變分原理在加速結構中應用的論證.pdf

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'變分原理在加速結構中應用的論證.pdf'
ú 26í ú 1ú2002ê 1?C o m m e n t s o n V a r i a t i o n a l o t e t h o d U s e di n A c c e l e r a t i n g S t r u c t u r eW A NC Ia n- Fa( IEMitutr of HiO Enerü Physics Chinese Academy d Sei- nem .BeUing 10T 39 Chma)Abú , ct ú Ee variauonal é em? for geneTal acceler aung gUUCM e m studied in detail . U e m ter wishes topoh t out mm ermm m previous papem and explains ,ome importm t pomu m the app licaIion d the varia-tional e? m aim .Key wo,2 variational method , acceleratine smlcttm , eleckomap etie fh ld1 I n t r o d u c U o n? l e variaUonal method has M gh ? curacy and needs small m E′ é space . TEemfom , man y peopleused vam uonal method ? study accelerating sm scu m in the past decades[ lú ] , especiall y for disk- loadedsh mtlue i n lim e . Al though they gave good mSUIts , them were some enwm in these papem about the vm a-d onal theoE7 ¤ For example , Masao Nakam um [ 1] di d not consider the non- metal conditi on at the two ends oftlm disk- loaded stm ctm , and theó is other mathematic em m i n the pm eedm to pmve the vam u onal for-mula . W ans Boci l2j pointed out these pm blems and obtained the vmt ationd formul a wtth new method . H ea rst asm m s that the elec?£magnetic fleld satid es M azwell efm Hom , metal boundary condi ti on on metaland periodi c condition at the two ends of one cell , then th e vad ational fOITEm la SJ = O is pmved by usingthe metal boundaEy conditi on E x n = O and periodi c condi ti on . × × is not what we want to pm ve . × EeconüCt way is to pm ve that the fK Ids wi H satisfV Mu well equatiom and boundaz7 condition if SJ = 0 . A ndthe metal boundar7 condition E á n = O cm ' t k us ed ? a k nown COZEdi Hon because the trial funcd ondoesi t need sati sfy this conditi on as i n Ref . [ 3 ] . ? " is explai ned i n the m xt sec ti on - Y ao [4] al so de-Et ved the vm ath nal form ul a . He Srst pmved that tbe Mu well equation will h sm d ed by selecti ng Omspecial functi on ? ( Eq . ( 5 . 2 . 14 ) in Ref . [ 4 ] ) on metal bounda17 ," x n = , - x n = 0 , ( 1)hem n is the unit vector ouw aM nom al - SUEfac e d th e accelerating str uetum - 1E en he concl uded thatthe metal boundaE7 condition will k sa id ed tbr an arbitm zy ê by using Maxwell eq m Uon that is dem edfrom Eq . ( 1) . ? Iis is inconsistent M th Eq . ( 1) that m quió s a spec ial functi on ê ¤The vad ati onal method for geneml accelem ti ng stru cture is stud ied in thi s paper and some i mponantpoints on the applicati on of the variati onal tbmull a wi ll h explai ned .2 V a r i a t i o n a I T h eo ? f o r E l e c t r o m a g n ′ c F i et d M S t r u c t u r eTTm Maxwell eq uations for fl eld with time dependence of ejM in vacuum space ar eV x Z o H = j kE , ( 2 )V x E = - j IzZ o H , ( 3 )? th boundaE7 COIl diHons on metal mv x H x n = O or m x E = 0 , ( 4 )Reeeived 4 ?-mu×7 a MO1? ü ? í ? ? ? í V01.26 , No. 1Jan . ,2 ? 2HIGH ENERGY PHYSICS AND NUCI ZAR PHYSICS74- 78
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加速 論證 變分原理 結構 應用
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