To study possible cures for multi-bunch instabilities observed with the present high intensity proton beam in the SPS, a fourth harmonic RF system was used during acceleration in bunch lengthening and bunch shortening modes of operation. The latter mode was found to be more efficient in controlling beam stability. We present an analysis of possible reasons

Bohl, T

Linnecar, Trevor Paul R

Shaposhnikova, Elena

Tückmantel, Joachim

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHCERN    SL DIVISIONGeneva, SwitzerlandJune, 1998CERN SL-98-026   RFStudy of Different Operating Modes of the 4th RFHarmonic Landau Damping System in the CERN SPST. Bohl, T. Linnecar, E. ShaposhnikovaAbstractTo study possible cures for multi-bunch instabilities observed with the present highintensity proton beam in the SPS, a fourth harmonic RF system was used duringacceleration in bunch lengthening and bunch shortening modes of operation. The lattermode was found to be more efficient in controlling beam stability. We present ananalysis of possible reasons.Presented at EPAC-98, 6th European Particle Accelerator ConferenceStockholm22-26 June 1998Study of Different Operating Modes of the 4th RF Harmonic Landau DampingSystem in the CERN SPST.Bohl, T.Linnecar, E.Shaposhnikova, J.Tu¨ckmantel, CERN, Geneva, SwitzerlandAbstractTo study possible cures for multi-bunch instabilities ob-served with the present high intensity proton beam in theSPS, a fourth harmonic RF system was used during accel-eration in bunch lengthening and bunch shortening modesof operation. The latter mode was found to be more effi-cient in controlling beam stability. We present an analysisof possible reasons.1 INTRODUCTIONThe SPS accelerator will be used as the injector for theLHC at present being constructed at CERN. At extractionto the LHC, 450 GeV, the longitudinal emittance of thebunches should be below 0.7 eVs, only 0.2 eVs above theinjected value. One area of concern in satisfying this re-quirement is due to multi-bunch instabilities already ob-served in the SPS on the fixed target beam.The fixed target cycle in the SPS accelerates protonsfrom 14 GeV to 450 GeV crossing transition at 22 GeV.This is done with a 200 MHz RF system (harmonic num-ber h=4620). Normally 10/11 of the ring are filled bybunches in every bucket with a maximum total intensityof 4:8 1013 protons.Beam with parameters close to those required for LHCwill be injected into the SPS for the first time at the endof 1998. We have used the existing fixed target proton cy-cle, which has similar intensity but different filling patternsin the machine, to study multi-bunch instabilities and theirpossible cures.2 OBSERVATION OF MULTI-BUNCHINSTABILITIESMulti-bunch instabilities are observed at injection and to-wards the end of the cycle, [1]. We see bunch shape os-cillations (different multipoles, from dipole to octupole,depending on cycle time and intensity) together with thegrowth of a wide band beam spectrum (see Fig.1) whichreaches maximum amplitude on the flat top.As a result of these instabilities, at maximum intensitythe longitudinal emittance increases by almost a factor 10(from 0.2 eVs to 2 eVs), filling completely the bucket. Re-ducing the voltage at any single point in the cycle immedi-ately leads to beam loss.At the moment the source of these instabilities is notclear but most likely is a mixture of the effect of 800 vac-uum ports (which will be shielded during the next 3 years)and higher order modes in the five different RF systems ofthe SPS.Figure 1: Beam spectrum from 0 to 2 GHz at 30 GeV with-out 800 MHz RF system (lower trace, left photo), with800 MHz RF system in BL (upper trace in both photos)and BS (lower trace, right photo) mode.We tried to cure these instabilities by increasing the syn-chrotron frequency spread and therefore Landau damping.We first studied the possibility of increasing the syn-chrotron frequency spread in the bunch by modifying thevoltage programme for the main RF system, [1]. By gradu-ally decreasing the voltage after transition we were able toarrive at the flat top with smaller emittances (1.4 eVs) thanfor normal operation, where the voltage amplitude aftertransition crossing is kept at its maximum value. Howeverbunch to bucket transfer to LHC requires short bunches(< 1:7 ns) and therefore an increase of voltage before ex-traction. In this case emittance was also increasing, practi-cally filling all space available in the bucket.Below we consider the effect on Landau damping of theparameters of the higher harmonic RF system assumingthat the voltage amplitude of the main RF system is fixed(in our case it was at the maximum value 6 MV).For studies we used the existing fourth harmonic(800 MHz) RF system in bunch shortening (BS) and bunchlengthening (BL) modes of operation. Surprisingly in thelatter case we not only did not observe any improvement inbeam stability, but even some degradation, see for examplethe left photo in Fig.1.Our difficulties in applying BL mode are similar to ex-perimental experience in HERA, [2], where only BS modeis used for operation. Problems of operation in BL modehave also been faced in other machines, [3]. Below weconsider possible reasons applicable to the SPS and mayberelated to other accelerators as well.3 EFFECT OF SECOND RF SYSTEMIn the double harmonic RF system the total voltage seen bythe particle has the formV = V1sin+ V2sin (n+2); (1)where V1and V2are the voltage amplitudes of the mainand high frequency RF systems, n is the ratio of harmonicnumbers of the two RF systems (in our case n=4) and 2isthe phase shift measured in radians at the higher frequency.3.1 Zero amplitude synchrotron frequencyIn action-angle variables the synchrotron frequency is afunction of the action J . The synchrotron frequency spread!sin a bunch of emittance " = 2Jbcan be definedas the maximum of [!s(0)   !s(J)] for J  Jb. For amonotonic dependence of !s(J), !s= !s(0)   !s(Jb).For a full bucket !s(Jb) = 0. One usually expects thatthe synchrotron frequency spread in a double RF system ismodified significantly in comparison with a single RF sys-tem if the synchrotron frequency at the center of the bunch!s(0) is also changed significantly from its previous value!s0(0). There are two possibilities, either it is reduced orincreased. Due to the effect on bunch length they are calledcorrespondingly bunch lengthening (BL) and bunch short-ening (BS) modes of operation. In the first case the maxi-mum change is obtained when the synchrotron frequency atthe center of the bunch is zero. Together with the require-ment of a quartic potential well at the bunch centre, this iswhat is usually called bunch lengthening mode in the liter-ature, [4]. We will call this special case BLM mode.In a double harmonic RF system!2s(0) =!2s0(0)coss0[coss+ n cos (ns+2)]; (2)where  = V2=V1and the synchronous phase sis con-nected with the synchronous phase in the single RF systems0by the equationsins0= sins+  sin(ns+2): (3)For a given value of V2one can find the phase shift m2,which gives the maximum change in !s0(0), and determinethe new synchronous phase ms. Let us assume that thechange in synchronous phase ms= ms s0 1, thenms=  s tans0n coss0+ s; (4)where s = sgnfcos (ns+2)g (s=1 for BL regime abovetransition and for BS below). The appropriate phase shiftm2can be easily calculated from eq.(3). Above transitionthis ism2=  ns0  nms+arcsin ; BL   arcsin ; BS (5)where  = s sins0n coss0+s. The opposite is true below transi-tion. As one can, see for a stationary bucket (sins0= 0)the maximum change is obtained when s= s0, and thenm2equals zero or .For the proton cycle in the SPS, ms 1 is valid ev-erywhere except very close to transition. We used formula(5) to programme the phase of the second RF system dur-ing acceleration for BL and BS modes of operation. Thenthe change in zero amplitude synchrotron frequency is:!ms(0)!s0(0)= [1+sncoss0(1+0:5 tan2s0n2+ sn= coss0)]1=2: (6)From this consideration it follows that for a given valueof V2, for n  1 and small changes of !s0(0), BL andBS modes should have a similar effect. Indeed, in this case!ms(0) ' !s0(10:5n= coss0). For larger values of thevoltage V2, such that n  1, in BLM mode the change incentral synchrotron frequency can be as big as !s0. For thesame value of V2in BS mode this gives only a factorp2increase in !s0(0).2-0.2 -0.1 0.1 0.2345678!s(0)=!s0(0)-0.2 -0.1 0.1 0.20.20.40.60.811.21.4sFigure 2: Phase shift 2and corresponding normalisedsynchrotron frequency !s(0)=!s0(0) as a function of syn-chronous phase shift sfor s0= 2:45, n = 4 and = 0:08 (dashed line) and  = 0:188 (solid line).In Fig.2 we show !s(0)=!s0(0) as a function of changein synchronous phase stogether with the phase shift2, which provides this change in synchronous phase, forn = 4 and s0= 2:45, the typical value for a large part(after transition crossing) of the cycle. The value  = 0:08was used in our experimental studies and  = 0:188 cor-responds to BLM mode. The latter can be found for givens0and n from equation, [4]:2=1n2 sin2s0n2  1: (7)Upper parts of the curves in Fig.2 correspond to BS andlower to BL modes. As one can see the region of 2givingBS mode is much wider than for BL mode.3.2 Frequency spread in BL and BS modesNow let us consider the results of the choice of regime ofoperation of the second RF system on the synchrotron fre-quency spread inside the bunch.In Fig.3 the normalised synchrotron frequency spread!s= [!s(0)   !s(Jb)]=!s0(0) in a bunch with longi-tudinal emittance of " = 2Jb= 0:3 eVs is presented asa function of 2for the 2 different values of voltage am-plitude used in Fig.2. In Fig.4 the synchrotron frequencyis shown as a function of action Jbnormalised to bunchemittance, for the same values of V2as in Fig.3, 1.15 MV(solid line) and 0.5 MV (dashed line), and the phase shifts2, which give maximum spread for V2= 1:15 MV in BLand BS modes.-1-0.8-0.6-0.4-0.200.20.40.60.810 1 2 3 4 5 6phase shift φ2 (rad)∆ωs/ωsoε=0.3 eVsV1=6.1 MVV2=0.5 MVV2=1.15 MVV2=0φso=2.45 radFigure 3: Normalised synchrotron frequency spread insidethe bunch of 0.3 eVs emittance for 2 different values ofvoltage amplitude V2as a function of phase shift 2.00.20.40.60.811.21.40 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.452pi J  (eVs)ωs/ωsoV1=6.1 MVV2=0.5 MVV2=1.15 MVV2=0φso=2.45 radφ2=2.76 radφ2=5.5 radFigure 4: Normalised synchrotron frequency as a functionof action normalised to emittance in a double harmonic RFsystem for BL and BS operation modes.For V2= 0:5 MV the spread produced in BS mode is afew times bigger than in BL mode. What is also important,in BS mode the spread continues to grow with increasingemittance, so that after reaching the instability thresholdthe bunch has a chance for self-stabilization by emittanceblow-up. This explains very well experimental results inthe SPS (see Fig.1), where no improvement in beam stabil-ity was observed in BL mode with low amplitudes of V2.For this emittance of 0.3 eVs the optimum phase shifts2in BL and BS modes are very close to values m2ob-tained from consideration of maximum change in !s0(0),(see Fig.2). For BS mode the optimum phase shift 2, giv-ing maximum spread for given V2, depends also on bunchemittance. In this example, for smaller emittances the op-timum phase shift in BS mode decreases (for " = 0:1 eVsthis would be 2= 4:5). However due to the quite flatdependence of spread on 2in BS mode this is not veryimportant for operation.For the higher value of V2the spread produced in BLmode becomes larger and larger while the region of phaseshifts where it works gets smaller. In Fig.3 one can imme-diately notice the extremely narrow region in phase shift2which gives a significant spread in BL mode.Another important point concerning stability in the dou-ble harmonic RF system is related to the creation of regionswhere the derivative of synchrotron frequency !0s(J) = 0,see Fig.4. The instability threshold for bunches with emit-tance reaching this region equals zero, [5]. Landau damp-ing for particles in this region is lost and instability grows/pt. Measurements of bunched beam transfer functionsdone by noise excitation in the SPS on an intermediate flattop at 120 GeV with the double RF system in BL and BSmodes, [6], showed in the first case a strong coherent signalwith an amplitude 3 times larger than in the cases of a sin-gle RF system or double RF system in BS mode. This prob-ably can explain the fact that beam stability when using BLmode was not improved but even degraded in comparisonto the single RF system, see Fig.1.This analysis shows that for producing the maximumsynchrotron frequency spread BLM mode has an advan-tage only for bunches with very small emittances (in com-parison with bucket area), see Fig.4, and the requirementof extremely accurate programming of phase shift between2 RF systems during the cycle is the price to pay. In theabsence of space charge effects and any requirements onbunch length increase, the regime of bunch shortening ismore efficient and much easier to handle.We are grateful to D.Boussard for comments on this pa-per and to U.Wehrle for hardware preparation.4 REFERENCES[1] T.Bohl et al, CERN SL-MD Notes 239, 246 and 258, 1997.[2] F.Willeke, private communication[3] J.M.Baillod et al, IEEE Trans. Nucl. Sci., NS-30, p.3499,1983.[4] A.Hofmann, S.Myers, Proc. 11th Int. Conf. on High-EnergyAccelerators, Geneva, 1980, p.610.[5] V.I.Balbekov, S.V.Ivanov, Atomnaya Energiya 62 (2), p.98,1987.[6] T.Bohl et al, CERN SL-MD Note 1998, to appear.

Study of Different Operating Modes of the 4th RF Harmonic Landau Damping System in the CERN SPS

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