变分原理在加速结构中应用的论证.pdf

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1、Ú26íÚ1ÚßÜïíëËïíV01.26,No.12002ê1ÂHIGHENERGYPHYSICSANDNUCIZARPHYSICSJan.,2ã2CommentsonVariationalºtethodUsedinAcceleratingStructureWANCIan-Fa(IEMitutrofHiOEnerüPhysicsChineseAcademydSei-nem.BeUing10Þ39Chma)Abú,ctÚEevariauonalÉemÃforgeneTalacceleraunggUUCMemstudiedindetail.Uemterwishesto

2、pohtoutmmermmmpreviouspapemandexplains,omeimportmtpomumtheapplicaIiondthevaria-tionale¼maim.Keywo,²variationalmethod,acceleratinesmlcttm,eleckomapetiefhld1IntroducUonÇlevariaUonalmethodhasMghäcuracyandneedssmallmE´Éspace.TEemfom,manypeopleusedvamuonalmethodØstudyacceleratingsmscuminthe

3、pastdecades[lú],especiallyfordisk-loadedshmtlueinlime.AlthoughtheygavegoodmSUIts,themweresomeenwminthesepapemaboutthevma-donaltheoE7¤Forexample,MasaoNakamum[1]didnotconsiderthenon-metalconditionatthetwoendsoftlmdisk-loadedstmctm,andtheÓisothermathematicemminthepmeedmtopmvethevamuonalfo

4、r-mula.WansBocil2jpointedoutthesepmblemsandobtainedthevmtationdformulawtthnewmethod.HearstasmmsthattheelecÇ£magneticfleldsatidesMazwellefmHom,metalboundaryconditiononmetalandperiodicconditionatthetwoendsofonecell,thenthevadationalfOITEmlaSJ=OispmvedbyusingthemetalboundaEyconditionExn=O

5、andperiodiccondition.××isnotwhatwewanttopmve.×EeconüCtwayistopmvethatthefKIdswiHsatisfVMuwellequatiomandboundaz7conditionifSJ=0.Andthemetalboundar7conditionEÁn=Ocm'tkusedØaknownCOZEdiHonbecausethetrialfuncdondoesitneedsatisfythisconditionasinRef.[3].Ä"isexplainedinthemxtsection-Yao[4]a

6、lsode-Etvedthevmathnalformula.HeSrstpmvedthattbeMuwellequationwillhsmdedbyselectingOmspecialfunctionÇ(Eq.(5.2.14)inRef.[4])onmetalbounda17,"xn=,-xn=0,(1)hemnistheunitvectorouwaMnomal•SUEfacedtheacceleratingstruetum-1EenheconcludedthatthemetalboundaE7conditionwillksaidedtbranarbitmzyÊby

7、usingMaxwelleqmUonthatisdemedfromEq.(1).ÇIisisinconsistentMthEq.(1)thatmquiÓsaspecialfunctionʤThevadationalmethodforgenemlaccelemtingstructureisstudiedinthispaperandsomeimponantpointsontheapplicationofthevariationaltbmullawillhexplained.2VariationaITheoÇforElectromagn´cFietdMStructu