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1、INTRODUCTIONThestructureisshowninthefollowing.Laserisincidentabovetheslot.Planewaveofthelaserfieldistransferredintoacceleratormodeintheacceleratorcavity.Thewayofestimatingtheacceleratingcapabilitywithoutconsideringbeamwillbetalkedaboutinthefollowing,includingtheQan
2、dtheenergytransfercoefficientofthestructure.DISCUSSABOUTTHEACCELERATINGCAPABILITYWhenanbeaminteractwithlaserfieldwithinthecavityoftheabovestructure,wehavetheenergybalanceequation,Eq.1Wheretheisthetotalpowerfromthelasersource,thepowerreflectedbackintheincidentdirect
3、ion,thepowerlostbythecomplexpermittivity,thepowertransmitthestructure,andthepowertransferredtothebeam.Weneglectthethepowerradiatingtospaceonotherdirectionsandthepowerintonon-acceleratingmodes.isthedecreasedpowerofthedepositedenergyofthecavity.Thehastwosections,Eq.2
4、isthepowerreflectedthestructureitself,andisthepowerreflectedbyoverflow.Thatmeans,ifweputanintensepowerabsorberinthecavitythewillbebecamezero,butthewillnotchange.Whenisnotzero,shouldbezero.Andwedefineasthepowerfluxfromthespacetothecavity,wehave,Eq.3Eq.4So,therearetw
5、ostates.Oneisthatthetransferredpowertothebeamislessthanthe,thenetpowertorechargethecavity.Theanotheristhatthetransferredpowertothebeamisbiggerthanthe.Andtheinteractionshouldborrowdepositedenergyfromthecavitytogiveittobeam.A.STABLESTATEWheninbalancestate,the.Atthiss
6、tate,thedepositedenergyofthecavityisstable.Andtheacceleratingelectricfieldamplitude,Eo,isstablealso,ifweneglectthewakefieldandthebeamloadingeffect.TheacceleratingelectricfieldEzcanbeexpressedas,()Eq.5Theenergytransferredtobeamis,∫()Eq.6Wecanexpresstimeasdistance,∫E
7、q.7Wecansetbezero.Thenwehave,∫∫()Eq.8Forsimplicity,weassumethechangeofthevelocityofbeamissmall,andweapproximatethebeamvelocityasc.Thenwehave,∫()∫()Eq.9Weassumetheiszero.Integratetheaboveequation,wehave,Eq.10Thetotaltimeoftheinteractionis,Eq.11Andtheis,Eq.12Wecanrel
8、atethedepositedenergyinthecavitywiththeacceleratingelectricfieldas,Eq.13Whereisthedepositedenergywithoutbeam.IfwedefineaQas,Eq.14Andwehave,()Eq.1
