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1、BeamcavityinteractionA.GampDeutschesElektronen-SynchrotronDESY,Hamburg,GermanyAbstractWebeginbygivingadescriptionoftherfgenerator–cavity–beamcoupledsystemintermsofbasicquantities.Takingbeamloadingandcavitydetuningintoaccount,expressionsforthecavityimpedanceasseenbythegeneratorandasseenbythebeama
2、rederived.Subsequentlymethodsofbeam-loadingcompensationbycavitydetuning,rffeedback,andfeed-forwardaredescribed.Examplesofdigitalrfphaseandamplitudecontrolforthespecialcaseofsuperconductingcavitiesarealsogiven.Finally,adedicatedphaseloopfordampingsynchrotronoscillationsisdiscussed.1.IntroductionI
3、nmodernparticleacceleratorsrfvoltagesinanextremelylargeamplitudeandfrequencyrange,fromafewhundredvoltstohundredsofmegavoltsandfromsomekHztomanyGHz,arerequiredforparticleaccelerationandstorage.Therfpower,whichisneededtosatisfythesedemandscan,forexample,begeneratedbytriodes,tetrodes,klystrons,orby
4、semiconductordevices.ThecwoutputpoweravailablefromsometetrodeswhichwereusedatHERApis60kWat208MHzandupto800kWforthe500MHzklystronsforthenewsynchrotronlightsourcePETRAIII.The1.3GHzklystronsfortheFree-ElectronLaserFLASHatDESYcandeliverupto10MWrfpeakpowerduringpulsesofabout1mslength.Evenhigherpowerl
5、evelscanbeobtainedfromS-andX-bandklystronsduringpulselengthsonthemsscale.SuchrfpowergeneratorsgenerallydeliverrfvoltagesofonlyafewkVbecausetheirsourceimpedanceortheiroutputwaveguideimpedanceissmallascomparedtotheshuntimpedanceofthecavitiesintheaccelerators.Typically,atetrodehasitshighestefficien
6、cyforaloadresistanceoflessthanawhereasthecavityshuntimpedanceusuallyisoftheorderofseveralThisistherealimpedance,whichthecavityrepresentstoageneratorattheresonantfrequency.Itmustnotbeconfusedwithohmicresistances.Optimumfixedimpedancematchingbetweengeneratorandcavitycaneasilybeachievedwithacouplin
7、gloopinthecavity.Thereis,however,thecomplicationthatthetransformedcavityimpedanceasseenbythegeneratordependsalsoonthesynchronousphaseangleandonthebeamcurrentandisthereforenotconstantaswewillshowquantitatively.Thebeamcurrenti