Bosser, Jacques

Maury, S

Meshkov, I N

Mustafin, E R

Möhl, D

Syresin, E M

Varenne, F

Zenkevich, P R

CERN Document Server

10/5/95 OCR OutputGeneva, SwitzerlandDallas, USA, 30 April · 5 May 1995Paper presented at the 1995 Particle Accelerator Conference*** ITEP, Moscow, Russia** IHEP, Protvino, Russia*]INR, Dubna, Russiaconference.LEAR (the Low Energy Antiproton Ring at CERN) are discussed in a companion paper at thisLandau damping, external feedback and clearing of reflected electrons. Experimental results atthreat to the stability. In the present report we analyse stabilising mechanisms includingcollaborators that two-stream instabilities, especially transverse dipole modes, are a seriousto reduce the cooling force. I-Iowever, it has been demonstrated by Parkhomchuk andresidual gas, is desirable to compensate the space-charge induced velocity spread which tendsCharge neutralisation of the cooling electron beam, e.g. by stationary ions produced from theAbstract**E. Syresin*, F. Varenne, P. Zenkevich*]. Bosser, S. Maury, I. Meshkov*, D. Mohl, E. Mustafin’**,STABILITY CONDITIONS FOR A NEUTRALISED ELECTRON COOLING BEAMCERN-Ps-95-16 Sw $$2 flII/II!llllllllIllllllllllllllllbllilllllllllllliillllllllllCERN LIBRARIES, GENEVACERN - PS DIVISIONCERNEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHmel' OCR Output+w§,,, , — 11,: &(z)e(U)""" FE = L-·EI5(z), 1% = ;$El¢$(z).(1.2)horizontal electric field Ee’“‘” one has e.g.:*+iwn— nw,,,Ut —Ur)+E§%£(dg For a short electrostatic kicker of length I at z = 0 with aexcitation by kicker electrodes (used e.g. for diagnostics).The r.h.s. of Eqs. (1.1) and (1.2) describe the extemal2+nywZ,Ue — U,= IQ(z)e_ _ ()"‘"'assumed).(1.1)Table 1 (where for simplicity trapped hydrogen ions are+iw,_e-—m,¢—Ue)+%3(Udi dtd¢& above are for "LEAR standard conditions" as defined inThe values for the frequencies given in parenthesisdensities. Then the equations of motion are :we assume that the beams have uniform transverse= zelectrons and the slow (neutralising) ions. For simplicity,effect experienced by the ions, (ca; = 210<646 kHz),Let us consider a system including only the cooling= (1-n)c0$,,, describes the incoherent space-chargeH. EQUATIONS OF MOTION trapped ions (me = 21c><27.4 MHz),the neutralisation factor with ni the density of theexamined. effect experienced by the electrons, ry = Zn;/ne isinfluence of extemal forces on the beam motion is = (mz-1)c03, describes the incoherent space-chargeand discuss resulting stability conditions. Moreover, the which we def"me here for convenience :We derive a dispersion relation to include this spread ln the following we will use three more frequenciesdue to the velocity spread of the neuualising ions. classical proton radius (anim, = 21c><835 kHz).necessary to take into accotmt the classical Landau damping the space-charge potential of the electrons, rp is thefrom the Debye boundary is absent. In such a system it is mgm = (21meZ/A)rpcz with 050,, the ion frequency indamping of the ion oscillations connected with reflectionsis the velocity of light (toe; = 21r><35 MHz),show that the neutralisation is less than unity and thereforeexperiments at LEAR [4] with a vacuum of l0‘torr (electrons! m3), re is the classical electron radius, cucompletely neutralised beams [3] was used. However, effect on an electron, ne is the electron densitywainstabilities [1,2]. In previous papers Nezlin's theory for = (2miJ7)rgcdescribes the electron space—charge32electron cooling system is constrained by transverse (wu = 21c><957 kHz),It is known that the maximum current in a neutralised charge number Z and mass M = A m p*01.1 = ZeB/M is the Larmor frequency of the ions withI. INTRODUCTION mass of the electrons (wl, = 21r><1.75 GHz),magnetic field of the cooler, mey is the relativisticpaper at this conference. quency) of the electrons in the longitudinalAntiproton Ring at CERN) are discussed in a companion = eB/wie is the Larmor frequency (= cyclotron freelectrons. Experimental results at LEAR (the Low Energy have the following significance:damping, extemal feedback and clearing of reflected orbit: d/dt = (9/8¢)+vz(3/32), etc. The different frequenciesreport we analyse stabilising mechanisms including Landau derivatives in Eq. (1) have to be taken along the particlemodes, are a serious threat to the stability. In the present the velocity distribution normalized to ,If(v)dv = 1. Thethat two·stream instabilities, especially transverse dipole mainly due to the velocity spread U = IUf(g)dv where f(v) ishas been demonstrated by Parkhomchuk and collaborators centre of charge: U = (1/N) EU, or if the dispersion isspread which tends to reduce the cooling force. However, it the motion of a single ion and U the motion of the beamdcsirablc to compensate the space-charge induced velocity vertical (_y) displacement in complex notation, U denotesc.g. by stationary ions produccd from thc residual gas, is respectively, U = x+iy describes the horizontal (x) andCharge ncutralisation of thc cooling cloctron bcam, Here the subscripts e and i refer to electrons and ionsP. Zcnkcvich, ITEP, Moscow, RussiaE. Mustatin, II-IEP, Protvino, RussiaI. Mcshkov and E. Syrcsin, JINR, Dubna, RussiaJ. Bosscr, S. Maury, D. M6h1, and F. Varcnnc, CERN, CH—1211 Gcncva 23COOLING BEAMSTABHJITY CONDITIONS FOR A NEUTRALISED ELECTRONElectron Cooling Beam ..., this conference. OCR Outputthese frequencies we expect strong response. This wasG. Tranquille, F. Varenne, Ncutralisation of the LEARfrequencies are in the 0.1 to 2 MHz region. By exciting atV. Polyakov, A. Smimov, O. Stepashkin, A. Syresin,examples given above that all the characteristic ionR. Maccaferri, S. Maury, I. Meshkov, G. Molinari,applied to a transverse kicker. We observe from the[4] J. Bosser, F. Caspers, M. Chanel, R. Ley,primary e-beam by "shaking" with a pure sine-wave signalInstitute of Physics, Bristol 1993.by this system. It was however possible to obtain a stable [3] M.V. Nezlin, Physics of Intense Beams in Plasmas,we have been unable to stabilise a strongly unstable beam Beam Cooling ..., CERN 94-03, 1994, p.230.The preliminary tests are commented in Ref. [4]. So far Storage Rings with Electron Cooling, Proc. Workshop onbeing applied to a kicker at the other end of the cooler. [2] A.V. Burov, Secondary Particle lnstabilities in thecooling section. It is duly amplified and phase shifted before (Translation of Novosibirsk Preprint 89-116).The signal is taken from a pickup, near one end of the Compensated State, CERN/PS 93-03 (AR), 1993extemal feedback system has been implemented at LEAR. Experimental Investigation of an Electron Beam in"intemal feedback" or the initial perturbations are strong, an V.V. Parkhomchuk, A.A. Sery, V.D. Shiltsev,To suppress the instability in the regime where the [1] A.V. Burov, V.I. Kudelainen, V.A. Lebedev,"SHAKING" VI. REFERENCESIV. EXTERNAL FEEDBACK ANDis required to see whether further improvements are feasible.neutralisation. more detailed analysis of the intemal and extemal feedbackother internal feedback has to be small to ensure stable have been achieved with a neutralisation of up to 40%. ARussia and at the LEAR electron cooler. In addition, any can be expected. Stable electron beams of 0.3 A at 2.8 keVbeen confirmed both at the test—bench at the CAPT in system, have to be included before quantitative agreementand/or clearing of reflected electrons is important This has as well as initial and boundary conditions for the finiteexpect 0t< AI,/l,_ Nevertheless, a high collector efficiency refinements, e.g. the non-linearity of the space—charge fieldsupstream end with the right phase for the growth. Thus we qualitative way - the observations made at LEAR. Severalfraction of the reflected electrons will get back to the The theory sketched above explains - at least in a2 ><l0" if the beam is badly adjusted, but probably only aThe current loss Ale/Ie from the coHector can be as high as V. CONCLUSIONSa very small "intemal feedback" (ot < l/800) is tolerable.of 50 eV, Eq. (7) yields X.-·=2.l, lL=6,7, K=800. Thus only WWconditions (Table 1) and taking an ion temperature 0.5 M0an essential ingredient of the theory described in the presentperturbation taken back to the entrance. For typicalsupports the hypothesis of a large velocity spread which iswhere ot is the "feedback coefficient" i.e the fraction of theremain trapped. The relatively large width of the resonancethe upstream end. Stability of the system requires 0tK S 1several ion species. It appears that ions of (A/Z) = 4 — 6migrating ions themselves can feed the perturbation back tostrong RF signals at the coherent frequencies of one orReflected electrons escaping from the collector or thetool [1,4]. The onset of the instability is accompanied by(cenue to edge) in the electron beam.without extemal excitation is also a powerful diagnosticwhere kATc[eV] = (30/B) Ie [A] is the potential differenceThe response of the beam ion system both with and. . . . , neutralisation section. Thus we estimate 6 = c Wstable at2 2 MT 0 I 0.4field of the trapping electrodes at either end of the Neutralisation with shakingpotential mechanism for this involves the reflections in the fluctuating between 0 - 0.2 I 0.5 - 0.7transverse spread couples into the longitudinal plane. One Neutralisation without shaking(ultra high vacuum) one can (perhaps) assume that this Voltage on trapping elecuodes I 0 I 6 kVCoulomb tield of the electron beam. For a long ion lifetime Electron current 0.3 Ato the transverse energy spread (typically 100 eV) in the Electron ene: 2.8 keVyields a relatively low (S 1 eV) ion temperature comparedTable 2 : An example ofthe effect of shaking(cs) of the ions. Heating due to collisions with the electronsA crucial parameter is the longitudinal velocity spread without shaking ('Table 2).large (A/Z) ensure a high degree of neutralisation 1; . somewhat lower than the one reached during fluctuationsWe conclude that a large spread 0, a large Held B and ions of between zero ("clearing by shaking") and a maximumobtain stable neutralisation at values which could be chosenselectively expelled. In this way we have been able tomT nZ 3° z 2 resonances of ions of the different masses which can thus bediscontinuities at frequencies corresponding to the(substituting wion, wd, ctc. in Eq. (7)) can bc cxpressed as:continued by the experiments. The response showed abruptOCR OutputThe upper limit for the stable neutralisation

Stability conditions for a neutralised electron cooling beam

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