Investigations of Electromagnetic Space-Charge Effects in Beam Physics

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1 Invesigions of Elecogneic Spce-Chge Effecs in Be Physics Chong Shik Pk Depen of Physics Indin Univesiy Indin Univesiy Cycloon effenson Lb Sep. 9

2 Ouline Moivions Exising Spce-Chge Modeling Spce-Chge Effecs in RF Phooinecos Spce-Chge Effecs wih Tnsvese Cuens Suy Fuue Plns 9//9 effeson Lb

3 Moivions Fuue cceleo-bsed expeiens dend high-bighness elecon bes fo phooinecos The elecon be hs low enegy so spce-chge foces cn be ipon elive o exenl gneic nd f fields Thee e wo in chllenges fo siulions of highbighness phooinecos: - Resoluion of sll lengh/ie scle spce-chge fields elive o long lengh/ie scles of ineco e.g. - ps bunch lenghs fo.3-.8 GH - Reovl of unphysicl siulion effecs such s nueicl gid dispesion nd nueicl Cheenkov effecs in FDTD ehods 9//9 effeson Lb 3

4 Exising Spce Chge Modeling 9//9 effeson Lb 4

5 Exising Elecosic Algoih SCHEFF (Spce Chge EFFec) - beks up he co-picles ino se of nnul ings - clcules he elecosic spce-chge foces in he be es fe nd Loen nsfos o he lb fe PARMELA (Phse And Rdil Moion in Elecon Line Acceleos) - Wokhose of phooineco design codes - iposes exenl f-fields copued fo SUPERFISH nd exenl gneic fields copued fo POISSON - cnno clcule wkefields self-consisenly ASTRA (A Spce chge TRcking Algoih) 9//9 effeson Lb 5

6 Exising Elecogneic Algoihs Yee/PIC lgoih (FDTD ehod) - solves Mxwell s equions on he wo ineleved E nd B gids MAFIA Nueicl Dispesion Nueicl Cheenkov Rdiion TREDI (Thee Diensionl Inecos) - Liend-Wieche Poenils - no conducing boundies 9//9 effeson Lb 6

7 Ohe EM SC Mehod Mode nlysis nd Seies Expnsions (Slh e l) - solves wve equions using seies expnsions nd Fouie nsfoion in nol odes. - clcules he spce-chge fields o biy ccucy fo given be chge nd cuen densiies - needs sufficien oun of eigenodes nd Fouie odes 9//9 effeson Lb 7

8 Spce Chge Effecs in RF Phooineco 9//9 effeson Lb 8

9 Elecogneic Spce-Chge Poenils nd Fields The elions of EM fields nd poenils A E φ B A Loen Guge A + c Wve Equions c φ φ ρ ε A µ effeson Lb ρ E B ε B E E B µ + c 9//9 *PRST-AB Mk Hess e l 9

10 Tie-Dependen Geen s Funcions Fo he specil cse of cuens in he xil diecion in n pipe wih chode he poenils e given by Tie Dependen Geen s Funcion: ( ) ( ) ( ) G d d ; 3 ρ ε φ φ ( ) ( ) ( ) G d d A A ; 3 µ chode wll side boundy A A φ Boundy Condiions: 9//9 ( ) ( ) G G c A δ δ φ ( ) ( ) ( ) ( ) ( ) ( ) [ ] λ θ λ λ θ λ π θ θ φ n n n i n n n A k k e c G G chode A wll side A boundy G G G φ effeson Lb

11 Elecogneic Spce-Chge Fields Abiy pipe coss-secion wih longiudinl cuens Recngul pipe coss-secion wih biy cuens Cicul pipe coss-secion wih longiudinl cuens E c 3 ( ) ψ ( ) ( )[ Γ Γ+ ] ( ) n ψ * n ρ d d ε n Fo cicul pipe ψ n Γ ± ( ) ( λ ) θ ( λ ) n ( ) ( ) ± / ± ( n ) e ( ) iθ π + n whee c ± 9//9 λ ± effeson Lb

12 Nueicl Ipleenion IRPSS (Indin RF Phoochode Souce Siulo) IRPSS is 3-D elecogneic picle/slice pushing lgoih Hndles ellic boundy condiions self-consisenly (boundy will consis of chode cicul side wlls) Uses elecogneic Geen s funcion folis fo solving fields Tie-dependen Geen s funcion foulion hs he dvngeous popey h elecogneic wves fo igh elecon bunches Specify ecoy nd chge densiy of he be Copue E nd B due o spcechge Siule be dynics of es picles effeson Lb 9//9

13 Bunched Be Model The uli-sliced bunch odel is inoduced o genelie he finie sie bunch lengh. We se up unifoly spced (in ie) eqully chged slices which fo one coplee bunch. Needs n enough nube of slices Equion fo chge densiy (Cicled) Q ρ( ) ( ) Θ b i i b i δ π b i [ ( ) ] 9//9 effeson Lb 3 i

14 Eigenode Suions The equied eigenode nubes cn be esied fo he expnsion of he chge densiy of he be. The nube of nsvese eigenodes necessy fo ccuely deeining he fields is invesely popoionl o he nsvese sie of he be. [ ] ) ( ) ( ) ( ) ( ) ( Θ i n i n i n i i i b i b i b Q ψ ρ δ π ρ 9//9 4 b /.5 b /. effeson Lb

15 Eigenode Suion (con d) Fo he expnsion of he be densiy funcion we cn ge he inequliy b M >> π In ode o odel he fields wihin % ccucy i is necessy o su ove les odes coesponding o BNL.856 GH Phoochode gun. 9//9 effeson Lb 5

16 Nueicl Tie Inegion In he E clculions he longiudinl field songly depends on he be ecoy. The oscillion peiods of he Geen s funcions e deeined by he nsvese eigenode nube M nd he inegion sep sie '. A slle ' educes he pliude of he oscillion. c τ b <<. 9//9 effeson Lb 6

17 Benchk Modeling Q v -Q v Q v IRPSS siulion of disk bunch of chge eied ie fo he chode sufce oving unifoly wih speed v Anlyicl odel of wo disks of chge oving unifoly in opposie diecions fo ll ie nd inesecing 9//9 effeson Lb 7

18 Benchk Copison E vs. E vs. Blue: Benchk Red: IRPSS effeson Lb 9//9 8

19 Siuling Be Dynics wih ANL AWA.3 GH RF Phooineco The f fields wihin AWA gun e ppoxiely E E cos( k Ek E sin( k )sin( ω + ϕ) Ek Bθ cos( k )cos( ω + ϕ) c The longiudinl f fields ke be ecoies )sin( ω + ϕ ) ff E ϕ.3 GH 5 MV/ 65 deg pc nc. ps Qb b lse effeson Lb 9//9 9

20 Tnsvese Spce-Chge Foces Lge discepncies fo elie ie Sll diffeences fo le ie F / Q E + β ( cb) c/.5 c/.4 effeson Lb 9//9

21 Longiudinl Spce-Chge Foces The diffeence is slle hn nsvese cse Fo longe bunch lengh his will be incesed c/.5 c/.4 effeson Lb 9//9

22 E Spce-Chge Fields A key esul is h s he lse pulse lengh is incesed he discepncy beween elecosic nd elecogneic SC fields is incesed he chode when he bck of he bunch is eied. The sie of he discepncy lso depends on he be dius. Quliively s he be dius is incesed i.e. he be becoes oe pncke like nd he discepncy becoes slle. 9//9 effeson Lb

23 Be Dynics w/o Spce-Chge Effecs Wih only f fields picles e dilly focused ne he chode P /c vs. phsespce. c.3 c.3 c 9//9 effeson Lb 3

24 Be Dynics wih Spce-Chge Effecs.3 c Q pc.3 c effeson Lb 9//9 4

25 Be Dynics wih Spce-Chge Effecs.3 c.3 c Q 5 pc effeson Lb 9//9 5

26 Be Loss Mesueens By vying he oun of lse powe P (popoionl o bunch chge) We esue he be cuen I I P Blue: Elecosic Red: Elecogneic effeson Lb 9//9 6

27 Expeienl Mesueens Pefoed n expeienl be loss esueen on he.3 GH f gun he ANL AWA expeien. Below e plos of esued be chge vs. esued lse pulse inensiy. If no be loss ws o occu hen he plo should be line wih unifo slope. Howeve ciicl bunch chge. i.e. E (f) E (ciicl) fo fixed lse pulse lengh nd dius one would expec be loss o occu nd educion in he slope of he cuve. b 3.4 psec effeson Lb b.4 psec 9//9 7

28 Spce Chge Effecs wih Tnsvese Cuens 9//9 effeson Lb 8

29 Elecogneic Field fo Cicully Syeic Souces Genelie he exc folis fo he SC fields of cylindiclly syeic be in cicul conducing pipe Include he effec of he nsvese cuens Consuc elecogneic SC fields using he iedependen Geen s funcion ehod in he cylindicl conducing boundy condiions Cn odel he high SC doined syses such s highpowe icowve souces Cope o Elecosic (ES) esul which is fequenly used o odel high-powe icowve souces such s klyson 9//9 effeson Lb 9

30 Expnsions of Chge nd Cuen Densiies Be souce nd he syse e cylindiclly syeic* 9//9 3 ( ) ( ) ( ) ( ) θ θ ρ ρ ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) d d d d θ θ ρ ρ effeson Lb *Subied o IEEE Tnscion equion : Coninuiy + + ρ

31 TM Mode Spce-Chge Fields 9//9 3 EM fields geneed by nd ( ) E E ( ) G d d E µ ε ρ ( ) ( ) λ λ θ c G effeson Lb E c B E c B B E E E E B E B B Mxwell'sEquions : µ µ ε ρ θ θ θ θ

32 Nueicl Exple Siule dilly behing be Rdil be cuen bu no longiudinl be cuen Cope EM SC fields wih ES SC fields ρ ( ) Q π ( ) ( ) b ( ) θ ( b ) b ( ) [ θ ( L + ) θ ( L ) ] b ( ) + δ δ cos ( ω ) > effeson Lb 9//9 3

33 Nueicl Requieens Siil o he phooineco odeling Less nube of eigenodes due o lge be dius effeson Lb 9//9 33

34 Tnsvese Spce-Chge Fields wih Tnsvese Cuens ES fields e lso found using Geen s funcion ehod The be oscillion ss wih he iniil be dius b / c ω c/./c. effeson Lb 9//9 34

35 Tnsvese Spce-Chge Fields wih Tnsvese Cuens (con d) Blue: Elecogneic Red: Elecosic.5T.5T.75T T effeson Lb 9//9 35

36 Longiudinl Spce-Chge Fields wih Tnsvese Cuens The effecs of he SC E fields e ipon ne he be edge /. /.5 effeson Lb 9//9 36

37 Suy Developed elecogneic spce-chge odels of elecon bes in he pesence of he conducing boundies Developed novel copuionl code IRPSS o copue he SC fields nueiclly Is cpble of siuling bes wih biily sll bunch Lenghs since i uses Geen s funcion ppoch Siuled he be dynics of he be ne he chode in he f phooineco Exended Geen s funcion ehods by including he nsvese cuens Invesiged he elecogneic SC fields fo dilly behing be oscillion effeson Lb 9//9 37

38 Fuue Plns Exend IRPSS code by including he effecs of iis(es) o disconinuiies of he cviy Ipove he code o self-consisenly clcule he ecoies due o boh he exenl nd SC fields Sudy how he be dynics e ffeced due o he SC fields in he designs of gneic focusing schees fo eince copensions Include n biy be cuens such s iuhlly vying cuens 9//9 effeson Lb 38

39 Thnk You! 9//9 effeson Lb 39

D zone schemes

Ch. 5. Enegy Bnds in Cysls 5.. -D zone schemes Fee elecons E k m h Fee elecons in cysl sinα P + cosα cosk α cos α cos k cos( k + π n α k + πn mv ob P 0 h cos α cos k n α k + π m h k E Enegy is peiodic