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Ú26íÚ1ÚßÜïíëËïíV01.26,No.12002ê1ÂHIGHENERGYPHYSICSANDNUCIZARPHYSICSJan.,2ã2CommentsonVariationalºtethodUsedinAcceleratingStructureWANCIan-Fa(IEMitutrofHiOEnerüPhysicsChineseAcademydSei-nem.BeUing10Þ39Chma)Abú,ctÚEevariauonalÉemÃforgeneTalacceleraunggUUCMemstudiedindetail.Uemterwishestopohtoutmmermmmpreviouspapemandexplains,omeimportmtpomumtheapplicaIiondthevaria-tionale¼maim.Keywo,²variationalmethod,acceleratinesmlcttm,eleckomapetiefhld1IntroducUonÇlevariaUonalmethodhasMghäcuracyandneedssmallmE´Éspace.TEemfom,manypeopleusedvamuonalmethodØstudyacceleratingsmscuminthepastdecades[lú],especiallyfordisk-loadedshmtlueinlime.AlthoughtheygavegoodmSUIts,themweresomeenwminthesepapemaboutthevma-donaltheoE7¤Forexample,MasaoNakamum[1]didnotconsiderthenon-metalconditionatthetwoendsoftlmdisk-loadedstmctm,andtheÓisothermathematicemminthepmeedmtopmvethevamuonalfor-mula.WansBocil2jpointedoutthesepmblemsandobtainedthevmtationdformulawtthnewmethod.HearstasmmsthattheelecÇ£magneticfleldsatidesMazwellefmHom,metalboundaryconditiononmetalandperiodicconditionatthetwoendsofonecell,thenthevadationalfOITEmlaSJ=OispmvedbyusingthemetalboundaEyconditionExn=Oandperiodiccondition.××isnotwhatwewanttopmve.×EeconüCtwayistopmvethatthefKIdswiHsatisfVMuwellequatiomandboundaz7conditionifSJ=0.Andthemetalboundar7conditionEÁn=Ocm'tkusedØaknownCOZEdiHonbecausethetrialfuncdondoesitneedsatisfythisconditionasinRef.[3].Ä"isexplainedinthemxtsection-Yao[4]alsode-Etvedthevmathnalformula.HeSrstpmvedthattbeMuwellequationwillhsmdedbyselectingOmspecialfunctionÇ(Eq.(5.2.14)inRef.[4])onmetalbounda17,"xn=,-xn=0,(1)hemnistheunitvectorouwaMnomalSUEfacedtheacceleratingstruetum-1EenheconcludedthatthemetalboundaE7conditionwillksaidedtbranarbitmzyÊbyusingMaxwelleqmUonthatisdemedfromEq.(1).ÇIisisinconsistentMthEq.(1)thatmquiÓsaspecialfunctionʤThevadationalmethodforgenemlaccelemtingstructureisstudiedinthispaperandsomeimponantpointsontheapplicationofthevariationaltbmullawillhexplained.
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