BBU Codes Overview. Outline Introduction Beam transport Equation How to solve (BBU-R, TDBBUU, bi, MATBBU etc.) Comparison of BBU codes
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1 BBU Codes Oveview asau Sawamua ad Ryoichi Hajima JAERI Outie Itoductio Beam tasot Equatio How to sove BBU-R, DBBUU, bi, ABBU etc. Comaiso of BBU codes
2 Itoductio ERL cuet imited by Beam Beaku asvese defect beam Logitudia aiva time diffeece HO-iduced eegy sead 2 o 34 HO 56 HO
3 Beam asot Equatio th Cavity -th Cavity asot + Kick due to Iduceded HOs +-th ass -th ass --th ass G Z : tasveseimedace : cavity egth s ω τ e q, m k : tasfe matix : umbe of buches i oe ecicuatio : asses kωτ 2Q : umbe of cavity sites I : aveage cuet si kω τ by Pevious Buches U tasot kick by HO +, U, +, G IZ U, + + k, k s ω τ Iduced HO k Decay & Phase shift
4 How to Sove Beam ackig Beam ositio vs. ime BBU-R JAERI DBBU JLab bi Coe Uiv. ew code JLab Eigevaue Soutio Cuet vs. Fequecy ABBU JLab
5 BBU-R featue asvese BBU Beam ositio vs. time time icemet f /2 Poit-ike buch X,Y HO oietatio X- & Y-axis ideedety Imuse of HO kick Usig 2X2 asfe atix wo-ass ecicuatio
6 BBU-R Agoism Exad beam ie ito a cosecutive time-ste aay Set iitia buch ove f/2 ste m oc- Buch i cavity? Y Udate buch ositio to ext cavity f/2 Udate HO owe Decay & Phase shift k f/2 Buch i cavity? Y Buch kicked by HO oc f/2 Last ocatio? Y Ceate ew buch Cavity Cavity
7 heshod cuet of JAERI ERL-FEL ayout A A x mm -2 x mm ime µ sec ime µ sec
8 Exame fo futue ERL desig 6GeV.3GHz 5V/m 48 cyomodues 47 extea Q β-fuctio i the iac heshod cuet vs. HO adomizatio heshod cuet vs. Cavity gadiet
9 DBBU asvese BBU a ove buch b cacuate ositio of buch eteig the cavity c udate a HO excitatio eve u the cuet u/dow to fid istabiity X- &Y-axis etiey ideedet Suitabe fo age HO umbes o shot chaacteistic time 2Q/ω
10 Exame of DBBU esuts [K.Bead et a., PAC23 Poc ]
11 bi asvese o ogitudia BBU Aow ay ERL tooogy tasiet effect fo abitay buch atte Abitay HO oietatio
12 Exame of bi esuts Logitudia istabiity.8 I 22. ma aiva time diffeece [s] I 22. ma I 23. ma 5 buch # 5
13 New code at JLab asvese BBU wo-ath machie Fu 2D atice tackig 4X4 o D 2X2 Abitay HO age Decoued tasvese motio ad coued motio effect of otated HO effects of otated HOs ad of otated otics Icude FB fo BBU suessio
14 Exame of ew code esuts Beam disacemet as a fuctio of time fo I b >I th FFs of the idicated sices of the beam disacemet heshod cuet vesus HO oietatio fo a sige cavity with oe HO ad a decoued ecicuatio matix [C.eat ad E.Pozdeyev, JLAB-N ]
15 ABBU Sove eigevaue of matix eesetig system asvese BBU X,Y axis teated sequetiay, etiey ideedety
16 Agoism of ABBU is aso ukow Sca ad fid ImI & I> < + i i i i D h Z I D h Z e I D 2, 2 2, τ &, >> V e U i τ + i V h e G IZ V V,, τ k k s k U IZ G U U,,,,, ω k k ik V e V τ assume a steady state soutio sum ove a asses V i of comoet x D i D I D Eigevaue obem : coheet fequecy cos 2 si 2 ω τ ω τ H H H h + τ τ ω i Q e e H 2
17 Exame of ABBU esuts Stabiity ot of comex theshod cuet amees fo oe site, two-ass cofiguatio Swee coheet fequecy ad seach Positive ea cuet [J.J.Bisogao et a., 987 PAC Poc ] [K.Bead et a., PAC23 Poc ]
18 Comaiso of BBU codes Name BBU-R DBBU bi New ABBU Deveoe JAERI JLab Coe Uiv. JLab JLab asvese /Logitudia /L Sove ackig ackig ackig ackig Eigevaue HO diectio X,Y X,Y Abitay Abitay X,Y Dimesio D D 2D D/2D D No. of Recicuatio 2 Abitay Abitay 2 Abitay Pogammig Laguage C Fota/C C++ C++ Fota/C
19 Othe obems hi cavity Imuse kick Whee does a kick wok -etace, midde o exit? Sige- o muti- kick fo ow eegy? Faste methods to detemie whethe stabe o istabe beam disace o HO votage?
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