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1、INTRODUCTIONThestructureisshowninthefollowing.Laserisincidentabovetheslot.Planewaveofthelaserfieldistransferredintoacceleratormodeintheacceleratorcavity.Thewayofestimatingtheacceleratingcapabilitywithoutconsideringbeamwillbetalkedaboutinthefollowing,inclu
2、dingtheQandtheenergytransfercoefficientofthestructure.DISCUSSABOUTTHEACCELERATINGCAPABILITYWhenanbeaminteractwithlaserfieldwithinthecavityoftheabovestructure,wehavetheenergybalanceequation,Eq.1Wheretheisthetotalpowerfromthelasersource,thepowerreflectedbac
3、kintheincidentdirection,thepowerlostbythecomplexpermittivity,thepowertransmitthestructure,andthepowertransferredtothebeam.Weneglectthethepowerradiatingtospaceonotherdirectionsandthepowerintonon-acceleratingmodes.isthedecreasedpowerofthedepositedenergyofth
4、ecavity.Thehastwosections,Eq.2isthepowerreflectedthestructureitself,andisthepowerreflectedbyoverflow.Thatmeans,ifweputanintensepowerabsorberinthecavitythewillbebecamezero,butthewillnotchange.Whenisnotzero,shouldbezero.Andwedefineasthepowerfluxfromthespace
5、tothecavity,wehave,Eq.3Eq.4So,therearetwostates.Oneisthatthetransferredpowertothebeamislessthanthe,thenetpowertorechargethecavity.Theanotheristhatthetransferredpowertothebeamisbiggerthanthe.Andtheinteractionshouldborrowdepositedenergyfromthecavitytogiveit
6、tobeam.A.STABLESTATEWheninbalancestate,the.Atthisstate,thedepositedenergyofthecavityisstable.Andtheacceleratingelectricfieldamplitude,Eo,isstablealso,ifweneglectthewakefieldandthebeamloadingeffect.TheacceleratingelectricfieldEzcanbeexpressedas,()Eq.5Theen
7、ergytransferredtobeamis,∫()Eq.6Wecanexpresstimeasdistance,∫Eq.7Wecansetbezero.Thenwehave,∫∫()Eq.8Forsimplicity,weassumethechangeofthevelocityofbeamissmall,andweapproximatethebeamvelocityasc.Thenwehave,∫()∫()Eq.9Weassumetheiszero.Integratetheaboveequation,
8、wehave,Eq.10Thetotaltimeoftheinteractionis,Eq.11Andtheis,Eq.12Wecanrelatethedepositedenergyinthecavitywiththeacceleratingelectricfieldas,Eq.13Whereisthedepositedenergywithoutbeam.IfwedefineaQas,Eq.14Andwehave,()Eq.1
