The LHC beam in the SPS is unstable with a threshold almost an order of magnitude below the nominal intensity. The cures used to stabilise this beam against coupled bunch instabilities apart from RF feedback, feed-forward and longitudinal damping, include a fourth harmonic RF system and controlled emittance blow-up. The limitations of the two last methods were studied experimentally and are analysed here from the point of view of beam quality requirements at extraction and future intensity increases up to ultimate value

Shaposhnikova, E

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  EUROPEAN  ORGANIZATION FOR NUCLEAR RESEARCH CERN – A&B DEPARTMENT   CERN-AB-2007-075     Cures for Beam Instabilities in the CERN SPS and their Limitations    E. Shaposhnikova, CERN, Geneva, Switzerland     Abstract   The LHC beam in the SPS is unstable with a threshold almost an order of magnitude below the nominal intensity. The cures used to stabilise this beam against coupled bunch instabilities apart from RF feedback, feed-forward and longitudinal damping, include a fourth harmonic RF system and controlled emittance blow-up. The limitations of the two last methods were studied experimentally and are analysed here from the point of view of beam quality requirements at extraction and future intensity increases up to ultimate value.        Presented at the 39th Advanced Beam Dynamics Workshop (HB2006, Tsukuba, Japan, May 29-June 2, 2006) High Intensity Brightness Hadron Beams.   Geneva, Switzerland   May, 2006 CURES FOR BEAM INSTABILITIES IN THE CERN SPSAND THEIR LIMITATIONSE. Shaposhnikova, CERN, Geneva, SwitzerlandAbstractThe LHC beam in the SPS is unstable with a thresholdalmost an order of magnitude below the nominal intensity.The cures used to stabilise this beam against coupled bunchinstabilities apart from RF feedback, feed-forward and lon-gitudinal damping, include a fourth harmonic RF systemand controlled emittance blow-up. The limitations of thetwo last methods were studied experimentally and are anal-ysed here from the point of view of beam quality require-ments at extraction and future intensity increases up to ul-timate value.LHC BEAM INSTABILITIESThe nominal LHC beam which consists of 4 batches,each of 72 bunches spaced by 25 ns with 1.2×1011/bunch,was obtained at the SPS top energy 450 GeV [1]. Thisbeam sufferers from both single and multi-bunch instabil-ities, which are cured by different methods. The longitu-dinal microwave instability is not observed up to the high-est injected intensities following the shielding of differentmachine elements (2001). The vertical single bunch in-stability due to e-cloud is cured by a scrubbing run andhigh chromaticity. Transverse mode coupling instability,observed recently at injection (26 GeV/c) with small longi-tudinal emittance ε, is expected to have a threshold belowthe ultimate LHC intensity of 1.7 × 1011/bunch for nomi-nal ε = 0.35 eVs. Horizontal multi-bunch instabilities aredamped by the transverse feedback system.The longitudinal coupled bunch instability observed atthe end of the acceleration ramp has the lowest threshold:one batch with 2×1010/bunch is unstable with the RF feed-back, feed-forward and longitudinal damper (low modes)in operation. Possible sources of this instability are thefundamental and HOMs (629 MHz and 912 MHz) of themain 200 MHz RF system. This beam is finally stabilisedby increased synchrotron frequency spread using a fourthharmonic RF system and controlled emittance blow-up.CURES AND THEIR LIMITATIONSHigh harmonic RF systemThe 800 MHz RF system is used from injection throughthe cycle. The total external voltage seen by the particle isVext(φ) = V1 sinφ+ V2 sin(h2φ/h1 + Φ2), (1)where above transition (the case considered below) and fora non-accelerating bucket, Φ2 = pi in bunch-shortening(BS) mode and Φ2 = 0 in bunch-lengthening (BL). Themain limitations of BL mode (which is attractive due to re-duced peak line density) for beam stabilisation in the SPShave been studied [2], [3] and are believed to be (1) verytight requirements on the accuracy of Φ2, difficult to fulfillduring the ramp in the presence of strong beam loading;(2) the region with zero derivative of the synchrotron fre-quency reducing the instability threshold; (3) absence ofself-stabilisation for long bunches. The second limitationalso should appear in the BS mode for sufficiently longbunches; studies continue [3].Controlled emittance blow-upThe controlled emittance blow-up is needed in additionto the high harmonic RF system to stabilise the nominalLHC beam on the flat top (the instability threshold ∝ ε2).This blow-up should be minimal due to the following in-jection into the 400 MHz bucket in the LHC and withoutlosses, tails and bunch to bunch emittance variation.Mismatched voltage at injection leads to emittance blow-up from 0.35 to 0.42 eVs. The technique using band-limited noise [4] introduced through the phase loop of the200 MHz RF system at 260 GeV gives 0.6 eVs. The nom-inal settings for emittance blow-up [5] (excitation at 15.5 sduring 500 ms with fc = 190±15 Hz) are shown in Fig. 1.10012515017520022525027530032535014 14.5 15 15.5 16 16.5 17 17.5 18Time (s)  fs (Hz)ε=0.42 eVs800 MHz off800 MHz bsmfsofsonoiseFigure 1: Noise excitation and synchrotron frequencyspread (low intensity case) at the end of the cycle for bunchof 0.42 eVs with 800 MHz RF system off (two internalcurves) and on (V2 = 700kV) in BS mode.For nominal intensity beam the settings found at low in-tensity should be reduced by∼ 10 Hz due to an incoherent2/4frequency shift produced by the SPS inductive impedanceImZ/n ' 7 Ohm. The problem, which has been discov-ered at the end of 2004 and is analysed below, is the non-uniform emittance blow-up leading sometimes to the insta-bility on the flat top with nominal settings or to particlelosses with increased excitation amplitude or bandwidth.Bunch to bunch variation of the incoherent synchrotron fre-quency due to the residual beam loading can explain theseobservations. The incoherent frequency shift due to induc-tive impedance being a function of bunch distribution alsovaries from bunch to bunch but, even for bunch length vari-ation along the batch of 10%, the effect is much smaller.The bunch position variation along the batch ∆t whichcorresponds in the stable situation to the synchronous phasedisplacement ∆φs = h1ω0∆t, found from bunch pro-files at the start of the controlled emittance blow-up [6],is shown in Fig. 2 for two different cycles. Measurementswere done at 15.5 s (260 GeV/c) for 72 bunches of the firstbatch with nominal intensity. Bunch positions are mainlydefined by the residual beam loading in the 200 MHz Trav-elling Wave RF system in the SPS with feedback and feed-forward system in operation. Patterns only slightly varythrough the cycle and from shot to shot.0 10 20 30 40 50 60 70Bunch number-100-50050100150Dt@psD0 10 20 30 40 50 60 70Bunch number-100-50050100150Dt@psDFigure 2: Bunch positions along the batch before emittanceblow-up at 260 GeV/s for two different cycles. Solid line -mode n = 18 used for calculation of Vind.A zero-amplitude synchrotron frequency for the k-thbunch ω2sk = ω2sk(0), k = 1, ...72, isω2sk = ω2s0 · V′tot(φsk)/(V1 cosφs0), (2)where ωs0 and φs0 are the linear synchrotron frequency andsynchronous phase in the single RF system with a voltageV1. In a double RF system, with intensity effects included,the frequency is defined by the slope of the total voltageVtot(φ) = Vext(φ) + Vind(φ), (3)0 10 20 30 40 50 60 70Bunch number230235240245250255260fs@HzDFigure 3: Synchrotron frequency variation along the batchfound from the measured bunch position variation shownin Fig. 2 (bottom) using Eq. (4).at bunch positions φsk = φs + ∆φsk . The change in syn-chronous phase ∆φsk from its zero-intensity value φs, de-fined by voltage Vext, see Eq. (1), is due to to the inducedvoltage Vind.Let us first estimate the change in frequency due to bunchdisplacement in a double RF system. For the phase be-tween the two RF systems Φ2 = −φs0h2/h1 + pi, the syn-chronous phase in a double RF system φs = φs0. Thisvalue was used in the SPS to programme the phase betweenthe 2 RF systems during the ramp. Then the synchrotronfrequency becomeω2extskω2s0= 1 + ∆φsk tanφs0 +h2V2h1V1cos (h2h1∆φsk + δΦ2)cosφs0.(4)The main contribution is from the high harmonic RF sys-tem, in the single RF system the frequency change wouldbe much smaller. The values fs = ωextsk /(2pi) found fromEq. (4) with phase offset δΦ2 = 0 for bunch positions fromFig. 2 (bottom) are shown in Fig. 3.This synchrotron frequency variation inside the batch al-ready can explain the observed problems with controlledemittance blow-up. However it could be additionally af-fected by the fact that the phase Φ2 most probably hadnonzero offset δΦ2 from the programmed value due to thelack of an absolute phase calibration, aggravated by thebeam loading in the 800 MHz RF system, making phasecontrol even more difficult. This offset leads (for δΦ2  1)to change in φs with opposite signδφs 'δΦ2V2h1V1h1 cosφs0 − V2h2, (5)reducing slightly the total effect on ωs variation. The ex-amples for δΦ2 = ±0.3 are shown in Fig. 4.The induced voltage Vind not only displaces bunchesfrom their zero intensity positions, but also affects the syn-chrotron frequency by a change in the voltage slope. Let usnow try and estimate this effect. The measured ∆φsk  1are connected with values of induced voltage by∆φsk ' −Vind(φs)V ′ext(φs) + V′ind(φs)(6)3/40 10 20 30 40 50 60 70Bunch number230235240245250255260fs@HzD∆Φ2=0.3∆Φ2=-0.3Figure 4: Effect of additional constant phase offsets δΦ2 =±0.3 on synchrotron frequency variation along the batch.Assuming that this voltage is determined by the beam load-ing in the main RF system, we can writeVind(φ) =∑nV˜n cos(φ + nφ/h1 + φn0). (7)The comparison of (7) with the Fourier transform of mea-sured synchronous phase shifts at positions φs + 2piknbb,k = 1, ...72,∆φsk =∑n∆φ˜n cos(2piknbbn/h1 + ψn0) (8)for V˜n  V1,2 gives for induced voltage an estimationof amplitudes V˜n ' −∆φ˜nV ′ext(φs0) and phases φn0 =ψn0 − φs0. Note that due to the bunch spacing nbb = 5,the revolution frequency harmonics higher than h1/nbb cannot be resolved by these measurements. Then the changein synchrotron frequency due to the induced voltage is de-fined by the expressionω2indskω2s0=V ′ext(φs0)V1 cosφs0[1 +∑nαn sin(2piknh1/nbb+ψn0), (9)where αn = (1+n/h1)∆φ˜n. The example for contributionfrom the single harmonic n = 18 is shown in Fig. 5 (top).In reality the frequency variation is the result of all ef-fects analysed above. The example corresponding to mea-sured ∆φs, assumed offset δΦ2 = −0.3 and induced volt-age with a single harmonic n = 18 is shown in Fig. 5 (bot-tom).Unfortunately this bunch-to-bunch synchrotron fre-quency variation is not sufficient itself for beam stability onthe flat top, but being comparable to the noise bandwidth itcan lead to the nonuniform emittance blow-up with tails oreven losses, as observed in the SPS experiments. Since theinduced voltage depends on injected batch structure, thepattern can vary from shot to shot (see Figs. 2). It can beestimated but it would be difficult to take into account inbeam control for blow-up. As can be seen from expres-sions (4) and (9) the frequency variation along the batchduring emittance blow-up can be reduced by operating atthe minimum 800 MHz and maximum 200 MHz voltages,by careful programming of the phase between the two RF0 10 20 30 40 50 60 70Bunch number230235240245250255260fs@HzD0 10 20 30 40 50 60 70Bunch number230235240245250255260fs@HzDFigure 5: Top: change in the synchrotron frequency due tothe induced voltage with a single harmonic n = 18. Bot-tom: the total frequency change corresponding to measured∆φs, assumed δΦ2 = −0.3 and a single harmonic n = 18from induced voltage.systems Φ2 during the ramp and in the longer term by afull feedback around 800 MHz which should provide bet-ter beam-loading compensation.Summary. The limitations of operating the high har-monic RF system, essential for beam stabilisation in theSPS, have been studied both theoretically and experimen-tally [2], [3]. The nonuniform controlled emittance blow-up can be explained by the effect of the residual beam load-ing which creates in a double RF system a significant vari-ation of the incoherent synchrotron frequency from bunchto bunch. Measurements of relative bunch positions at themoment of blow-up allow both the effect from external RFand induced voltage to frequency change to be estimated.Some of the ideas to reduce this effect can be tested withthe LHC beam already this (2006) year.All measurements were done together with T. Bohl,T. Linnecar and J. Tuckmantel. The author is also grate-ful to T. Bohl for providing the data for bunch positionsand to T. Linnecar for useful comments.REFERENCES[1] P. Baudrenghien et al., Proc. PAC 2003, p. 3050.[2] T. Bohl et al., Proc. EPAC 1998, p. 978.[3] E. Shaposhnikova, T. Bohl, T. Linnecar, Proc. PAC 2005,p. 2300.[4] T. Toyama, NIM-A 447 (2000), p. 317.[5] J. Tuckmantel et al., Proc. EPAC 2004, p. 617.[6] T. Bohl, private communication, 2004.4/4

Cures for Beam Instabilities in the CERN SPS and their Limitations

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