cooled has been bunched intoshort bunches, then of course it will be reasonable touse electron bunches of the same length, with the elec-tron bunching coefficient reducing the average circulatingelectron current for a constant cooling effect.

With a circulating electron beam the ratios between thefrequencies of orbital motion of the protons and of thecooling electrons apparently become important and itmay be possible to achieve resonance enhancement ofthe cooling.

Another method of introducing average friction at highenergies is the periodic brief lowering of the energy ofthe particles being cooled and turning on of electroncooling at a comparatively low energy. The phase vol-ume of the beam is preserved on reduction of the ener-

gy, and its emittance and size are increased; neverthe-less the cooling time (for a fixed cooling current or cur-rent density) drops rapidly and the frictional force canbe made much more effective.

2. KINETICS OF ELECTRON COOLING (THE CASE OF

SINGLE TRAVERSAL BY THE ELECTRON BEAM)

Let us consider in more detail the simplest case inwhich each electron traverses the cooling region onlyonce; this case is at the present time, apparently, alsothe most important—just this arrangement is proposedfor use in storage of antiprotons and other first-echelonexperiments. In addition, this case has been theoretical-ly investigated the most completely and has beenachieved and studied experimentally.

a) To start with we consider the nonrelativistic mo-tion of a proton in a stationary electron gas with a giventemperature Te (generally speaking, different for thelongitudinal and transverse degrees of freedom) and den-sity n'e (which is equal to njy, where ne is the density ofthe electron beam in the laboratory system).

The effect of collisions with the electrons on the mo-tion of the protons can be approximately broken down in-to two parts. One part gives the frictional force, andthe second part leads to diffusion.

We shall estimate the magnitude of the frictionalforce, neglecting the influence of the accompanying long-itudinal magnetic field, the interaction of the electronswith each other, and the finiteness of the time of tra-versal of the interaction region by the proton. In addi-tion we shall assume at first that all electrons are atrest. The frictional force is equal to the magnitude ofthe proton energy loss per unit length. Transfer of pro-ton energy to electrons in our simple case is due totheir acceleration perpendicular to the direction of mo-tion of the proton. In motion of protons in matter thisslowing down is referred to as ionization loss. Using theknown formula for ionization loss, we find that on a pro-ton moving in the moving system with a velocity vp

through an electron gas of density n'e there is acting africtional force directed opposite to v,, and equal in mag-nitude to

|F, r |= ine>"'Lc . (2 l)

here Lc^ln{e^iix/emin) is the so-called Coulomb logarithm,which appears in integration over the impact parametersof the proton collisions with electrons. Here 6max=2w/-Mis the maximum possible deflection angle of a proton inone collision and θτΛη = β2/Μν2ρΒΛΧ corresponds to the im-pact parameter pm a x beyond which the Coulomb nature ofthe proton-electron interaction is destroyed. The maxi-mal impact parameter can be determined by the trans-verse size of the electron beam, Debye screening, andso forth. However, in all practical cases Lc varies onlyfrom 5 to 20.

If we neglect the dependence of Lc on the proton vel-ocity, the frictional force as a function of the relativevelocity will have the form of Coulomb's law in velocity

space. The case considered here of stationary elec-trons corresponds to the case of a point charge at theorigin of coordinates. If the electrons are distributed in

280 Sov. Phys. Usp. 21(4), April 1978 G. I. Budker and A. N. Skrinskn 280

velocity space with a density f[ve) (with a normalizationJA^e, r)d3ve=n'e(r)), the total frictional force can be rep-resented in the form

(2.2)ρ, /γ r) ilxe"Lc f / ( Τ ί - Γ ) Ύ"~Ύ'«•frOp.n- m j 7Vp_T p)> | v p _ v e |

where it has been taken into account that the electrondensity and the velocity distribution function depend onthe coordinates r.

It can immediately be seen by means of this electro-static analog, for example, that if in the electron beamthe electrons have in the moving system a Maxwelliandistribution in velocities with a velocity temperature ujidentical in all directions, then the frictional force isproportional to the proton velocity vp for v, < vl and fallsoff in proportion to Vp2 for νρ>νζ(Fig. 1).

b) Let us now find the damping decrement of the pro-ton oscillations due to this frictional force. The de-crement of one-dimensional oscillations is equal to theratio of the dissipative energy-loss power averaged overthe period of these oscillations to the energy of the oscil-lations. It is simplest to find δ,—the decrement of oscil-lations perpendicular to the plane of the proton orbit inthe storage ring or, in accelerator terminology, axialbetatron ζ oscillations.

For the region of small proton velocities vp<vl (in themoving system), in which the frictional force is propor-tional to vp, the power of the frictional force averagedover the period is

where v0 is the amplitude of the velocity of ζ oscilla-tions. The energy of these oscillations is Mr%/2. If wetake into account in addition that the protons spend onlypart of their time inside the electron flux (the fractionof the orbit occupied by the cooling section we shall des-ignate by η) and that the time of cooling in the laboratorysystem is greater by a factor γ than in the moving sys-tem, we obtain

(2.3)

The decrement can be expressed in terms of the anglesθβ in the electron flux (6»e=y"1vJ/j3c):

e^Oiy-pcLc/Mrr^-ae;' for e,<cee. (2.4)

Calculation of 5, for large one-dimensional oscilla-tions of protons for which the amplitude of the oscilla-tions of velocity is v0» υξ (correspondingly, θρ» ee)gives a similar formula but with θρ replacing 6e:

-3ei' for θρ > θ,. (2.5)

Calculation of the decrements in the remaining de-grees of freedom (in the case vt0 « υζ) can be carried

FIG. 1 .

out similarly. Here it is only necessary to take into ac-count the possible dependence of the electron distribu-tion function on the transverse coordinates. For ex-ample, if the average velocity of the electrons dependson the radial coordinate, the decrement of the radialbetatron oscillations varies in comparison with the de-crement of ζ oscillations. This occurs as the result ofthe fact that the proton in its radial betatron oscillationsenters regions where the electron velocity differs fromthe equilibrium value and in this case the proton energywill also undergo oscillations. Correspondingly the ra-dial position of the equilibrium orbit of the proton turnsout to be modulated in a resonance manner with the ra-dial betatron-oscillation frequency, and an additionalpower appears which increases or decreases the beta-tron-oscillation amplitude. The damping decrement ofthe energy oscillations (or deviations) of the proton alsovaries in this case. However, it can be shown that thesum of the decrements over all three degrees of free-dom, i.e., the damping decrement of the complete six-dimensional phase space occupied by the protons, isdetermined only by the electron density along the equi-librium phase trajectory of the protons and does not de-pend on the variability of the distribution function overthe transverse coordinates or on possible acceleratorcouplings between the different forms of proton oscilla-tion. In the simple case vp<vlthe sum of the decre-ments is equal to

^ Γ for „, (2.6)

c) For distributions of electrons in velocity, relativeto the equilibrium orbit of the protons, which differstrongly from a symmetric Maxwellian distribution, theaction on the protons may turn out to be qualitativelyquite different. This can be seen particularly clearly inthe case of the so-called monochromatic instability.

Let us consider the case in which electrons with anextremely small velocity spread in the cooling sectionare moving at some average angle directed, say, alongthe vertical to the equilibrium proton trajectory. Letthis angle be such that the general transverse velocityve is much greater than the spread in the electron vel-ocities Δνβ, but not greater than the permissible trans-verse velocities of the protons (i.e., the correspondingoscillation amplitudes of the protons are less than theworking aperture of the accelerator). In this case, ifthe protons execute small vertical oscillations the workdone by the frictional force will be positive in the partof the oscillation period in which the protons are movingin the direction of the general electron velocity and neg-ative for motion in the opposite direction. Here positivework will be performed for a relative proton-electronvelocity smaller than Ve, and negative work for a valuelarger than ve, and therefore the total work over a peri-od will be positive for \ve -vp\»&ve the frictional forcefalls off with increase of the relative velocity). Conse-quently the amplitude of the vertical oscillations of theprotons will increase—these oscillations will becomeunstable under the influence of the electron beam. Theoscillations will increase until the oscillation amplitudeof the proton's transverse velocity is equal to ve.

281 Sov. Phys. Usp. 21(4), April 1978 G. I. Budker and A. N. SkrinskiT 281

We note that this phenomenon, which on the face of itis only harmful, can be used to accelerate the dampingof large proton oscillation amplitudes (at least if theseoscillations are strictly one-dimensional). The fact isthat the rate of damping of proton oscillations to the newequilibrium motion described above can be much greaterthan the rate of damping of protons with this amplitudefor an electron beam moving parallel to the equilibriumorbit of the protons. Then, by decreasing the generalangle of the electrons as rapidly as possible in orderthat only protons will have time to be damped to the(varying) equilibrium amplitude, we can much morerapidly damp the initially large oscillations of the pro-tons. This procedure may turn out to be useful, for ex-ample, in the storage of antiprotons.

d) In discussing the friction experienced by protonsmoving in the accompanying, electron flux, we limitedourselves to the simplest situations. There may be asubstantial influence, in particular, of the fact that theinteraction of the protons with the electrons is occurr-ing in a longitudinal magnetic field. For real situationsthe size of the Larmor circle corresponding to thermaltransverse velocities of the electrons turns out to be ofthe order of tens of microns or even smaller, which isseveral orders of magnitude less than the transversesize of the electron beams. Therefore there is a sub-stantial region of impact parameters (correspondingCoulomb logarithm of about 3-5) for which the electronsturn out to be "magnetized" and cannot shift perpendicu-lar to the magnetic field direction. Accordingly, part ofthe transverse frictional force due to these collisionsdoes not fall off linearly with decrease of the proton vel-ocity when the latter becomes less than the spread in thetransverse electron velocities, but continues to rise rap-idly until the proton velocity is equal to the character-istic longitudinal electron velocities. On acceleration ofthe electrons by a potential the spread in their longitu-dinal velocities drops rapidly (see Eq. (1.1)) and there-fore the effective transverse frictional force may turnout to be much greater than that calculated from the in-itial formulas (2.1) and (2.2). The average longitudinalforce also increases, although when a proton movesstrictly along a line of force of the magnetic field thecontribution of this region of impact parameters to thelongitudinal frictional force decreases rapidly, since inthis case the magnetization of the electrons preventstransfer of energy from the proton to the electrons.

In a detailed calculation of the frictional force it isnecessary to take into account also the finiteness of theinteraction time, which is limited to the time of flight ofthe proton over the cooling region, and the influence ofthe interaction between electrons, which leads to effectssuch as non-steady-state Debye screening, and manyother factors.

e) In addition to friction, the protons moving in theelectron flux experience random thrusts which lead to adiffusion growth of the squared deviation of the protonmomentum (Δρ)2 from the initial value ρ = Mvp. In cal-culation of the average rate of increase we can neglectthe variation of the electron motion and consider thisdiffusion process as the multiple scattering of protons

moving with velocity vp relative to randomly locatedCoulomb centers with a density n'e. Here, if the elec-trons are at rest, we have

d (Ap)' _ 8IK'JI;L C

dt '~ vp

The total diffusion action of the electron beam is foundby averaging over the distribution function f(ve):

Going over to the increase of the proton kinetic energyΕ =ρ2/2Μ, we obtain

dE

dt A?• \-1&L. (2.7)

This diffusion process places a limit on the minimumvelocity spread to which the proton beam is cooled.This limit corresponds to equality in absolute value ofthe average friction power Vfrvp and the average rate ofthe .diffusion increase of the energy (2,3). For the regionvp«Ve, and it is just this case that in simple situationscorresponds to the limiting cooling, we obtain

u \i>,/~ » (•£)» VT/·

from which it follows that

("i-U-•/¥»!· ( 2 · 8 )

That is, in this simplest case the equilibrium state cor-responds to thermodynamic equilibrium, in which thetemperatures or average kinetic energies of the protonsand electrons are equal.

Of course, multiple Coulomb scattering by the elec-trons of the cooling beam is not the only diffusion pro-cess which prevents cooling of the proton beam. Astrong influence can be exerted by multiple scattering inthe residual gas, irregular fluctuations of the electron-beam density, noise in the high-frequency system (forthe case of a bunched proton beam), pulsations of themagnetic field, and other diffusion-type perturba-tions.2·3

f) A completely different effect of the interaction withthe cooling electron beam, which is important only forpositive particles being cooled—protons and ions—isthe capture of electrons into bound states (recombina-tion)—a process leading to formation of fast neutralatoms of hydrogen or of ions with a charge reduced byunity.

The principal form of recombination for the low elec-tron flux densities utilized at present is radiative re-combination, with emission of a photon of the corre-sponding energy. Here mainly the lower levels of thehydrogen atom or ion are populated; this is true atleast if we neglect the influence of the accompanyingmagnetic field. The fast neutral hydrogen atoms formedafter recombination, retaining the angular spread whichexists in the proton beam, leave the storage ring. Theprobability of their breaking up in the magnetic fieldwhich guides the protons will be low in this case if theproton energy is not too high.

The lifetime of a proton against radiative recombina-tion at relative velocities small compared to atomic

282 Sov. Phys. Usp. 21(4), April 1978 G. I. Budker and A. N. Skrinskil 282

velocities in the lower levels (and just this relation is chaacteristic of the cooled beam) is proportional to theelectron velocity determined by temperature νζ andfalls off rapidly with increase of the ionic charge:

r\ne In ((2.9)

The lifetime against recombination Trec for the protonbeam is usually several orders of magnitude greaterthan the damping time of small oscillations, but in thecase of heavy ions the excess becomes insignificant—the cooling time is proportional to the mass of the ion.Therefore we can succeed in cooling a beam of heavyions but it is impossible to maintain it in a cold statefor an extended period. Use of a special procedure—proton cooling—completely removes this difficulty (seeabove).

At very high electron and proton densities the mainrole in recombination may be played by ternary colli-sions. Mainly upper levels will be populated in thiscase. The further fate of such neutrals will be morecomplicated and depends strongly on the specific condi-tions.

In addition to recombination, which is the most funda-mental limitation on the lifetime of positive ions in elec-tron cooling, particles, whatever their charge may be,are knocked out of the beam as the result of interactionwith the residual-gas atoms.

Without cooling, the main process determining lossesis multiple Coulomb scattering by the nuclei of the re-sidual-gas atoms, which leads to a gradual increase inthe betatron-oscillation amplitudes to the maximum per-missible value. With effective cooling this diffusion pro-cess is suppressed, and single Coulomb scattering bythe nuclei remains (the lifetime against this process isseveral times greater than in the previous case), aswell as the nuclear interaction of the beam particleswith the nuclei.

g) New effects arise on cooling of intense beams ofheavy particles. Here even the well known high-currenteffects must be analyzed anew in the presence of elec-tron cooling.

Thus, with unusually small currents the Coulomb re-pulsion can be felt between the particles of the beam—the equilibrium size and energy spread of the cooledbeam can be extremely small. Weakening of the focusingas the result of transverse repulsion can shift the beta-tron-oscillation frequency to dangerous "machine" reso-nances, and further compression as the result of coolingturns out to be impossible. Compensation of this shiftof betatron frequency by retuning the focusing structureof the storage ring turns out, as is usually the case in aspace-charge problem, to be of little effect, as a resultof the strong nonuniformity of the shift for particles withdifferent betatron-oscillation amplitudes.

Longitudinal repulsion of the beam particles is par-ticularly dangerous if the frequency of revolution -in thestorage ring (with a constant magnetic field) falls offwith increasing energy (the negative-mass effect). Thisoccurs when, in accelerator terminology, the equili-

brium energy of the storage ring becomes greater thanthe critical energy. Then a spontaneous breakup of thebeam into bunches occurs; the threshold for this in-stability depends on the spread in the frequencies ofrevolution and in a cooled beam can be very low.

This instability, and also the transverse and longi-tudinal instabilities due to electromagnetic interactionof the beam with the surrounding structures, for suf-ficiently low proton currents can be effectively sup-pressed by the existence of friction—the electron cool-ing. For instability of the beam it is required that thedecrements of small oscillations be greater than the in-crements of all instabilities.

However, the presence of an intense electron beamstrongly interacting with a circulating beam leads toqualitatively new effects, and the problem of coherentstability requires special discussion, which has alreadybeen begun.4"5 Coherent interaction of an intense beamof heavy particles with a cooling electron flux can leadboth to accelerated damping of coherent beam oscilla-tions, which can be effectively used in combatting "ex-traneous" instabilities of the proton beam, and also tonew instabilities.

h) Another effect which appears in an intense protonbeam, especially one with maximal cooling, is the scat-tering of protons by other protons of the same beam —the internal-scattering effect. If the frequency of revo-lution of the protons in the storage ring (for a fixed mag-netic field) increases with increase of their energy—thissituation is similar to the case of straight-line motion ofa proton beam with the same characteristics—internalscattering will lead only to equalization of the tempera-tures over all degrees of freedom, which in the labora-tory system will lead to appearance of a longitudinalspread of the momenta larger by a factor γ than thetransverse spread.

A completely different situation arises if the protonrevolution frequency in the storage ring (for a fixedmagnetic field) drops with increasing energy. Two pro-tons executing, say, radial betatron oscillations andhaving strictly the equilibrium energy, after scatteringcan change energy discontinuously (the sum of their en-ergies, of course, is conserved); this simultaneouslyexcites additional radial betatron oscillations and, if theenergy is above the critical energy, the resulting beta-tron oscillations will be on the average larger than theinitial ones. Therefore what occurs is not a simpleequalization of the temperatures over all degrees offreedom, but so to speak a "self-heating" of a protonbeam which can be limited only by the presence of fric-tion, in our case—electron cooling.

We have only touched on the problems evident at thistime in obtaining electron-cooled beams of heavy par-ticles with high intensities. Study of these problems hasjust begun.

3. EXPERIMENTAL STUDY OF THE ELECTRON

COOLING PROCESSIn order to achieve electron cooling for the first time

and to study it experimentally, a special proton storage

283 Sov. Phys. Usp. 21(4), April 1978 G. I. Budker and A. N. Skrinskii 283

ring NAP-M and a system producing an electron beamwith the necessary parameters in the cooling portionwere developed.

a) The storage ring NAP-M was built as the prototypeof an antiproton storage ring, as we visualized it in1970,43 and hence its designation—Nakopitel' Anti-Protonov, Model' (Antiproton Proton Storage Ring,Model). This particular circumstance explains both thegeneral size of the storage ring and its structure withvery long straight sections and use of purelyedge focus-ing; here the edges of the plane bending magnets weredirected strictly toward the center of symmetry of thestorage ring—to provide focusing independent of theaverage radius of the proton equilibrium orbit. Thegeneral scheme of the storage ring and its general formare shown in Figs. 2 and 3, and its main parameters aregiven in Table I.

TABLE I.

Main Parameters of the Storage Ring NAP-M

Energy of accelerated particles up to 100 MeV

Injection energy 1.5 MeV

Length of perimeter 47 m

Number of magnets and straight sections 4 of each

Radius of curvature 3 m

Length of straight sections 7.1 m

Useful aperture in bending magnets 4 cm χ 7 cm

Betatron oscillation frequencies: QR = 1.2

Duration of acceleration cycle 30 sec

Accelerating high frequency voltage (firstharmonic) 10 V

Stability of magnetic field during cooling ± 1 χ 10~5

Average residual gas pressure (withelectron beam turned on) 5 χ 10"10 torr

In one of the straight sections of the storage ring wasplaced the apparatus with the electron beam,12 the dia-gram and general appearance of which are shown inFigs. 4 and 5, and the main parameters of which aregiven in Table II.

TABLE Π.

Main Parameters of Electron Cooling System

Accelerating

Length of cooling region

Electron energy in experiments

Electron current

Relative transverse velocity ofelectrons

Energy stability

Accompanying magnetic field

1 m

up to 50 keV

up to 1 A

±3 xlO"3

±1 xlO"5

1 kG

The apparatus has three straight sections, in two ofwhich are placed the gun and collector, while the thirdis the cooling region, in which the protons move to-gether with the electron flux. For shaping and trans -

Electrosteticinjector (1.5 MeV)

Beamprofilemeasure-ment

station

Slow probe

3-μ quartz wire

Scanning mag-nesium jet

Neutral hydrogeiatoms

\ \ Electron,n \ \ installati

Scintillationcounterbeam

ion

FIG. 2. Diagram of proton storage ring NAP-M.

porting the electron beam we use an .accompanying longi-tudinal magnetic field in which the electron gun is im-mersed.9 The straight sections are connected by twosections with a toroidal magnetic field which serves toinflect the electrons into the cooling region and to ex-tract them from it. The centrifugal drift in the bends iseliminated by application of a transverse magnetic fieldwhich guides the electrons along a trajectory whosecurvature coincides with that of the line of force of thelongitudinal field.

The apparatus employs recovery of the electron en-ergy, so that the power consumed bv the high-voltagesource does not exceed a few percent of the reactivebeam power.10·11

The operating cycle of the complex as a whole is asfollows. Protons of energy 1.5 MeV are injected in asingle turn into the storage ring. In the course of 30sec the field is raised to the necessary value. The high-frequency accelerating system provides a proton energyincrease matched to the rise of the magnetic field. Onreaching the necessary level the rise of the magneticfield and the change in the frequency of the acceleratingvoltage are halted, and the protons, which have beenformed into a bunch of length about one quarter of theorbit perimeter, can "live" many hundreds of secondsin the storage ring, gradually leaving it as the result ofscattering by the residual gas. If one wishes to workwith a continuous beam, the high-frequency voltage isremoved. After the acceleration the electron beam isturned on and the electron-cooling process proper be-gins.

b) The experimental achievement of electron coolingrequired solution of a number of complicated technicalproblems. For example, in a storage ring with a vacu-um chamber length of about 50 m and an internal intenseelectron beam with a power of several kilowatts, anaverage vacuum of about 5xlO"1 0 torr is maintained.The stability of the magnetic field and of the electron en-

FIG. 3. The storage ring NAP-M.

284 Sov. Phys. Usp. 21(4), April 1978 G. I. Budkerand A. N. Skrinskii 284

FIG. 4. Diagram of electron beam installation. 1—electrongun, 2—anodes, 3—solenoid, 4—electron beam bending re-gions, 5—cooling region, 6—vacuum chamber, 7—collector,8—vacuum pumps, 9—correcting magnets.

ergy amounts to 1 χ 10"5. The entire process of acceler-ation and transition to the cooling regime is accom-plished automatically by computer. The same computeris used for recording and immediate processing of ex-perimental information, for providing the output in aform convenient for the experimenter on the display unitand printer, and for subsequent long term storage.

In the experiments on electron cooling we used vari-ous means of observation—pickup electrodes (integraland differential) to measure the time structure and posi-tion of the bunched beam, ferromagnetic magnetometersto measure the circulating current, destructive probesto measure the integral distribution of betatron oscilla-tion amplitudes, and micron-size wires rapidly cross-ing the beam for recording protons scattered into anangular aperture to measure the proton-beam densitydistribution with high resolution.

Particularly useful devices were a magnesium jet andthe detection of fast hydrogen atoms arising in radiativerecombination.

The magnesium-jet method (Fig. 6) is based on de-tection of ionization electrons arising from a thin jet ofmagnesium vapor intersecting the proton beam. Theionization electrons are accelerated and collected on aphosphor; the luminescence of the phosphor is detectedby a photomultiplier. The experiments utilized a rib-bon-shaped jet with transverse dimensions 0.5x20 mm2

(the long dimension was along the direction of protonmotion) and a vapor pressure of about 10 "6 torr. Thisjet results in practically no additional scattering. Ahorizontal jet can be shifted (scanned) along the verticaldirection; the photomultiplier signal is then proportionalto the density distribution of the proton beam along thevertical direction. Similarly, a vertical jet permits in-

FIG. 6. Arrangement for measuring proton beam density(magnesium jet method). 1—proton beam, 2—magnesiumjet, 3—container with magnesium, 4—collecting electrode,5—luminescent screen.

formation to be obtained on the radial distribution ofprotons. A jet can be stopped at any point; in this caseit is possible to trace the change in the proton-beamdensity as a function of time.

By observing the flux of fast hydrogen atoms, it ispossible to estimate the average relative velocity of theprotons and electrons from the total flux of such atoms(see Eq. (2.9)) and to measure the equilibrium size andangular spread in the proton beam with very high reso-lution (Fig. 7).

c) A nontrivial effect of the electron beam on the mo-tion of the protons appeared only when the average veloc-ities of the protons and electrons in the cooling regionwere brought together with a relative accuracy betterthan lxlO" 3 . In the experiments we observed the follow-ing effects:

damping of betatron oscillations;

the existence of an equilibrium size of the protonbeam;

decrease of the energy spread in the proton beam andentrainment (acceleration or retardation) of the protonsby the electron beam;

existence in the proton beam of an equilibrium energyspread;

increase in the lifetime of the proton beam.

These phenomena have a particularly simple naturefor low proton currents (<50 μΑ) and electron currents

FIG. 5. General appearance of electron beam installation.

285 Sov. Phys. Usp. 21(4), April 1978

FIG. 7. Photograph of nuclear emulsion exposed to a beam offast hydrogen atoms (v/c = 0.35) arising in recombination ofproton and electron beams in the cooling section. The emulsionwas located 10 m from the interaction region. The fiducialmarks are every one millimeter. The size of the image cor-responds to a proton beam diameter 0.5 mm and an angulardivergence 3 χ 10"5 rad.

G. I. Budkerand A. N. Skrinskii 285

\

FIG. 8. Change with time of the density at the center of theproton beam after turning on the inflector. The horizontalscale is 0.1 sec/cm.

(<300 mA) and in describing the experiments we shallhave in mind this case, and only mention briefly whatnew phenomena are observed at higher currents.

If the electron beam is not turned on, then after ac-celeration the transverse size of the proton beam (inother words, the proton betatron-oscillation amplitudes)gradually increases as the result of scattering by theresidual gas atoms. This is clearly visible from the in-crease in the width and decrease in the amplitude of thesignal from the secondary electrons obtained in scan-ning with the magnesium jet over the storage-ring cham-ber cross section. The size increases up to that per-mitted by the aperture (average diameter of the protonbeam up to 1.5 cm). If after this the electron beam isturned on with a correctly chosen average velocity, theproton beam is compressed to a fraction of a milli-meter, the small amplitudes being damped first, and thelarge ones being "collected" only gradually.

It is particularly convenient to measure the betatron-oscillation decrement and to bring out the correspondingfunctional dependences by stopping the magnesium jet inthe center of the proton beam and observing the depen-dence of this density on time after special pulsing of aninflector exciting betatron oscillations in the cooledbeam, which were identical for all protons (Fig. 8).Here, if the proton current is small, the measuredcooling time does not depend on this current, i.e., cool-ing occurs completely incoherently, and the oscillationamplitude of each proton decreases independently.

For large proton currents a portion of the initial am-plitude in certain regimes is damped very rapidly (inless than 10 msec), the fraction of this coherent loss ofamplitude increasing with increase of the number ofprotons. Then the betatron oscillations apparently losetheir initial in-phase relation and further damping oc-curs independently of the proton current. It is possibleto obtain a damping time for the amplitude of small beta-tron oscillations of less than 0.1 sec.

The damping of the deviations of the proton velocityfrom the average longitudinal velocity of the electronsmanifests itself clearly in the "entrainment" of the pro-ton beam with the electron energy undergoing only asmall change. For example, if the electron energy israised discontinuously, the energy of the freely circula-ting protons also begins to increase and the proton beamtransfers to a new equilibrium orbit of larger radius.

Particularly impressive is the possibility of acceleratingprotons with the aid of an electron flux with the electronenergy and the magnetic field of the storage ring in-creasing simultaneously in a coordinated manner» Bythis means we were able to raise the proton energy from60 to 80 MeV in three minutes.

d) In the experiments we were successful in obtainingvery small equilibrium dimensions of the proton beam.A measurement of the transverse dimensions can bemade with the utmost reliability and very high resolutionby measuring the flux of fast atoms formed in recombina-tion in the cooling region, detecting them by means of anuclear emulsion placed behind a thin foil at a distanceof 10 m from the cooling section (see Fig. 7). The pro-ton beam size calculated from the spot size on the emul-sion could be reduced to 0.4 mm.

The energy spread in the freely circulating beam wasmeasured by observing the spread in frequencies of rev-olution. For this purpose from a closed cooled protonbeam about half of the total azimuth was knocked out andthe time of disappearance of the phase grouping of theprotons was measured (from the disappearance of thesignal from a pickup electrode). At low currents thistime reached 3 sec; when the diffusion nature of thespreading of the bunch in the presence of strong longi-tudinal damping is taken into account, this correspondsto an energy spread of lxlO~5. This spread increasesas the proton current is increased.

The overall effectiveness of electron cooling is wellcharacterized by the ratio of the initial six-dimensionalphase volume of the beam, which corresponds to a beta-tron-oscillation amplitude of 1 cm and an energy spreadof 0.1%, to the steady-state phase volume at a betatronoscillation amplitude of 0.25 mm and an energy spreadof lxlO" 5 . This gives an increase in the phase densityof I 4 x 10-3/(2.5 χ ΐ(Γ2)4 χ ΙΟ"5 = 2 χ ΙΟ8 times !

Effective cooling naturally excludes completely theloss of protons as the result of multiple scattering bythe residual gas atoms, and the lifetime is determinedonly by direct, single knockout. The experimentally ob-served dependence of the proton current on time be-comes purely exponential, and the lifetime is severaltimes greater than without electron cooling.

e) The set of experimental dependences, especiallythose obtained recently,2 5·2 8·2 9 shows that the elec'.ron-cooling process is substantially more complicated thansimple cooling of a gas of protons in a cold electron gas.In particular, it can be seen that an impor'ant role isplayed by proton-electron collisions with impact param-eters greater than the Larmor radius of the electrons.New effects appear also as the electron and proton cur-rents are increased.

Thus, electrr η cooling has been tried successfully andhas been investigated in the energy range from 1.5 MeV(the inject'on energy) to 85 MeV (momentum 0.4 GeV/c)both for χ freely circulating proton beam and for abunched oeam. Table III shows the best results obtainedup VJ he present time and the corresponding experi-m ital conditions.

286 Sov. Phys. Usp. 21(4), April 1978 G. I. Budker and A. N. Skrinskii 286

TABLE ΠΙ. (ftp)

Proton momentum

Electron energy

Electron current

Electron beam diameter

Fraction of orbit occupied by coolingsection

Effective electron temperature:transverselongitudinal

Longitudinal magnetic field

Damping time (small amplitudes)

Steady-state proton-beam diameter

Steady-state angular spread

Steady-state energy spread

Lifetime

0.4 GeV/c

45 keV

0.8 A

2 cm

2 x ΙΟ"2

0.2 eV10"4 eV

1 kG

0.1 sec

0.4 mm

±4xl0" 5

1 χ ΙΟ"5

10 hours

Apparently a further increase in the effectiveness ofelectron cooling is also possible. In any case the cool-ing time can be reduced several fold as the result offilling a larger fraction of the proton orbit with elec-trons.

4. STORAGE OF INTENSE ANTIPROTON BEAMS

The principal purpose for which we undertook develop-ment of the electron-cooling method was the storage ofintense beams of antiprotons, although it was first pro-posed for compression of beams of heavy particles.

a) According to Liouville's theorem, without dissipa-tive forces it is impossible to add new quantities of anti-protons into regions of phase volume of a storage ringwithout removing particles already present in them.The best that can be accomplished in this operation is tofill the entire phase volume of the storage ring with adensity given by the antiproton generator. However, thephase density achievable today for antiproton beams ob-tained as beams of secondary particles in proton ac-celerators, without going over to very thin and accord-ingly very inefficient target-converters, is far fromproviding the needs, for example, of installations withcolliding proton-antiproton beams of high luminosity.The possibility exists, it is true, of accumulation ofantiprotons with no fundamental limitations by use ofantihyperon beams.44 In this arrangement a beam of,say, Λο hyperons traverses a region of the storage ringalong a tangent to the trajectory and those antiprotonswhich in the decay

turn out to be at appropriate points of the storage-ringphase space (near the equilibrium trajectory with mo-mentum of the proper magnitude and direction) will re-main in the storage ring. However, the efficiency ofthis arrangement (i.e., the ratio of the number of storedantiprotons to the number of accelerated protons) turnsout to be very low and in reasonable times does not pro-vide the storage of the necessary number and necessaryphase density of antiprotons.

m1 w1 η1

p0, GeV/c

FIG. 9. Average multiplicity of antiprotons in p+p collisionsas a function of the incident proton momentum p0.

Use of electron cooling permits a solution of the prob-lem. This was shown in the Novosibirsk colliding p r o -ton-antiproton beam project, 4 3 and in the proton-antipro-ton projects which have appeared recently for the ac-celerator-storage ring complex at Serpukhov (the p r o -posal of our Institute at Novosibirsk 4 5), at CERN,4 6 andat the Fermi National Accelerator Laboratory in theUSA.47

b) Let us consider in somewhat more detail the basiccharacter is t ics of the antiproton beams produced.

The ratio of the total number of produced antiprotonsto the number of incident protons for proton energiesconsiderably above threshold, which for the case of aproton target is 6.5 GeV, increases from 3 x l O " 3 at 20GeV to 0.1 at 1000 GeV (Fig. 9). In principle it is pos-sible to use a nuclear cascade in which in each step anti-baryons a re extracted from the total flux with low en-ergy (below 10-20 GeV), which prevents their nuclearabsorption in the target. Here it is possible to raise thetransformation coefficient of the initial proton energy in-to antiproton res t mass to a level somewhat higher than10~3. However, such complete transformation is at thepresent time an extremely awkward affair and in thefirst stage we will be clearly forced to limit ourselvesto the cascade-free version with use of a small fractionof the energy spectrum and perhaps also only a smallfraction of the transverse phase volume of the antipro-tons produced.

In the cascadeless version for a "light" target thespectrum of antiprotons corresponds to the spectrum ofan "elementary central event." Here antiprotons havinglow energies in the center of mass system of the col-liding nucleons a r e produced with the greatest proba-bility, which corresponds to the situation in the labora-tory system that the peak of the antiproton spectrum oc-curs at Ef'x~-jMpc

2E m .

In the antiproton energy region substantially lowerthan Εψχ—and just this region is most convenient forstorage of antiprotons—the spectrum falls off ratherrapidly and at a kinetic energy of 1 GeV turns out to begreatly reduced (Fig. 10). Use of a target with heavynuclei shifts the antiproton spectrum somewhat towardthe low energy region.

The angles of antiproton production are determined bythe momentum p and a r e approximately given by

287 Sov. Phys. Usp. 21(4), April 1978

Correspondingly, the effective phase volume of the anti-

G. I. Budkerand A. IM. Skrinskn 287

0 S 10 13p. GeV/c

FIG. 10. Distribution of antiproton momenta in the laboratorysystem, expressed in units of n(po,p) = (8π/3)ΜτΜρ(ρ/σ1α)(13σ/dp3 (σ1η is the cross section for inelastic interaction of a pro-ton, σ is the cross section for production of an antiproton)from the experimental data58"60 for various primary-protonmomenta p^.

protons (one-dimensional) for a very small transversedimension of the initial proton beam is determined bythe target-converter length lc and by the antiproton mo-mentum:

Ω-!

In the simplest case the maximal yield of antiprotonswill be obtained if the converter used is a cylinder ofsmall radius with a length equal to the nuclear-absorp-tion length of the primary protons Znuc. However, theantiproton phase volume obtained in this case Ω ^ turnsout to be too large and in practical projects it is nec-essary for the time being to limit oneself to the use of asmall fraction of the phase volume of the produced anti-protons.

The ratio of the useful number of antiprotons to thenumber of primary protons turns out, thus, to be

here Δρ/p is the momentum bin captured by the antipro-ton storage ring, fistc is the transverse phase volumeaccepted by the accelerator (in one direction), andn(po,P) characterizes the spectrum of produced antipro-tons and depends on the momenta of the primary protonsp0 and of the antiprotons utilized p(see Figs. 9 and 10).

The yield of antiprotons entering a given volume of thestorage ring can be increased by several times by thefollowing procedure. Instead of one target converter,several short targets are used, between which areplaced very high-aperttire lenses48 which transmit animage of the antiproton beam from target to target.Here the phase volumes of the antiprotons from all tar-gets are combined with each other. Scattering in thetargets and in the shortfocal-length lenses can be madesufficiently small, and the final phase volume of theantiprotons turns out to be equal to the phase volume ofa short single target.

The cooling time for antiprotons increases rapidlywith increase of their phase volume (see Eq. (2.5)):

o.i wo*τ5 ' " L !

ρ conversion

NAP cooler FIG. 1 1 . Arrangement ofproton-antiproton complex.

NAP storage ring

njection of ρ

rL,rpLc\\ J,

Straight section of one-TeVaccelerator-storage-ring

value of the storage-ring β function in the cooling region(the analog of the focal length of the focusing system).Since the number of captured antiprotons increases withincrease of the storage-ring phase volume only linearly,the optimum phase volume turns out to be that for whichthe cooling time (with a technically achievable electroncurrent) will be equal to the period between the injectioncycles provided by the proton accelerator used.

c) The first antiproton storage-ring project was de-veloped in 1966 for the Novosibirsk proton-antiprotoncolliding-beam project.43 This project already includedthe use of electron cooling. After its complete realiza-tion the project was supposed to provide an antiprotonstorage rate of about 106 p/sec.

After the experimental demonstration of the possibili-ties of electron cooling, "antiproton" activity increasedgreatly also in other laboratories. In the last two yearsantiproton storage-ring projects have been developedfor the proton-antiproton colliding beams for the pro-jected accelerator—storage-ring complex at Serpukhov45

(UNK), for performance of proton-antiproton experi-ments in the ISR storage ring,46 and for conversion of thepresently largest proton synchrotrons at the Fermi Na-tional Accelerator Laboratory (USA) arid the EuropeanCenter for Nuclear Research (CERN) to proton-antipro-ton colliding-beam operation.47·49

We have shown in Fig. 11 for illustration the schemeof antiproton storage proposed by our Institute at Novo-sibirsk for UNK. With the complete arrangement plan-ned this system will permit storage of 108 £/sec.

We should note that, even after achievement of theseantiproton storage rates, a tremendous field remainsfor further improvements and inventiveness. At an in-itial proton energy of about 100 GeV and the planned in-tensities of proton synchrotrons it is possible in prin-ciple to obtain more than 1012 p/sec.

5. NEW POSSIBILITIES IN ELEMENTARY-PARTICLE

PHYSICS

The main purpose of the present review is to draw theattention of experimenters working in various fields ofelementary-particle and nuclear physics to the new and,frequently, fundamentally new possibilities opened up bythe use of electron cooling. For this purpose we shalltry to touch, if only briefly, upon the most varied fieldsof possible applications of this method.

where Je is the current of cooling electrons and (30 is the a. Experiments with super-thin internal targets

288 Sov. Rhys. Usp. 21(4), April 1978 G. I. Budker and A. N. Skrinskii 288

The first results in storage of antiprotons will alreadypermit one to carry out a broad range of new experi-ments.

1) In the storage rings themselves for antiprotonswith electron cooling it will be possible to perform anextensive group of experiments with super-thin internalgas and vapor targets. In the super-thin target regime50

the energy losses of the antiprotons, the fluctuations ofthese losses, and the multiple scattering of the antipro-tons by the atoms of the target are suppressed by elec-tron cooling and the lifetime of the antiprotons is deter-mined only by single interactions with the target. Scat-tering by the residual gas at modern vacuum levels canbe made negligible. At antiproton energies of the orderof 1 GeV and above, the dominant interaction is the nu-clear interaction with cross sections of about 10~25 cm2/nucleon; at lower energies Coulomb scattering by anangle greater than the aperture angle becomes more im-portant (the "loss" cross section increases as Ζ2Θ^Χ).To reduce the cross section for loss of antiprotons asthe result of the Coulomb interaction and to reduce theinfluence of multiple scattering on the antiproton beamsize it is reasonable to install internal targets in theparts of the storage ring which have sharp minima ofthe β functions.

The luminosity in such experiments is determined bythe rate of storage of antiprotons N-p and by the losscross section σ. :

L = -"tou

(5.1)

For example, at high energies and a storage rate 10s p/sec the luminosity reaches 1033 cm"2 sec"1, which issufficient for an extremely wide range of experiments.For example, the number of cases of production of therecently found />/>(1939) resonance may reach 10s persecond. Performance of experiments in the super-thintarget regime is facilitated by the 100% duty cycle of thereactions in time and by the small target thickness,which permits detection even of very slow reaction pro-ducts such as nuclear fragments. We note that fromthis point of view it may turn out to be useful to use thesuper-thin target regime even for proton beams.

2) It is particularly effective to use super-thin inter-nal targets for precision spectrometric experiments.50

The use of electron cooling will permit achievement ofan energy resolution of the order 10~4-10"6 with com-pletely satisfactory luminosity in antiproton-proton andantiproton-nucleus experiments. Similar experimentswith proton beams will provide the same high resolutionand luminosity, which is comparable with that which canbe obtained with equal resolution in tandem acceleratorsand meson factories. At higher energies a proton stor-age ring with electron cooling and a super-thin internaltarget will provide a luminosity for spectrometric ex-periments many orders of magnitude higher than con-temporary proton accelerators.

A circumstance important for spectrometric experi-ments is the possibility of extremely accurate measure-ment of the absolute energy of particles of known mass

in the storage ring by measuring the voltage which ac-celerates the cooling electrons. The accuracy alreadyachieved at this time is better than 10"5

3) It is interesting that for a study of antiproton-neu-tron interactions it turns out to be possible to use a tar-get of free neutrons (which, apparently, is particularlyattractive at low energies). For this purpose it is mostreasonable to use high-current pulsed deuteron acceler-ators with a target located adjacent to the storage-ringvacuum chamber and surrounded by a moderator. Theluminosity in such an arrangement can be made clearlysufficient for the study of nuclear cross sections, espe-cially of annihilation processes, and the main problemwill be obtaining the vacuum necessary because of back-ground conditions in the interaction region with intenseneutron irradiation.

4) An interesting application of an antiproton storagering with electron cooling and an internal target is theproduction of intense directed fluxes of antineutrons andantihyperons of the required energy in charge-exchangereactions of the type pp ~YY. At an energy of, say, 2GeV with the luminosity estimated above it is possibleto obtain up to 3 χ 104 «/sec and 104 Λ/sec. Here detec-tion of the neutron or hyperon or their decay productspermits the subsequent antineutron and antihyperon re-actions with the targets being studied to be separatedfrom the general background of secondary reactions.

b. Acceleration of stored antiprotons

New experimental possibilities will be opened up if ina portion of the acceleration cycles of the main protonsynchrotron the stored antiprotons are accelerated.With the projected rates of storage of antiprotons, usinga slowly extracted accelerated antiproton beam and ex-isting experimental systems, it is possible to carry outa detailed study of antiproton-nucleon and antiproton-nucleus collisions. The high intensity of the antiprotonbeam and its complete purity and extremely small phasevolume will permit the necessary information to be ob-tained with present-day "proton" accuracy over the en-tire energy range from a few MeV to the limiting energyof the main accelerator.

In addition, it will be possible to obtain well colli-mated beams of clearly "labeled" antineutrons and anti-hyperons of high energy and appreciable intensity.

c. Continuously cooled colliding beams

Unique possibilities appear in the study of proton-anti-proton interactions on performing experiments with con-tinuously cooled colliding beams in the energy region<10 GeV in each beam. Simultaneous cooling of the col-liding beams is possible even in a single guide field—thepoint is that the flux of electrons which is cooling, say,the protons is moving against the antiprotons and there-fore their mutual collisions in no way perturb the anti-proton beam. An experimental installation of this typecan turn out to be interesting, in comparison with thesuper-thin target arrangement, if it is necessary to re-move completely the unnecessary interactions with elec-trons of the target and/or to obtain the best possible

289 Sov. Phys. Usp. 21(4), April 1978 G. I. Budkerand A. N. Skrinskii 289

monochromaticity.

In particular, it is possible to investigate φ mesonswith a resolution much better than their intrinsic width,which cannot be done even with contemporary experi-ments using electron-positron colliding beams. Ofcourse, only a very small fraction of all atoms of pro-ton-antiproton annihilation will proceed via φ mesons,even at the peak of the curve. Therefore it is reasonableto detect leptonic decay modes

The cross sections for these processes just at the peakof the resonance are of the order of 100 nb. In a spe-cialized storage ring with strong focusing at the pointof collision it is possible to obtain tens of thousands ofsuch events per day.

We note that in proton-antiproton collisions it is pos-sible to obtain directly narrow states of the ψ-mesontype with less severe restrictions on quantum numbersthan in the case of electron-positron colliding beams,where the quantum numbers of such a state must beequal to the photon quantum numbers. It will be par-ticularly easy to pick out states which have appreciableprobabilities of decays which are not purely hadronic.An example of this type of meson is the γ(2750), whichdecays into two γ rays.

d. The ultimate in low energies

Completely new possibilities appear in the study ofantiproton-proton (and antiproton-nucleus) interactionsat extremely low energies. Stored antiprotons can bedecelerated in the synchrotron regime to an energy ofthe order of 1 MeV and then further cooled. Sometimesit may be more convenient to decelerate stored and con-tinuously cooled antiprotons by means of a coordinatedreduction of the storage-ring magnetic field and the en-ergy of the cooling electrons. The minimal energy isdetermined by Coulomb repulsion effects in the antipro-ton beam at the required intensity.

1) Several possibilities exist for the transition to ex-periments at extremely low energies. The simplest ar-rangement is to release antiprotons, slow them downwith an electric field to the required energies (down tothe energy spread in the antiproton beam), and to directthem at a target made in the form of a gas jet. The fol-lowing somewhat exotic arrangement is also possible:in one of the straight sections in a small region with aminimum of the β functions it is possible to reduce theelectrostatic potential in such a manner that the antipro-tons are slowed down to the required energy, passthrough the target, and then are again accelerated to thestorage-ring energy. Of course, the contributions of theregions of deceleration, uniform motion in the target re-gion, and acceleration must be taken into account in thefocusing structure of the storage ring. In this arrange-ment it is possible to use both gas jets and ion beams ofthe same low energy as a super-thin target for annihila-tion experiments with very slow antiprotons.

2) Investigation of the interaction of antiprotons and

protons (nuclei) at extremely low energies is possibleby using two storage rings with a common straight sec-tion in which continuously cooled antiprotons and protonsare moving parallel to each other with quite close oreven equal average velocities. In the latter case as theresult of radiative recombination it is possible to forma rather significant flux of protonium atoms—electro-magnetically bound states of the proton and antiproton.However, the most interesting arrangement for per-forming experiments at extremely low energies, whichpermits the antiproton-proton bound states to be studiedthe most completely, is as follows. Along one of thestraight sections of a storage ring in which a cooledbeam of antiprotons with energy of the order 1 MeV iscirculating, a beam of hydrogen atoms with the same orvery nearly the same average velocity and small spreadis transmitted parallel to the antiprotons. The neces-sary beams can already be obtained at the present timeby stripping accelerated negative hydrogen ions, for ex-ample, by means of a laser.

We note that in some cases it may be useful to obtaina flux of neutral hydrogen atoms by neutralization of aproton beam in a special storage ring, in particular, asthe result of radiative recombination with the coolingelectrons. The "used" hydrogen atoms, after traversingthe region of interaction with the antiprotons, can becaptured by removal of an electron into an additionalstorage ring with electron cooling, with subsequenttransfer of the proton beam back into the first protonstorage ring.

3) If in a collision of an antiproton with a hydrogenatom the kinetic energy in their center-of-mass systemis less than the electron energy, the cross section forformation of protonium will be close to the geometricalcross section of the hydrogen atom. In this case anelectron will be emitted and will carry away the excessenergy (close to the average kinetic energy of the elec-tron in the atom). Under these conditions, highly ex-cited levels of protonium with principle quantum num-bers of the order -JM/2m will mainly be populated, theorbital quantum numbers also being large on the aver-age. The fraction of states with high angular momentumwill be particularly great if the initial relative energyof the atom and the antiproton is close to the ionizationenergy of the hydrogen atom; for this purpose it is nec-essary to provide the appropriate difference between theaverage velocities of the atomic beam and the antiprotonbeam.

4) The lifetime of such highly excited and high-angu-lar-momentum states of protonium against annihilationturns out to be very great; annihilation occurs effective-ly only from states with orbital quantum numbers nogreater than 1. Transitions to these states occur as theresult of emission of photons. The lifetime of suchtransitions turns out to be greater than 10"8 sec and theprotonium can travel a distance of tens of centimeters,so that it is possible to separate spatially the flux ofthese "atoms" and the antiproton beam. All of this willpermit study of the further fate of protonium under thepurest and best defined conditions. For example, by re-cording the x-ray cascade of radiative transitions in

290 Sov. Phys. Usp. 21(4), April 1978 G. I. Budker and A. N. Skrinskii 290

coincidence with annihilation quanta and mesons, it ispossible to pick out annihilation from states with non-zero angular momenta, which is extremely difficult withother experimental arrangements.

Similarly it is possible to study also antiproton-deu-teron bound states.

e. Antiatoms

By using stored antiprotons it is possible to obtainbeams of antihydrogen atoms. For this purpose it isnecessary to pass through an electron-cooled antiprotonbeam in one of the straight sections of the storage ringa beam of cold positrons parallel to it and with the sameaverage velocity. As the result of radiative recombina-tion it is possible to convert a major part of the antipro-tons into antihydrogen. In fact, using the NAP-M withno special efforts 10% of the protons go over into a beamof fast atoms.

A beam of antiatoms can be used, for example, forextremely precise comparison of the properties of hy-drogen and antihydrogen atoms. The most accurate datacan apparently be obtained in experiments on the inter-ference of states,51 which in their sensitivity to possibledifferences in the properties of matter and antimatterare equivalent to measurements of the Lamb shift.

It is possible by the method described to obtain beamsof antiatoms of very low energy, which provides thehope of accumulating neutral antihydrogen in specialcyclic magnetic systems by acting on the antiatoms viathe magnetic moment of the positron.

f. Polarization experiments

1) An important possibility made available by antiprotonstorage rings with electron cooling is the production ofpolarized antiproton beams. At the present time theprincipal method of accomplishing this must be con-sidered to be the interaction of a stored antiproton beamwith super-thin polarized targets of atomic hydrogen.On the basis of existing data it is still difficult to chooseoptimal conditions which permit a high degree of polar-ization to be obtained with the lowest possible loss ofantiproton intensity.

One of the possible schemes is to utilize interactionwith longitudinally-polarized protons in a section of thestorage ring where longitudinal polarization of antipro-tons is stable.52"54 Here use is made of the differencein the total cross sections for interaction of antiprotonsand protons with different relative helicities. Estimatesfor a proton beam show that for protons in the region ofexcitation of the Δ++ resonance (the optimum momentumof the proton in the storage ring is about 1.4 GeV/c) it ispossible by this means to obtain a degree of polariza-tion of the order of 50% with an intensity loss by a fac-tor 30. For antiproton-proton interactions the spectrumof resonances is much richer and it will perhaps be pos-sible to obtain polarized antiproton beams with an evensmaller loss of intensity.

2) A completely different arrangement is the scatter-ing of an extracted cooled antiproton beam by a polar-

ized proton or nuclear target, and collection in somemanner of the scattered antiprotons, followed by injec-tion of them into a storage ring with electron cooling.To obtain the required degree of polarization, apparent-ly, it is necessary to carry out several such cycles.

3) The possible rate of production of polarized anti-protons will therefore be 10-100 times lower than thenumber of initially stored antiprotons (per second).However, even this level is sufficient to carry out avery wide range of polarization experiments with anti-protons. Thus, in an antiproton storage ring with elec-tron cooling with utilization of the best polarized gaseousproton and deuteron targets (thickness up to 1012 />/cmz),a luminosity up to 1029 or even 1O30 cm"2 sec"1 can beobtained. Moreover, polarized antiprotons can be ac-celerated in the main accelerator and used in experi-ments of the usual type. It is also a very attractive pos-sibility to carry out polarized proton-antiproton experi-ments in colliding beams, which will become possibleon achievement of the full rate of antiproton storagewhich is proposed in current projects.

4) Polarization experiments in storage rings withelectron cooling are appropriate not only with antipro-ton beams. This method is adequate also for experi-ments with polarized protons and deuterons. Only to ob-tain polarized beams it is necessary, of course, to storedirectly the accelerated polarized particles. The beamsof accelerated polarized protons obtained today and theexisting polarized gas targets permit attainment of aluminosity of at least 1030 cm"2 sec"1 under very cleanconditions.

We note that today systems with use of electron cool-ing are already in sight which can enable us to raise theintensity of accelerated polarized proton beams to thelevel of the existing proton beams in high energy accel-erators.

g. AntkJeuterons

1) The use of electron cooling opens up the possibil-ity of storage also of completely pure beams of antideu-terons. The rate of storage of such beams is 10"4 of therate of storage of antiprotons. This permits us to ob-tain—by using a super-thin deuteron target—luminosi-ties up to 1029 cm"2 sec"1, and this provides the pos-sibility of studying in some detail the strong neutron-antineutron interactions, including also the annihilationprocesses. To pick out these interactions it is neces-sary to record the antiprotons which have essentiallypreserved their motion and to select events with zerototal charge of the remaining final particles or to detectalso the low-energy proton remaining after the breakupof the deuteron.

At low energies it may turn out to be of interest to in-vestigate the interaction of antideuterons with complexnuclei, including the study of bound antideuteron-nucleusstates.

It is not excluded that the number of stored antideu-terons is sufficient for studying similar processes atextremely high energies in colliding deuteron-antideu-

291 Sov. Phys. Usp. 21(4), April 1978 G. I. Budkerand A. N. Skrinskii 291

teron beams. Identification of neutron-antineutronevents is possible by means of the protons and antipro-tons which remain almost unperturbed.

2) The process of storage and purification of antideu-teron beams may appear as follows. A beam of negativesecondary particles is injected into a storage ring; me-sons, antiprotons, hyperons, antihyperons, and antideu-terons will be captured with a momentum correspondingto the magnetic field and radius of the storage ring. Allmesons and hyperons decay rapidly, and there will re-main antiprotons and, as a small impurity, antideu-terons. If the velocity of the electron beam is chosenequal to the average velocity of the antideuterons, whichas a result of the greater mass of the deuterons is muchless than the velocity of the antiprotons, then the anti-deuteron beam will be efficiently cooled; at the sametime the influence of the electron beam on the antipro-tons will be negligible. If after cooling the electron en-ergy and the magnetic field of the storage ring arechanged in a coordinated manner, the antideuterons willchange their energy correspondingly (the entrainmenteffect described above), while the antiprotons, retainingtheir initial energy, will change their orbit radius, leavethe storage ring aperture, and be lost. After carryingout the necessary number of cycles a comparatively in-tense and absolutely pure beam of antideuterons will beobtained.

In principle it is possible in exactly the same way tostore also pure beams of antitritium nuclei and anti-helium-3 nuclei; however, their intensity will be lowerby another four orders of magnitude.

h. Experiments with ion beams

1) Electron cooling opens up interesting prospects forexperiments with storage of ions. The principal variantof such experiments will apparently be carried out in thesuper-thin target mode. The advantage of this arrange-ment of experiments will be the possibility of precisionexperiments utilizing the high monochromaticity of acooled beam and the availability for detection and anal-ysis of all reaction products, including even slow, highlyionizing fragments. It becomes possible, in particular,to study precisely the quasimolecular states of nuclei.

The use of electron cooling is particularly importantfor experiments with hard-to-obtain ions, mainly heavyions. A fact which turns out to be convenient here isthat in a storage ring with electron cooling there is anideal separation of isotopes, which makes possible op-eration with the very lightest isotopes under absolutelyclean conditions.

The super-thin target mode described above signifi-cantly enriches the possibilities of experiments on theinteraction of nuclei, especially heavy nuclei, at ener-gies from the MeV range to the range of GeV per nu-cleon.

2) However, quite unusual possibilities arise in usingthis mode when both beams consist of stored, continu-ously cooled nuclei of the desired type, stripped of theirelectron shells. Here, in particular, even reactions

with emission of nuclear y quanta become completelybackground-free. In just this way it may be convenientto study Coulomb excitation processes and to investi-gate quantum electrodynamics in the critical and "super-critical" electric fields of superheavy compound nuclei.

If the compound nucleus formed in collision of the in-itial nuclei may have long-lived states (with a lifetimegreater than 10"8 sec) it is useful to go over to the so-called transverse-beam mode. In this case two storagerings have orbits which intersect, for example, at anangle of 90°. For this purpose the centers of the storagerings can be separated by a distance comparable withtheir average radius. The compound nucleus will havea momentum equal to the sum of the momenta of the in-itial nuclei, and after a time of the order 10~8 sec willleave the inter acting-beam region (if necessary this timecan be made even smaller). This mode is of particularinterest in the study of superheavy (Z > 100) nuclei andprovides the possibility both of obtaining detailed infor-mation on all such nuclei and of finding their long-livedisotopes, which can be considered as the observation ofnew elements. If necessary such nuclei can be sloweddown in light material and "supplied" with electronshells, and these candidates for new superheavy ele-ments can be subjected to all the procedures of chemicalcontrol. The luminosity of such experiments will beclearly sufficient for studying processes occurring withstandard nuclear cross sections.

It is not excluded that a cooled beam of "bare" heavyions will turn out to be of interest for use as the inter-nal target of electron or positron storage rings.

3) In working with heavy ions, a complicating circum-stance is the enhancement of the rate of loss of ions asthe result of radiative recombination with the coolingelectrons. Indeed, the lifetime against radiative re-combination and the cooling time are inversely propor-tional to the square of the ionic charge, but the coolingtime is in addition proportional to the mass of the ion.For this reason for the heaviest ions one can succeed inhaving time to cool the ions but one can not maintainthem cooled for an extended period (much longer than thecooling time). This situation canbe improved by severaltimes as the result of using the magnetized regime ofthe electron beam.7 In fact, in this case the rate ofcooling is determined by the relative velocities of theions or by the spread in the longitudinal electron velo-cities, while the large transverse electron velocitieshave almost no effect on the cooling process. At thesame time the rate of recombination is determinedmainly by the maximum relative velocities, and the in-fluence of the magnetic field should be weaker.

For containment of cooled ions for unlimited periods,which may be of interest, say, in studying the radioac-tive decay of heavy nuclei stripped of their electronshells, it is possible to use proton cooling. For thispurpose an ion storage ring is supplemented by a protonstorage ring with a straight section common to the twostorage rings. The average velocities of the protons andions must be made identical. A low temperature of theprotons must be maintained by electron cooling. For a

292 Sov. Phys. Usp. 21(4), April 1978 G. I. Budker and A. N. Skrinskii 292

given temperature and current density of the coolingparticles the cooling time is proportional to ΑΖ~2Μά£,{2,where A and Ζ are the atomic weight and charge of theions and Mmol is the mass of the cooling particles, sothat the efficiency of such cooling in practice can becompletely satisfactory.

It is possible to obtain cooled beams also of ions onlypartially stripped of their electron shells, and of nega-tive ions, and even molecular ions. It is not excludedthat such beams may be useful for certain experiments.

i. Colliding proton-antiproton beams at the ultimate in highenergies

However, the most important and most exciting of theapproaching applications of the electron-cooling methodeven today remains the use of this method to carry outexperiments with colliding proton-antiproton beams atthe highest possible energy.

1) One of the main problems in carrying out these ex-periments is obtaining high luminosity. The limitingpossible luminosity is determined by the average rate ofstorage of antiprotons and at these energies (see Eq.(5.1)) is equal to

N-p

°k>u '(5.2)

For the presently projected storage rates of 106-108 p/sec this gives a luminosity of ΙΟ31—1033 cm"2 sec" 1. Ofcourse, realization of luminosities close to this limitimposes strict requirements on the storage ring in whichthe pp collisions are achieved. Let us consider the prin-cipal ones of these requirements for the case of a stor-age ring with a single guide field. It is just this ar-rangement which will be used first, since the proton-antiproton projects closest to realization at ultrahigh en-ergy propose to use proton synchrotrons now existing orbeing built with conversion of them to the storage mode(SPS at CERN, and the accelerators at the Fermi Na-tional Accelerator Laboratory). To achieve the maxi-mal luminosity in such a case it is necessary to workwith short bunches of the colliding particles, in orderthat all interactions between them be localized in re-gions scanned by the detecting apparatus. The lumi-nosity summed over all collision regions is determinedby the number of particles Np and Nj, by the areas ofthe beam cross sections at the points of collision S, andby the frequency of revolution in the storage ring /:

JV..V- (5.3)

With use of electron cooling, the size of the beamswill be determined only by collision effects (the distor-tion of the particle motion by the field of the collidingbeam) and it becomes reasonable to work with an equal

number of colliding particles,cannot be greater than

, = Np=N. This number

(5.4)

Αν is the allowable shift of betatron-oscillation frequen-cies which does not yet lead to a nonlinear buildup of theoscillations. The permissible shift has a value from0.1 to 0.001, depending on the time of damping or of ex-istence of the beams, on the magnet system selected,and on the care in its adjustment. We note that if theacceleration of the particles is carried out in the stor-age ring itself, the orbits of the colliding beams mustbe separated at low energies to avoid their loss as theresult of collision effects. Here the number of particlesin each of the colliding beams in a storage ring with asingle guide field cannot be greater thanATme.

Accordingly, the maximal possible luminosity of thestorage ring will be

£mai = J-T5 Τ!Γ· (°Λ>

where Ώ is the one-dimensional phase volume of thestorage ring (the admittance), rp is the classical protonradius, γ is the relativistic factor of the particles, and

where j30 is the value of the β function of the storage ring(the analog of the focal length) at the collision point.

The phase volume Ω for the largest proton synchro-trons mentioned above is of the order of 10"4 cm-rad,the collision frequency is /2 = 5 χ 104 Hz, and Av canhardly be made better than 10"2. For complete utiliza-tion of the possible average rates of storage of antipro-tons and, accordingly, for obtaining the indicated lumi-nosities (1031 - 1033) cm*2 sec"1 it is necessary to go overto extremely strong focusing at the collision point withvalues of β0 less than 1 m. Here the length of the proton(antiproton) bunches must also be less than 1 m.

The problem of obtaining bunches of such short lengthand long life is far from simple and requires for its so-lution careful suppression of noise in the magnetic fieldand the accelerating voltage, good feedback systems tosuppress possible coherent oscillations of the bunches,and apparently a transition to short wavelengths whenhigh values of the accelerating voltage are used.

If the rate obtained for storage of antiprotons assuresa luminosity (see Eq. (5.2)) higher than that which canbe obtained in a stroage ring with a single guide field(see Eq. (5.5)), it becomes useful to go over to a stor-age ring with two independent guide fields (as in the caseof proton-proton colliding beams). The limiting lumi-nosity of such a two-track storage ring of this type canbe increased substantially by filling the entire peri-meter of the storage rings with bunches, with thesebunches being made to collide only in the special sec-tions which have small values of the β functions andwhich are scanned by the detecting apparatus.

2) In the first years after the first proton-antiprotoncolliding-beam project was reported (the project VAPP-NAP at Novosibirsk),43 proton-antiproton experiments atthe highest possible energies have been considered bymany only as an extremely elaborated addition to pro-ton-proton experiments at the same energies. Ofcourse, even then it was clear that this addition is veryimportant. In fact, obtaining sufficiently complete in-formation even concerning the general properties of thestrong interaction requires the most complete possibleset of initial states. Therefore it is necessary to haveboth proton-proton and proton-antiproton experiments,

293 Sov. Phys. Usp. 21(4), April 1978 G. I. Budker and A. N. Skrinskii 293

and preferably also deuteron-antideuteron experiments.Of course, even this set is not complete and with time itwill be necessary to have colliding meson-nucleon andmeson-meson beams. It can be shown that the lumi-nosity of arrangements already forseeable today forsuch experiments is sufficient for studying hadron inter-actions occurring with a cross section of the order ofthe total cross section.

There have been discussed also two classes of experi-ments which are specific just for proton-antiproton col-liding beams—first, the study of hadron annihilationand, second, investigation of two-particle charge-ex-change reactions, i.e., reactions with conservation ofbaryon charge of each of the colliding particles. Theannihilation cross section evidently drops off only as thereciprocal of the colliding-beam energy and even at anenergy of 2x1000 GeV will be of the order of 1O"30 cm2.Therefore the principal problem will be the identifica-tion of annihilation processes from the great bulk ofevents comprising the total cross section. At the sametime the cross section for processes of the type

ρρ->-ΛΑ

drops off (in the region known at this time) as E~" andonly with a luminosity of the order of 1032 cm"2 sec"1

will it be possible to obtain information on these pro-cesses at energies above 100 GeV.

3) In recent years the attitude toward proton-antipro-ton colliding beams has changed greatly. The quarkmodel is acquiring more and more dynamical contentand more and more "public opinion" is inclined to con-sider hadrons as consisting of quarks interacting aspoint particles. Accordingly, processes with very largemomentum transfers will occur through the interactionof quarks, the components of the colliding hadrons.Here proton-proton collisions give quark-quark reac-tions, while proton-antiproton collisions give quark-antiquark reactions. In this sense one can say that inexperiments in colliding proton-antiproton beams it ispossible to obtain the same fundamental information asin colliding electron-positron beams of the same lumi-nosity and with an energy of the order of a third of theenergy of the baryons. Similarly, proton-proton collid-ing beams are equivalent to electron-electron collisions.Of course, for strongly interacting particles such asprotons and antiprotons we cannot say that they consistonly of quarks of one "polarity." However, accordingto contemporary neutrino data55 the content of antiquarksin a proton is about 5% (this is also the estimate of thecontent of quarks in the antiproton). Therefore quark-antiquark interactions are dominant in proton-antipro-ton collisions, and quark-quark interactions provide on-ly a small admixture. For proton-proton collisions theratio will be the reverse. In addition, the average en-ergy of quark-antiquark reactions in proton-proton col-lisions will be substantially lower than in proton-anti-proton collisions.

By studying, say, the lepton-pair-production reac-tions

which occur both as the result of the electromagneticinteraction and as the result of the weak interaction ofquarks, the factors cited will permit obtaining informa-tion of fundamental importance on these interactions atthe highest possible energies. In particular, if thereactually are neutral intermediate bosons of the weak in-teraction Z°, they can be observed in these reactions ifthe combined energy of the proton and antiproton ex-ceeds the rest mass of the proton by a factor of 3-6.According to current estimates, this requires a proton-antiproton colliding-beam energy in the region of 2χ (150-500) GeV. In the same energy range it is alsopossible to observe, if they exist, charged bosons of theweak interaction, W*.

The search for heavy leptons is also possible in sim-ilar experiments.

We note in addition that it is also possible to study re-actions in which a quark-antiquark pair annihilates intoa neutrino-antineutrino pair. The occurrence of such areaction can be recorded by the "disappearance" of asignificant fraction of the initial energy of the proton-antiproton pair (of the order of a third), this loss occur-ring almost symmetrically with respect to the initialparticles.

An even more detailed investigation will be possiblewhen experiments with polarized proton-antiproton col-liding beams become possible, as well as proton-protonand deuteron colliding beams. At the limiting high en-ergies considered it is particularly important56·57 thatthere is the possibility of experimenting with particleswhich are longitudinally polarized (at the point of col-lision).52'61 Electron cooling permits solution of theproblem of obtaining polarized antiproton and protonbeams of the necessary intensity.

The quark treatment of the interactions of protons andantiprotons reveals high promise for experiments incolliding proton-antiproton beams. However, it is notexcluded that the real physics of the interaction of mat-ter and antimatter at ultrahigh energies will turn out tobe even more interesting and completely unexpected.

CONCLUSION

In the present review we have attempted to show whatinteresting prospects are opened up by the application ofelectron cooling. Together with other methods for cool-ing beams of heavy particles, this method provides thepossibility of performing qualitatively new experimentsin diverse fields of elementary-particle physics and nu-clear physics.

We wish to thank our colleagues in the development ofthe electron-cooling method: Ya. S. Derbenev, N. S.Dikanskii, I. N. Meshkov, V. V. Parkhomchuk, D. V.Pestrikov, R. A. Salimov, B. N. Sukhina, V. I. Kude-lainen, and others. We are also grateful to V. N. Baler,V. E. Balakin, L. M. Barkov, S. T. Belyaev, A. I.Vainshtein, T. A. Vsevolozhskaya, V. G. Zelevinskii,A. S. Patashinskil, S. G. Popov, I. Ya. Protopopov,D. D. Ryutov, V. A. Sidorov, G. I. Sil'vestrov, I. B.Khriplovich, and other members of the Nuclear PhysicsInstitute for helpful discussions.

294 Sov. Phys. Usp. 21(4), April 1978 G. I. Budker and A. N. SkrinskiT 294

*G. I. Budker, in: Proceedings of the Intern. Symposium onElectron and Positron Storage Rings, Saclay, 1966, p. Π—1—1; Atomnaya Energiya 22, 346 (1967) [Sov. Atomic En-ergy].

2Ya. S. Derbenev and A. N. Skrinskii, Preprint, Nuclear Phys-ics Institute, Siberian Division, USSR Academy of Sciences,No. 225, Novosibirsk, 1968; Particle Accelerators 8, 1(1977).

3G. I. Budker, Ya. S. Derbenev, N. S. Dikanskii, V. V. Park-homchuk, D. V. Pestrikov, and A. N. Skrinskii, in: TrudyIV Vsesoyuznogo soveshchaniya po uskoritelyam zaryazhen-nykh chastits (Proceedings of the Fourth All-Union Conf.on Charged-Particle Accelerators), Vol. Π, Moscow, Nauka,1975, p. 300.

4N. S. Dikanskii and D. V. Pestrikov, Preprint No. 76-40,Nuclear Physics Institute, Siberian Division, USSR Academyof Sciences, Novosibirsk, 1976; Doklad na V Vsesoyuznomsoveshchanii po uskoritelyam zaryazhennykh chastits (Paperat the Fifth All-Union Conference on Charged-Particle Ac-celerators), Dubna, 1976.

5N. S. Dikanskii, V. V. Parkhomchuk, and D. V. Pestrikov,Preprint No. 74-99, Nuclear Physics Institute, SiberianDivision, USSR Academy of Sciences, Novosibirsk, 1974;Zh. Tekh. Fiz. 46, 2551 (1976) [Sov. Phys. Tech. Phys. 21,1507 (1976)].

"V. V. Parkhomchuk and D. V. Pestrikov, Preprint No. 77-37,Nuclear Physics Institute, Siberian Division, USSR Academyof Sciences, Novosibirsk, 1977.

7Ya. S. Derbenev and A. N. Skrinskii, Preprint No. 77-40,Nuclear Physics Institute, Siberian Division, USSR Academyof Sciences, Novosibirsk, 1977.

8A. I. Arenshtam, I. N. Meshkov, V. G. Ponomarenko, R. A.Salimov, A. N. Skrinskii, B. M. Smirnov, and V. G. Fain-shtein, Zh. Tekh. Fiz. 41, 336 (1971) [Sov. Phys. Tech.Phys. 16, 252 (1971)].

*V. I. Kudelainen, I. N. Meshkov, and R. A. Salimov, Zh.Tekh. Fiz. 41, 2294 (1971) [Sov. Phys. Tech. Phys. 16, 1821(1972)].

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Translated by Clark S. Robinson

296 Sov. Phys. Usp. 21(4), April 1978 G. I. Budker and A. N. Skrinskii 296