Fujieda, M

Hashimoto, Y

Mori, Y

Muramatsu, R

Ohmori, C

Sato, Y

Takagi, A

Uesugi, T

Yamamoto, M

Yoshii, M

CERN Document Server

BEAM LOADING EFFECTS ON HIGH GRADIENT MA-LOADED CAVITYM. Yamamoto, M. Fujieda, Y. Hashimoto, Y. Mori, R. Muramatsu,C. Ohmori, Y. Sato, A. Takagi, T. Uesugi, M. Yoshii KEK-Tanashi, JapanAbstractWe studied the beam loading effects on the High GradientCavity(HGC) loaded with Magnetic Alloy(MA) by multi-particle tracking simulation. The Q-Value of the cavity isvariable from 0.6 to more than 10. From the view pointof multi-bunch effect, it was found that either very highQ-value or low Q-value was preferable to suppress the pe-riodic transient beam loading. The experimental results ofthe beam loading compesation using an electron beam arealso described.1 INTRODUCTIONWe have developed a HGC loaded with MA and achievedthe high accelerating field gradient of 50 kV/m [1]. TheHGC has some advantages such as the variable Q-value,high stability at the large rf amplitude and realizing low to-tal impedance. Because of these merits, the aspects on thebeam loadings are different from that of ordinary ferrite-loaded cavity especially on the transient effect and bucketdistortion.So far, smallR=Q of the cavity, that is, increasing the Q-value has been prefered to cure the transient beam loadingeffect. However the particle tracking simulation shows thatthe transient effect becomes only a single bunch problemin the low-Q cavity, while it is a multi-bunch effect in thehigh-Q one. For the HGC, there are two choices to suppressthe transient effect because the Q-value of the MA can bechanged using radial cut core [2].On the single bunch effect, the beam-induced voltageis composed of both fundamental frequency and higherharmonics in the low-Q cavity although the high-Q cav-ity has only fundamental component. However the higherhamonics can be quickly controlled in the low-Q cavity be-cause of the broad-band impedance. In order to study thebeam loading effect, an electron-gun and one-path beamline were prepared. Then, the beam-induced voltages up to3rd higher harmonics were significantly compensated bythe beam signal feedback method.2 PERIODIC TRANSIENT BEAMLOADINGIn the previous paper [3], the results of the particle track-ing simulation under the periodic transient beam loadingwere shown, and it was found that very low-Q or veryhigh-Q were preferable to avoid the periodic transient beamE-mail: masanobu@tanashi.kek.jploading. It is seemed that the transient effect is most se-vere around Q  h=2. It is understood qualitatively thatwhen the cavity damping time is near the revolution fre-quency, that is, 2Q=h!rev 1=!rev, then the differenceof the wake field on each bunch will be largest. It meansQ  h=2.The simulation results under the periodic transient beamloading were shown in [3], where 8 of 17 buckets wereoccupied by the bunch and the others were empty. Simula-tions for 4 bunches in the 10 buckets and 2 bunches in the 5buckets were newly performed in the same ring parametersexcept the harmonic number. Number of the particle perbunch is same in all Q value, 1.251013, and cavity shuntimpedance is 6 k.Trajectory of Bunch Center-0.002-0.00100.0010.0020 20 40φ(Deg.)dp/p Q=16 kΩ-0.002-0.00100.0010.0020 20 40φ(Deg.)dp/p Q=26 kΩ-0.002-0.00100.0010.0020 20 40φ(Deg.)dp/p Q=56 kΩ-0.002-0.00100.0010.0020 20 40φ(Deg.)dp/p Q=106 kΩ-0.002-0.00100.0010.0020 20 40φ(Deg.)dp/p Q=206 kΩFigure 1: Trajectory of the bunch center in the longitudinalphase space (harmonic number 10, 4 bunches).Trajectory of Bunch Center-0.002-0.00100.0010.0020 20 40φ(Deg.)dp/p Q=16 kΩ-0.002-0.00100.0010.0020 20 40φ(Deg.)dp/p Q=26 kΩ-0.002-0.00100.0010.0020 20 40φ(Deg.)dp/p Q=36 kΩ-0.002-0.00100.0010.0020 20 40φ(Deg.)dp/p Q=56 kΩ-0.002-0.00100.0010.0020 20 40φ(Deg.)dp/p Q=106 kΩ-0.002-0.00100.0010.0020 20 40φ(Deg.)dp/p Q=206 kΩFigure 2: Trajectory of the bunch center in the longitudinalphase space (harmonic number 5, 2 bunches).In Fig. 1 and 2, each line shows a trajectory of a bunchcenter in the longitudinal phase space. Vertical axis andhorizontal axis are momentum difference and the phase0-7803-5573-3/99/$10.00@1999 IEEE. 860Proceedings of the 1999 Particle Accelerator Conference, New York, 1999measured from the nominal synchronous particle, respec-tively.Each bunch is oscillated apart from a locked phase ofthe -feedback by the transient effect. In case of h = 10,increasing Q up to 5, the oscillation of each bunch centerbecomes larger. And increasing Q further, the oscillationbecomes smaller again. In the same manner, the oscillationbecomes largest around Q = 2  3 in case of h = 5.In the longitudinal motions of multi-bunches includingthe energy loss by the wake field, the arrival time of m-thbunch on the cavity, ^m, is expressed by the perturbativetheory as;^m= ~m+ m(1)where mand ~mare a perturbation and an equilibriumpart, respectively. For the equilibrium part, ~mis definedthat the energy gain of the bunch by the cavity gap voltageis equal to the energy loss by the wake field;eV0sin(!rf~m) =XW (t); (2)where W (t) is the wake function, and the summation isperformed for the past turns and all bunches. In the peri-odic transient beam loading, ~mbecomes different value oneach bunch.In order to calculate ~msimply even under the periodictransient beam loading condition, the assumption which thewake field affects only one turn is employed, and resonanttype impedance is assumed. Figure 3 shows the calculationresult of Eq. (2) in the case of 2 bunches m = 0; 1 filled inthe 4 buckets.Equilibrium Time Difference(h=4,NB=2)024681012140 2 4 6 8 10 12Qτ 1-τ 0 (ns)Figure 3: Difference of the equilibrium time ~min the caseof 2 bunches in the 4 buckets.The difference between the equilibrium time ~0and ~1islargest around Q  2:5, and it is near the suggestion by thesimulation, Q  h=2.3 THE EXPERIMENT OF BEAMLOADING COMPENSATIONIn order to investigate the beam loading effects on theHGC, the beam test using electron has been performed.The detail of the electron gun and its setup are describedin [4]. In the low-Q cavity, since the bucket distortion bythe higher hamonics of the beam-induced voltage is severeproblem, the beam loading compensation by the beam sig-nal feedback has been considered.The beam signal picked up by a Fast Current Trans-former is attenuated and delayed by cable line arbitrary,then fed into the cavity through amplifiers. When the at-tenuation and delay can be optimized, it is expected thatthe wake voltage is compensated clearly.The simple scheme of the beam loading compensationwas already demonstrated using the electron beam, wherethe beam signal was simply returned to the amplifier, andit was effective for compensating the one component ofthe beam-induced voltage [3]. In order to compensate thehigher harmonics of the beam-induced voltage as well, thebeam signal was separated into each harmonic and the ad-justment were done for them, then each signal were com-bined and fed into the cavity. The setup of the filtering thebeam signal is shown in Fig. 4. In this experiment, up tothe 3rd higher harmonics of the beam signal were returnedto the cavity.Low PassFilter3 MHzCableDelayVariableAttenuatorFilterBand Pass6 MHz9 MHzCombinerCombinerBeamSignalDividerDividerCableDelayCableDelayto Amp.VariableAttenuatorVariableAttenuatorFilterBand PassFigure 4: The setup of filtering the beam signal.The measured voltage of the cavity gap without com-pensation and with compensation are shown in Fig. 5-(a)and -(b), respectively, and frequency spectrum is shown inFig. 6, white bar is the spectrum without compensation,and black one is the spectrum with compensation. In thisFourier analysis, ten bunches were counted by a period. Asclearly seen in Fig. 6, the fundamental component of thegap voltage became about one hundredth. The second andthe third higher harmonic also became one tenth and onefourth, respectively.Gap Voltage-600-400-20002004006001 2 3 4 5 6 7 8Time(µsec.)Gap Voltage(V)Without Compensation(a)-600-400-20002004006001 2 3 4 5 6 7 8Time(µsec.)Gap Voltage(V)With Compensation(b)Figure 5: The measured gap voltage with compensationand without compensation.861Proceedings of the 1999 Particle Accelerator Conference, New York, 1999Spectrum of the Gap VoltageMultiple of RF Freq.Gap Voltage Fourier Coeff.Without CompensationWith Compensation0204060801001201401600 1 2 3 4 5Figure 6: The spectrum of the gap voltage.In order to study the transient effect, the beam which hassome missing bunches is prepared. the test will be done bythe variable-Q HGC.4 SUMMARYBeam loading effects on HGC were investigated, especiallyfor the periodic transient beam loading. From the results ofparticle tracking simulation and analytic calculation, it wasfound that the Q-value around a half of a harmonic numbershould be avoided.The experiment of the beam loading compesation by thebeam signal feedback were done with filtering the beamsignal, then three harmonics of the beam-induced voltagewere cleary compensated.5 REFERENCES[1] C. Ohmori et al., ' High Field-Gradient Cavities Loaded withMagnetic Alloys for Synchrotrons, in this conf., 1999[2] Y. Mori et al., ' A New Type of RF Cavity for High Inten-sity Proton Synchrotron using High Permeability MagneticAlloy' , p299-p301, Proc. of EPAC98, 1998[3] M. Yamamoto et al., ' Beam Loading Effects in JHF Syn-chrotron' , Proc. of APAC98, p399-402, 1998[4] Y. Hashimoto et al., ' Beam Loading Experiment with ShortBunched Electron Beams for New Type of AcceleratingRF System of High Intensity Proton Synchrotron, Proc. ofEPAC98, p1770-1772, 1998862Proceedings of the 1999 Particle Accelerator Conference, New York, 1999

Beam Loading Effects On High Gradient Ma-loaded Cavity

Beam Loading Effects On High Gradient Ma-loaded Cavity

Abstract

Similar works

Full text

Available Versions

CERN Document Server