During LEP operation in 1995 studies have continued on the subject of synchro-betatron resonances; their strength and their effect on the beam in terms of emittance blow-up. Specifically data is presented on the effect of beam energy on the strength of such resonances

Collier, Paul

Cornelis, Karel

Myers, S

Schmickler, Hermann

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Synchro-Betatron Resonances in LEPP. Collier, K. Cornelis, S. Myers and H. Schmickler,CERN, Geneva, SwitzerlandAbstractDuring LEP operation in 1995 studies have continued onthe subject of synchro-betatron resonances; their strengthand their effect on the beam in terms of emittance blow-up.Specifically data is presented on the effect of beam energyon the strength of such resonances.1 MOTIVATIONThe single bunch intensity in LEP is limited by the Trans-verse Mode Coupling Instability (TMCI) [1]. In order toachieve highest possible bunch currents a high synchrotrontune qsis needed. At one moment during the energy rampthe high synchrotron tune has to be lowered and hence thebeams will cross amongst others the synchro-betatron res-onance 2qs= qv. At 20 GeV beam energy this resonancehas found to be very strong resulting in beam blowup andintensity losses. As a result many ramping schemes havebeen proposed and discussed. During 1995 an experimen-tal program was carried out in order to find at which beamenergy this resonance can safely been crossed.2 ENERGY DEPENDENCE2.1 Measurement ProcedureIn order to measure the strength of a synchro-betatron res-onance the beamsizes and the beam lifetimes have to berecordered as a function of the betatron tunes. This is oneapplication of a measurement procedure in LEP called ”tunescans”. During a tune scan the betatron tunes of LEP arechanged by acting on the main quadrupole strings via a mea-surement sequencer [2]. The available trim range is qh= qv= 0:15 with a resolution of 0.001. The maximumnumber of trim steps is 400 and the time interval betweentune changes is 2 seconds, hence a complete scan takesabout 12 minutes measurement time. Synchronous to thetune variations several beam parameters are recorded. Thetunes themselves are tracked by the LEP q-meter in PLLmode [3]. The transverse beam dimensions are recordedfrom the UV-monitors and beam lifetimes from the bunchcurrent transformers.Fig. 1 shows as example the data obtained at 45.6 GeVbeam energy.Figure 1: Measurement example of a tune scan. The verti-cal beam size is measured as a function of the vertical tune.In the top diagram the data is presented as a function ofthe vertical tune divided by the synchrotron tune. VerticalSBRs show up at integer values in x. In the bottom tracethe same data is displayed as a function of the differencebetween the horizontal and vertical tune normalized to thesynchrotron tune. In this form the coupling resonance andits synchrotron side bands show up at integer x-values.2.2 Previous Experimental ResultsDuring machine studies in 1993 and 1994 we have studiedthe dependence of the vertical synchro-betatron resonanceson the following machine parameters: mean residual vertical dispersion < Dy> offsets in the Rf-cavities chromaticity bunch intensityTwo measurement result, which have already been pub-lished in [4] are recalled, because they are relevant for thediscussion of the energy dependence in the next chapter.Figure 2 shows the strength of the vertical synchro-betatronresonances for different values of the average vertical dis-persion< Dy> and figure 3 for two bump amplitude in theregion of the Rf-cavities (sundelin bumps). Strength of SBRs as Function of Vertical Dispersion0.00.51.01.52.02.53.03.51 2 3 4 5 6Qvinc/QsincVertical Beam Sigma D isp8cmDisp44cmQs Measured = 0.06Figure 2: Tunescans across vertical synchro-betatron reso-nances for 2 different values of the average vertical disper-sion < Dy>. The base line of the second curve has beenshifted upwards in order to make a better distinction of thecurves. Influence of Orbit Displacements in the RF cavities0.00.51.01.52.02.53.03.51 2 3 4 5 6Qvinc/QsincVertical Beam SigmaZero Sundelin Bumps200uA10mm SundelinBumps 200uAQs Measured = 0.06Figure 3: Tunescans across vertical synchro-betatron reso-nances for 2 different orbit bumps (called sundelin bumps)in the region of the LEP Rf-cavities. The base line of thesecond curve has been shifted upwards in order to make abetter distinction of the curves.2.3 Driving MechanismsThe driving mechanism for the excitation of synchro-betatron resonances are discussed for example in [5].From [5] we recall the formulae describing the growth rateof the resonance for the following two driving mechanisms:1. For the case of dispersion (Dy) at the accelerating cav-ities one can write:<ddt> =qsfrevDyy^^EE(1)as ^EEincreases with beam energy one would expectthe strength of the synchro-betatron resonances to in-crease with energy2. For the case of transverse deflecting fields which varywith longitudinal position, such as misaligned Rf-cavities or orbit offsets in the Rf-cavities one canwrite:<ddt> =ec22E2tQsZEysdt^y0^EE(2)In this case the strength of the resonance will decreasewith beam energy due to the term EQsin the denom-inator.The question which are the relevant driving mechanism forLEP is answered by the measurements described in the nextchapter.2.4 Measurements on the qv= 2  qssateliteIn order to measure the energy dependence of a synchro-betatron resonance each other parameter affecting theirstrength (see above) had to be kept constant while the en-ergy of the beams was variied.The followingexperiment was carried out: 200A bunchcurrent was accumulated into a single positron bunch. Bymeans of closed orbit corrections < Dy> was adjusted toabout 10 cm and the horizontal and vertical chromatictieswere set to +2 units.In all cases the strength of the vertical SBR qv= 2  qswas measured by tune scans.The 200 A bunch was ramped from 20 GeV to the fol-lowing beam energies: 28.5 GeV, 37.1 GeV and 45.6 GeV.At each energy the orbit was corrected towards the referenceorbit establised at 20 GeV. This way the residual vertical dis-persion< Dy> was controlled and reproduced within val-ues of 7 to 11 cm. The chromaticities were adjusted in eachcase to +2 units. The data points just arround the verticalSBR 2qs= qvwere extracted and a resonance curve was fit-ted to the data.Figure 4: Beam blow up as measured on the vertical SBRqv= 2  qsat 28.5 GeV beam energy. The solid curve is aresonance curve fit to the data.Fig. 4 shows the result at 28.5 GeV beam energy. Thedata obtained at the four beam energies is summarized infig. 5. The top graph shows the measured emittance blowupcalculated as the square of the measured blowup in beamsize and the bottom graph shows the width of the resonance(in units of tune). The data indicates clearly that the strengthof the satelite qv= 2  qsgrows with energy.3 CONCLUSIONThe measurements have shown that the strength of thesynchro-betatron resonances in LEP increases with beamenergy, in terms of emittance blowup as well as in resonancewidth. From this we have to conclude that residual disper-sion at the Rf-cavities is the dominant driving term at LEP.For running LEP at beam energies around 90 GeV thisleaves less space for the working point of the machine asnot to affect the small vertical emittance due to the increasedwidth of the synchro-betatron resonances.If the observed beam blowup was strictly linked to inten-sity losses the consequence for the acceleration scheme ofLEP would be to cross synchro-betatron resonances at en-ergies as low as possible. But the effect of lifetime reduc-tion could not been included in the above tune scan measure-ments and has been treated in different measurements [6].Here the result was that at 20 GeV beam energy the reso-nance qv= 2  qscauses significant intensity losses, butabove 35 GeV beam energy the resonance could be crossedsafely with 500 A bunch currents.Figure 5: Emittance blowup at the vertical SBR 2qs= qvasa function of beam energy (top diagram) and width of thisresonance (bottom diagram)4 REFERENCES[1] K. Cornelis, How can we get 1 mA per Bunch at 20 GeVProceedings of the 5th Chamonix Workshop on LEP Perfor-mance, Jan. 13-18, 1995, p 71.[2] H. Schmickler,Tune Scans in LEPProceedings of the 2nd European Workshop on Beam Diag-nostics (DIPACII) in Travemu¨nde, DESY Report M-95-07[3] K. Lohmann, M. Placidi and H. SchmicklerQ-Monitoring in LEP, LEP-BI Note 88-45.[4] S. Myers, Measurements of the Parameter DependenceofSynchro-Betatron Resonances in LEPProceedings of the International Workshop on Particle Dy-namics in Accelerators,Madeira 1995, KEK Report 95-7, p 97.[5] S. Myers, Synchro-Betatron Resonance Excitation inLEPProceedings of the IEEE Particle Conference, Washington,D. C., March 16-19, 1987 and references therin.[6] H. Schmickler, Can we finally stop talking about crossingSynchro-Betatron resonances during the Ramp?Proceedings of the 6th Chamonix Workshop on LEP Perfor-mance, Jan. 15-19, 1996, p 58.

Synchro-Betatron Resonances in LEP

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