Beam physics for FAIR May, 2012

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Elctron Cloud Studis for FAIR Fdor Ptrov, Olivr Boin-Franknhim, Thomas Wiland Bam physics for FAIR 01 10-11 May, 01 Work

1 Elctron Cloud Studis for FAIR Fdor Ptrov, Olivr Boin-Franknhim, Thomas Wiland Bam physics for FAIR May, 01 Work supportd by BMBF undr contract 06DA May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 1

2 Outlin Motivation Elctron cloud sourcs and ffcts Numrical modl Rsults of -cloud simulations in FAIR bunchd bams Rsults of simulations in FAIR coasting bams If I hav tim LHC: Wak-filds and stopping powrs. 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov

3 Motivation FAIR FAIR is a nw acclrator facility with incrasd intnsitis of havy ion bams. Havy-ion bam nrgy rangs from 11.4 MV/u at injction in SIS18 up to 1.7 MV/u at xtraction in SIS100 In this nrgy rang th rsidual gas ionization by bam ions is vry fficint. This lctrons can accumulat in th coasting bam or srv as a sd lctrons for multipacting in th bunchd bam opration. Elctron Cloud is a known problm of LHC rf phas shift du to th lctron cloud spac charg was obsrvd. 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 3

opration SIS18 SIS18 L=16m Can b dbunchd

opration 8 bunchs mpty buckts Inj on i t c

Coasting bam can b continuously xtractd to

cloud problms show-up diffrntly dpnding on

4 Opration Rgims. Bunchd and Coasting Bams Bunchd bam opration SIS18 SIS18 L=16m Can b dbunchd to gt coasting bam SIS100 havy ion opration 8 bunchs mpty buckts Inj on i t c Constant lin dnsity SIS100 L=1080m Coasting bam can b continuously xtractd to xprimntal ara for svral sconds Elctron cloud problms show-up diffrntly dpnding on th rgim 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 4

mission wall wall Undr FAIR conditions th most concrn ar th uppr two.

5 Possibl Elctron Cloud Origin Rsidual gas ionization U73+ U73+ CO wall Ion inducd scondary mission U73+ Elctron scondary mission Photon inducd scondary mission wall wall Undr FAIR conditions th most concrn ar th uppr two. 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 5

6 Possibl Elctron Cloud Origin Rsidual gas ionization U73+ U73+ CO wall Ion inducd scondary mission U73+ Elctron scondary mission Photon inducd scondary mission wall wall Undr FAIR conditions th most concrn ar th uppr two. 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 6

7 Main Elctron Sourcs Dpnding on th Bam Form Bunchd Bam Sd lctrons from th slow sourcs multiplid xponntially by multipacting Elctron dnsity can grow rapidly until th nutralization ~ 100 μs 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 7

rsidual gas ionization, trappd in th bam potntial. It can tak 0.1-1 s until w gt into troubl i.

8 Main Elctron Sourcs Dpnding on th Bam Form Bunchd Bam Sd lctrons from th slow sourcs multiplid xponntially by multipacting Elctron dnsity can grow rapidly until th nutralization ~ 100 μs Coasting Bam Elctrons com from rsidual gas ionization, trappd in th bam potntial. It can tak s until w gt into troubl i.. two-stram instability or mittanc growth. 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 8

9 How Many Elctrons Producs On Ion Pr Scond? Vi, Elctrons ion-1 s-1 Expctd prssur in vacuum chambr is P=10-11 Torr= cm-3 Gass in SIS18 chambr Ar, N, CO, CO,H For ralistic gas dcomposition ~Z Enrgy / [MV/u] V i =σ β c ρ g Th highr is th charg of ion th fastr it can b nutralizd by th rsidual gas ionization. Tim scal ~ 1 s * Kaganovich t al, Nw Journal of Physics 8 (006) May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 9

10 Wall Effcts. Rflction. Scondary Emission Whn lctron hits th wall it can produc scondary lctrons or b rflctd. Both of ths ffcts dpnd on nrgy of th incidnc lctron. δ sy E E+E 0 δ rfl ( E)=δ0 E+ E+E 0 ( ) E0 nrgy scal(how fast it dcays for biggr nrgis) δ0 - rflction probability at zro incidnc nrgy E Scondary mission yild(sey) Emax nrgy at which SEY has maximum δsy,max valu of scondary mission at maximum δrfl ( ) δ SEY ( E)=δmax E E E max 0.35 (1 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov E.3 ( ) E max )

Elctron Intraction with Coasting Bam Initial lctron vlocity v0=0 Immdiatly aftr production it starts to oscillat Z N ω= =Q ω0 π ϵ0 a m t Bam rsponds to ths oscillations much slowr Z n m ω= =Q ω =Q ω

11 Elctron Intraction with Coasting Bam Initial lctron vlocity v0=0 Immdiatly aftr production it starts to oscillat Z N ω= =Q ω0 π ϵ0 a m t Bam rsponds to ths oscillations much slowr Z n m ω= =Q ω =Q ω χ Z mi γ π ϵ0 a m γ i i 0 0 Elctron-bam coupld motion is dscribd by this systm of quations { +ω y +Q ω y = Q ω ( y y )+Q ω ( y y ) i 0 θ i b 0 i i 0 i ps 0 p t d y = Q ω0 ( y y i )+Q s ω0 ( y y ) dt *Ng book, Chaptr 19. ( ) 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 11

12 Bam-Elctron Systm of Coupld Equations. To find ignfrquncis of th systm on has to solv th 4-ordr algbraic quation. If it has complx solutions thn th instability starts. (Q Q )[(n Q) Q b Qi ] Q Qi=0 E / [V/m] In rality* lctrons gain larg amplituds much fastr than ions ~mi/m Strongly non-linar motion. Up to now it was studid only numrically. In on of th works* it was indicatd that linar instability is ncssary for non-linar. For ral bam Landau damping trm should b includd as No n -l in ar fi dp ld γd = π ω0 ηn p Distanc from bam cntr 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 1 *Startsv **M. Channl

13 Gnral Principl of Simulation in On Slid. Modl of th machin Modl of th bam-cloud intraction bunch kickd EC production and kick point cloud kickd t1 damping MTr This is almost th sam principl as in CERN HEADTAIL and ECLOUD Cods. * t4 tn In our cas on and th sam cod is usd for th build-up studis and for th instabilitis simulations. 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 13 *G. Rumolo

FFT (k 0, k 1,..., k N ) (α 0 k 0, α1 k 1,..., α N k N ) ( x 0, x 1,.

14 Landau Damping in Rigid Slic Modl. Mod Transvrsly xcitd coasting bam Damping rat of th signal on th n-th band* νn= π σω, n 0 on turn amplitud dcras π σω, nt α n= 0 FFT (k 0, k 1,..., k N ) (α 0 k 0, α1 k 1,..., α N k N ) ( x 0, x 1,..., x N ) Invrs FFT givs us a nw dampd st of bam coordinats which is usd in th nxt itration. W nd a broad band damping bcaus EC acts on a vry wid spctral rang. *A. Hofmann,, Landau Damping, CERN school 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 14

15 Comparing Rigid Modl with Full Particl-in-Cll Modl. Elctron cloud ffcts hav similaritis with impdancs. To chck th corrctnss of our modl w apply th broad band impdanc to our rigid bam and compar with th full Particl-in-Cll modl as wll as with analytical thory. Broad band impdanc ωr Z Tr (ω)= ω Z0 ωr ω 1+i Q ω ω r ( ) Stability Bordr N q β dp π ωr p η= 8 π m γ R Q R (Z Tr ) i x 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 15

16 Elctron Cloud Build-up During Bunchd Bam Opration in SIS18. Scan ovr bunch paramtrs in SIS18 to rval dangrous conditions Circumfrnc 16 m Dsign bunch lngth, σz 4 m Ion typ U8+ Intnsity 1011 Enrgy 1 GV/u Pip siz:15cm 15cm Total lngth 13.1 m Pip siz:35cm 35cm Total lngth ~ 3 m In drift sction build-up can happn for bunchs far shortr than it is dsignd. No build-up for th scan paramtrs in drift and dipol sctions bcaus of th NEG coating. 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 16

Elctron Cloud Build-up During Bunchd Bam Opration in SIS100 Scan ovr bunch paramtrs in

U8+ Intnsity 5 1011 Enrgy 1 GV/u Possibl dangr: SIS100 will not b covrd by any

Bam pip siz is significantly smallr and potntial Uwall should b also smallr.

17 Elctron Cloud Build-up During Bunchd Bam Opration in SIS100 Scan ovr bunch paramtrs in SIS100 to rval dangrous conditions Circumfrnc 1080 m Dsign bunch lngth, σz 4 m Ion typ U8+ Intnsity Enrgy 1 GV/u Possibl dangr: SIS100 will not b covrd by any coatings. Advantag: 1. Bam pip siz is significantly smallr and potntial Uwall should b also smallr. mpty buckts = 16 m of fr spac whr lctrons dcay Elctron cloud dnsity is ngligibl. 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 17

18 Coasting Bam Opration in FAIR. Simpl Analysis of Paramtrs. Dpndnc of th main simulation paramtrs on th typ of ion and nrgy. Y,A,W,P constants for givn nrgy Maximum intnsity N i =Y mi Z Momntum sprad dp P = p β γ S β γ mi ω= Z Total ionization rat V i = A (β, γ)β mi n =V i T Damping trm mi ψ=w η Z Driving trm at th fixd momnt ω i = X (β, γ)z β W s that with incrasing Z driving trm incrass and damping trm on trapping frquncy dcrass. U73+ wors than U8+ and Ar May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 18

19 Intnsitis of particls ar scald according to Z/mi spac charg limit. Cloud is fixd. dp/p= 10-3 β=0.86 Ar18+ U8+ U73+ Growth rat / ω0 Elctron bounc tun / Q Thrsholds in Linar Thory with Landau Damping du to dp/p Nutralization dgr U8+ has th biggst stabl ara. Ar18+ has th smallst stabl ara. Z N ω = =Q ω0 π ϵ0 a m Z n m ω= =Q ω =Q ω χ Z mi γ π ϵ0 a m γ i i 0 0 Taking into account spd of nutralization th thrshold will b first rachd by U May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 19

20 Build-up and Instability in SIS100 To rduc th simulation tim ionization rat was incrasd by factor 100. Ions ar Ar18+ and U73+, nrgis 400 MV/u and 1 GV/u Linar growth of amplitud no xponntial growth Ar18+, N=3 1011, E=1 GV/u, dp/p=10-4 U73+, N=3 1010, E=1 GV/u, dp/p=10-4 Svr oscillation amplitud T / ms Ampl / mm Nutralization / % Ampl / mm Nutralization / % How it looks whn thr is a nonlinar instability. No instability in rasonabl tim T / ms 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 0

21 Scan Ovr Intnsitis for U73+ with Lowst Momntum Sprads U73+, 400 GV/u,dp/p= 10-4 Ampl / m U73+, 1 GV/u,dp/p=10-4 Nutralization Dnsity aftr 50*100 ms Dnsity aftr 100*100 ms 100% Probably Not ralistic Numbr of particls Numbr of particls Incrasing momntum sprad to dp/p= rmovs th xponntial instability. Amplituds stay at lvl mm. Evn for small dp/p Ar18+ - no instability. 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 1

22 Coulomb Hating Elctron Gts Enrgy from Collisions Hating rat dw 4 π c ρi r Z i =E 0 LCoul β dt U73+ U73+ Coasting bam paramtrs at 1 GV/u assuming radius of th pip 5 cm Ion Intnsity Hating rat Potntial Estimatd liftim Instability tim Ar V/s 6 V 0.18 s >10 s U V/s 104 V 0.1 s >10 s U V/s 38 V s -3 s Tims ar much smallr than tim ndd for th instability. This factor significantly rducs th dangr. *Znkvich, Adiabatic Thory of Elctron Oscillations 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov

23 Simplifid Modl of Emittanc Growth of an Oscillating Bam What happns with th mittanc whn bam oscillats? W hav bam with initial mittanc σ r, 0 ϵ x, 0 =N i βx σ coh W bring it to oscillations with cohrnt nrgy ϵ coh =N i β x W hav damping rat and th nrgy sourc rstoring th amplitud - EC dp γdamp = π ω 0 n η p Enrgy fraction 1 γdamp dt = γ damp dt Emittanc growth is thn a linar function of tim ϵ x (t)=ϵx, 0+ γdamp ϵ coh t 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 3

24 PIC Cod and Analytical Modl Comparison. Emittanc Growth. mittanc / arb. Units. Th bam was xcitd at n=30, dp/p= Tabl 1. How fast dos mittanc doubl if oscillation amplitud is 10-4 m, β=0.86 dp/p Th lins harmonic ar vry clos n=0 n=30 n= s 10.3 s 6. s 7.7 s 5.1 s 3.1 s 3.1 s.1 s 1. s Tim / ms Agrmnt is good Growth tims ar long. If th bam is coasting for ~10 s thn th mittanc can incras significantly. 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 4

Gap in Th Bam Can Also Solv th Problm of Elctron Accumulation If th bam is stabl th lctron quation of motion is a Hill's quation x =K (t, z0 ) x=(ω+ ω (t, z 0 )) x Until th dnsity of lctrons is low

25 Gap in Th Bam Can Also Solv th Problm of Elctron Accumulation If th bam is stabl th lctron quation of motion is a Hill's quation x =K (t, z0 ) x=(ω+ ω (t, z 0 )) x Until th dnsity of lctrons is low ω+ 0 This quation can b solvd to find maximum amplituds of lctrons If it is biggr than th bam siz thn lctrons ar lost sharp cosin with diffrnt pntration dpth Som simpl thory* was prviously dvlopd * to find out if th lctrons ar trappd in th gap. Simulations indicat that in cas of ralistic Gaussian transvrs profil for clan gap accumulation nvr happns in contrast to KV bam. *Ng, Intnsity Dpndnt Bam Instabilitis 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 5

26 Conclusion for FAIR Projct Bunchd bams Elctron cloud ffcts wr studid for conditions rlvant to FAIR projct No multipacting happns in SIS18 and in SIS100 for th dsignd bunch lngth and intnsitis Coasting bams A nw ralistic way to trat Landau damping in rigid slic coasting bam modl is introducd Elctron clouds ar a much biggr dangr for highly chargd ions. Simulations indicat th two-stram instability if slow xtraction tim is longr than s Howvr, Coulomb scattring of lctrons on bam ions can significantly rduc th chanc for instability spcially for high Z 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 6

27 Outlook To clarify if on can scal th problm by incrasing th ionization rat (long trm diffusion, Coulomb hating). Mak coupl of simulations of instabilitis including Langvin hating trm Still ncssary to mak a finr scan ovr bam intnsitis and momntum sprads including Coulomb hating 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 7

28 LHC Wak Filds and Stopping Powrs Dnsity profil of lctron cloud pinchd in th fild of th bunch * O. Boin-Franknhim, F. Ptrov, Th. Wiland E. Gjonaj, F. Yaman, G. Rumolo If thr is alrady an lctron cloud whn th bunch passs it is attractd towards th cntr of th bunch. Th rsulting non-uniformity of th cloud rsults into th longitudinal lctric fild which tris to stop th bunch * O. Boin-Franknhim 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 8

29 RF Phas Shift in LHC J. EstbanMüllr, E. Shaposhnikov a Th slop of th phas shift with intnsity has gradually dcrasd ovr th priod of th scrubbing run (50 ns bams) Th slop φs/ N has lost on ordr of magnitud thanks to scrubbing! 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 9

ρ(r,t) Enrgy loss pr turn and particl: Δ W z= L dw N i ds rf phas shift: Elctron s quation of motion:

30 Enrgy Loss and RF Phas Shift Enrgy loss pr unit lngth (stopping powr): dw = ρi (r ) E z (r) dr= q λ (z) E z ( z) dz ds Bunch lin dnsity: Ni z λ z= xp( ) π σ z σz n m 3 --cloud vz c j(r,t) ρ(r,t) Enrgy loss pr turn and particl: Δ W z= L dw N i ds rf phas shift: Elctron s quation of motion: ΔW p sin (Δ ϕs )= qv rf 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 30

31 Comparison of Longitudinal Waks in D cod and VORPAL Bunch rms lngth 0.11 m Bunch intnsity 1011 Bunch radius mm Plasma oscillations n=101 m-3 n=1016 m-3 VORPAL rsults agr vry wll with th simplifid D ES simulations 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 31

32 Enrgy Loss of Short Bunchs [ q λ (z,t) r E (r, z)= 1 xp( ) π ϵ0 r σr i r ] If th bunch is short most of th lctrons s a short transvrs kick Elctron spac charg: κ = ω p / c S S0 xp( κ σ z ) (Plasma frquncy) (Dby lngth) 1 Δ p(b)= F (b, s)ds c i F = E (b, s) Stopping powr for a short bunch Th nrgy usd to kick lctrons coms to stopping powr dw n R p π Δ p (b) b db = ds m 0 For KV-bam stopping powr and phas shift 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 3

33 Longitudinal Waks with Multi-Bunch Effcts Saturatd -cloud dnsity: Ring lik dnsity distribution Longitudinal wak fild (bunch at th nd of th train) Ralistic wak acts wakr on th bunch wakr stopping powr 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 33

34 Transvrs Wak Filds for th k=0 Had-Tail Mod (offst) In comparison with longitudinal cas transvrs waks ar obtaind using D solvr dirctly in th cod Δr=0.004 mm Pinching of th cloud around th bunch with and offst Transvrs wak filds obtaind with D PIC and VORPAL Th only disagrmnt is sn at th nd of th bunch. Howvr, th fraction of bam particls affctd is vry small. 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 34

35 Transvrs Wak Filds for th k=1 Had-Tail mod (tilt) In this simulation bunch is travling along th pip with an angl btwn th pip and th bunch axis tan(φ)=0.01 Pinching of th cloud Transvrs wak filds obtaind around th tiltd bunch with D PIC and VORPAL Th agrmnt is again vry good. 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 35

36 Conclusions and Outlook Analytical thory to connct rf phas shift and lctron cloud dnsity was proposd. It was shown that talking into account ralistic cloud shap rducs significantly th stopping powr if th lctron numbr is prsrvd. It was shown that lctron cloud wak fild obtaind in D lctrostatic simulations and 3D lctromagntic VORPAL simulations agr vry wll D Poisson solvr can still b usd for short rlativistic bunchs Futur work: - fast -cloud solvr on GPUs - Paramtrization of th wak filds 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 36

37 Thank you for your attntion! Thank you for your attntion. Qustions? 11 May 01 TU Darmstadt Fachbrich 18 Institut Thori Elktromagntischr Fldr Fdor Ptrov 37

de/dx Effectively all charged particles except electrons

de/dx Effectively all charged particles except electrons de/dx Lt s nxt turn our attntion to how chargd particls los nrgy in mattr To start with w ll considr only havy chargd particls lik muons, pions, protons, alphas, havy ions, Effctivly all chargd particls