Beam-ion Instabilities in SPEAR3

Transcription

1 Beam-ion Instabilities in SPEAR3 KEK accelerator phsics Seminar /5/ Lanfa Wang, SLAC

2 Outline Introduction to SPEAR3 Introduction to FII(Fast Ion Instabilit) Observations in SPEAR3 effect of emittance Effect vacuum pressure Effect of beam current Effect of beam filling pattern Effect of chromaticit Effect of feedback Effect Vacuum burst Summar /5/ Slide

3 SPEAR3 Laout Arc cell: QF QD BEND SD SF QFC SF SD BEND QD QF o 34 m circumference racetrack o 7 standard cells per arc (SF, SD) o 4 matching cells (SFM, SDM) /5/ Slide 3

4 Emittance of SPEAR3, ε x Achromat Low emittance Lower emittance Superconducting damping wigglers now Working in progress Future ε x (nm) <5. ε x, IDs (nm) ε x,eff (nm) η, ID (m)... σ E (permil) ν x x x Effective emittance, ε x,eff includes η x : ε σ σ ε β x, eff = x x' = x x + η σ E ε x β x

5 Adding nonlinear knobs (simulation). New sextupole magnets Two families On steering magnets SHA SHB. Octupole magnets SD+OD SF+OF 3. Independent power suppl. MOGA (multi-objective Genetic Optimizer) elegant tracking, 6.7 nm lattice, with sextupole families start best results

6 Main 4.7% ion clearing gap.9µs Phsics Smbol/Unit Horizontal Emittance nm Vertical Emittance pm 4 Beam Current ma (5) Bunch Number 8 Harmonic Number 37 Beam Energ GeV 3 Circumference m 34 Bunch spacing ns. RF frequenc MHz Revolution frequenc MHz.838 Horizontal tune 4. Vertical tune 6.77 Momentum compaction factor.6-3 Energ Spread Radiation Damping time τ x /τ /τ z [ms] 4./5.3/3. Vacuum ntorr.~ /5/ Slide 6

7 Introduction to FII(Fast Ion Instabilit) Ions generated b beam-gas ionization Ions are trapped along the electron-bunch train; The ions created b the head of the bunch train perturb the bunches that follow. Occur in rings, linacs or beam transport lines; Characteristic of ion instabilities Broadband spectrum Normall onl in vertical direction due to the small vertical beam size The amplitude saturated at order of beam sigma 7

8 Coupled motion M. Kwon, PRE Vol. 57,998 /5/ Simulation Slide 8

9 Broad band Spectrum Spectrum depends on the beam current, optics(emittance, betatron function), vacuum Amp(db)+ Ib=5mA, Bunch Number=8, Bunch Train,3// f(mhz) Experimental 9

10 Saturation of beam-ion instabilit When the bunches amplitude is larger (compare with beam size), the nonlinear force automaticall slow down the instabilit! Different from other instabilities, ions induced instabilit rarel causes beam loss. (T.R & F.Z) ~ ( s, z) exp + z l t τ c *... Amp (σ) - - σ Simulation, FII -3 Electric field vs. amplitude Turns (/) FII Theor: Phs. Rev. E5, No. 5, p (995))

11 Ion species in vacuum P λ i = δi kt N e n b Here P is the vacuum pressure, δ i is the ionization cross-section, N e is the number of electrons per bunch, T is temperature and k is Boltzmann constant Total pressure <.5 ntorr Vacuum in Gas Species Mass Number Crosssection Percentage in Vacuum H.nTorr CH4 HO CO CO H.35 48% CH4 6. 5% CO 8. 4%.ntorr CO % HO %

12 Ion distribution (stead status) ρ( x) = π πσ the distribution at x is [] x e x 4σ x K x 4σ x (P.F. Tavares, CERN PS/9-55 ) x 4σ x ( e ρ x) π πσ x x log( ) + γ 8σ x γ= ρ e ρ ion ρ ion, Asmptotic form.8 beam size σ x =.mm σ =.447mm Beam Ion(Analtic) Ion (numerical) ρ ρ x(σ) X (mm)

13 Space Charge Wake from ion cloud W ( z) = N rpn AS b i / 4 3 σ ( σ + σ x) 3/ Where N i is the ion number; N is e-beam population; Sb is bunch spacing Frequenc of the wake f i, c 4Nr 3 ( ) p π ASb σ x + σ σ e πfi, z Q c / πf i sin( c W (m - ) , z ) Wake, Q=7.4, λ=.m Numerical Method Analtical Method The wake is long range, which causes coupled bunch instabilit Z (m) Comparison with analsis 3

14 What we expect to be observed When the beam is evenl filled along the ring, the exponential growth rate of the coupled bunch instabilit for j n mode µ πµ / b j e is [Alex Chao s book, for example] τ µ = N n γ r c e b e T ωβ p= Re { Z (( pn + ν + µ ) ω )} ion b f ion (MHz) CO H H O f i, c 4Nr 3 ( ) p π ASb σ x + σ σ / The frequenc of the unstable modes depends on the optics! 3 CO S (m) Calculated ion frequenc along the ring for a beam current of ma 4

15 Observations with high pressure (gas injection) Instabilit has been observed at man laboratories when vacuum is not good Artificiall increasing the vacuum pressure (ALS, PLS, ATF) At commissioing times or restart after a long shutdown (ESRF, DIAMOND) After installation of new (insertion device) chambers (SPring-8, ESRF) C. J. Bocchetta, et. al. 994 ELETTRA ALS σ ~3µm PF (M. Kwon et al., Phs. Rev. E57 (998) 66) 5

16 Observations at Nominal conditions Instabilit has been observed at man laboratories when vacuum is not good Artificiall increasing the vacuum pressure (ALS, PLS, ATF) At commissioing times or restart after a long shutdown (ESRF, DIAMOND) After installation of new (insertion device) chambers (SPring-8, ESRF) The instabilit also occurs at nominal condition (SOLEIL, SSRF, SPEAR3 ) For existing light sources it does not pose a problem. Ma become a problem for lower emittance rings Vertical amplitude along the bunch train SSRF, nominal vacuum SSRF, B. Jiang, NIMA 64 ()

17 Observations in SPEAR3 Effect of emittance Effect of vacuum pressure Effect of beam current Effect of beam filling pattern Effect of chromaticit Effect of feedback Effect of vacuum burst 7

18 Ion instabilit at Experiment condition: Beam Current: 9mA Bunch Number: 8 Bunch Train Vertical low sideband was observed at frequenc from 5~6MHz, which agrees with the analsis The sidebands move to low frequenc region when the beam emittance increases, which agree with the theor, and confirms this is FII(fast ion instabilit) f i, x, = c N e p π,, ( ) AS bk x σ x σ + σ x Lower instabilit rate with a larger emittance r / Amp(db)+5 Beam Current 9mA, Bunch Number 8,One Bunch Train,// 3 Normal Coupling Skew Quadpole off f(mhz) Vertical sideband

19 Effects of coupling.5 skew quadrupole magnets are on k=.% Ib=5mA, Bunch Number=8, 6 Bunch Train,3// 4 Normal Coupling Skew Quadpole off 35 3 Amp(µm).5.5 k=.3% skew quadrupole magnets are off Amp(db) f(mhz) 9mA single bunch train f(mhz) 5mA Six bunch trains 9

20 Bunch oscillation along the bunch train Single bunch Vertical bunch oscillation amplitude saturated at the amplitude around sigma (um) 4 Amplitude (µm) Bunch No. 5 Time (ms) 5 RMS amplitude (µm) Bunch number

21 Effects of beam current 4 I= ma 4 I=3 ma Amp(µm) 4 I=4 ma 4 I=5 ma f(mhz) Observed vertical lower sidebands at different beam currents. The beam has single bunch train with 8 bunches

22 Effects of bunch train gap Single bunch-train, ma Amp(µm) 3 Train Gap=89ns 3 Train Gap=38ns Train Gap= 7ns ns gap f(mhz) No gap

23 Mitigation with multi-bunch train beam filling Bunch Missing bunch 3

24 Effects of beam filling Filling : Bunch Train (3pm) Bunch Train; ma 8 Bunches Sideband found Filling 3: Bunch Train (4:5pm) Bunch Train; ma 8 Bunches No sideband Amp(db) One Bunch Train,NB=8, I=mA, /3/ f(mhz) Vertical sideband with bunch train Growth time about.5ms~5ms? 4

25 Effects of beam filling 4 3 One Bunch Train Amp(µm) Four Bunch Train Six Bunch Train f(mhz) Beam current 5mA 5

26 ρ i (m -3 ).5 x One Bunch Train Two Bunch Train Four Bunch Train Six Bunch Train Simulation of ion cloud build-up Ion densit reduction due to multi-bunch train ρ i (m -3 ) f gap x N train e τ / τ gap diffusion The required train gap is onl about ion oscillation period. A short gap for high intensit beam (PEPX uses more than bunch trains) = Train gap=3ns = wavelength for 33MHz Time (ns) Number of Bunch Train Build-up of ions with different beam filling pattern@5ma 6

27 Effect of chromaticit Amp bunch train, 5mA 3 ξ =.,τ=hrs 3 ξ =3.,τ=8.8hrs 3 ξ =4.,τ=8.hrs 3 ξ =5.,τ=7.hrs 3 ξ =6.,τ=6.hrs 3 ξ =7.,τ=4.7hrs f(mhz) 7

28 Effect of bunch train 4 bunch train 6 bunch train Increase chromaticit, lifetime drop from hrs to 9.hrs With vertical chromaticit 4.6, the sideband still appear. With vertical chromaticit 3.6, the sideband becomes weak. With vertical chromaticit.6, the sideband disappear. 5 One Bunch-Trains,5mA,5/4/ Four Bunch-Trains,5mA,5/4/ Six Bunch-Trains,5mA,5/4/ 6 4 bunch train 4 bunch train 6 bunch train 5 Amp(db)+7 5 Amp(db)+7 Amp(db) Vertical Chromaticit Vertical Chromaticit Vertical Chromaticit 8

29 Amp(µm) 5 Effects of vacuum pressure Six bunch train P=.37nTorr P=.86nTorr P=.9nTorr f(mhz) P=.75nTorr The beam consists of six bunch trains with total bunch number of 8. The beam current is 3 ma. There are no sidebands with the nominal pressure of.37ntorr. The vacuum pressure is increased b partiall turning off the ion pumps. 9

30 Preliminar feedback test There is no bunch-b-bunch feedback in SPEAR3, we tested once of the feedback from Dimtel, Inc Almost uniform filling pattern: 448mA, six bunch train, bunch number 366, (onl missing bunch in each train gap) The oscillation amplitude has been reduced. Some bunches still have residual oscillations Possible reasons: () The bandwidth of the feedback kicker is not large enough () The instabilit is too fast Amplitude (µm) (µm) Bunch No Time(ms) Measured beam s unstable mode 354 when the bunch-b-bunch feedback is on and off, Time (ms) (a) 3 3

31 Effect of Vacuum burst In nominal case, the beam ion instabilit can t case beam loss due to the saturation mechanism. However, when there is a vacuum burst, partial beam loss and strong beam ion instabilit 3

32 Comparison with simulation.5ntorr total pressure is used in the simulation(nominal pressure is order of.3ntorr) Simulated growth time with 6 bunch-trains beam is.6ms(.7 ms for.3ntorr pressure) Simulation doesn t include chromaticit and radiation damping, The vertical radiation damping times is 5.3ms.The real growth time should be <5.3ms 8 bunch train Y (µm) - one bunch-train, τ=.38ms - two bunch-trains, τ=.93ms four bunch-trains,τ=.6ms six bunch-trains, τ=.6ms Time (ms) 5mA 8 bunches.5ntorr Simulated beam ion instabilit for different beam filling patterns bunch train; ntorr 3

33 W Comparison of simulation with analsis (6 bunch train) Multi-bunch train Instabilit C ωi ( s) z 4 ωi, ( s) λi ( s) Q c ωi ( s) z ring ( z) = e sin( ) ds 3 c λe σ ( s)( σ ( s) + σ x ( s)) c f = (MHz), W.5 x = 93.78m -, Q=4.864 τ=.5547(ms) τ= ms 4 x τ r cβ γ ρq both nonlinear space-charge effect and optics are included e ˆ ω L ρ i W t = i, eff c λe Tau=.5ms (PRSTAB, e844) Data Fitting X,Y (σ) - Tau=.74ms Wake (m - ).5 Optics effect is included Time (ms) S (m) six trains, CO onl.5ntorr

34 Beam ion instabilit at nonlinear region (>σ) Strong nonlinearit Slow growth with amplitude beating experiment - Amp (σ) Turns Beam-ion 34

35 Summar of Mitigations Better vacuum Clearing electrode (onl practicable for small ring, add impedance) Multi-bunch-train (simple, cheap, ver effective for high intensit beam) Chromaticit (useful with side-effects: lifetime & injection rate drop) Feedback Sstem (ver effective, need more R&D?) 35

36 Summar The observations in SPEAR3 agree with theor & simulations This tpe of instabilit can be mitigated b multi-bunch train beam filling SPEAR3@5mA: 6 bunch-trains filling pattern ma: bunch trains Multi-bunch train is ver effective for high intensit beam such as ILC, SuperKEKB, PEPX. (up to two orders of magnitude) Chromaticit can mitigate the instabilit at the cost of lifetime Bunch-b-bunch feedback is ver effective(need more test? FII can be ver fast although the amplitude is small ) The beam ion instabilit is not a problem for SPEAR3 although we don t have feedback Beam-ion Instabilit can be important for future small emittance rings, such as ultimate storage ring light source ~pm, especiall for collider. 36

37 Acknowledgements Thanks James Safranek, Jeff Corbett, John Schmerge, Jim Sebek, Dmitr Tetelman, and other SSRL members for the data taking and discussions 37

38 Thank You! 38

39 Backup slides 39

40 Comparison of FII in various electron rings (single bunch train mode is assumed) For present da light sources/e-rings, FII does not pose a serious problem. It can be a problem for future low emittance light sources and damping rings. RING E (GeV ) Cir(m) n b I (ma) L SP (m) E X /σ x nm rad/µm E Y /σ Y nm rad/µm PEPII /66.4/44. KEKB /5.49/75. ALS /6.6/3. APS /76.5/.4 PLS /35./35.3 ATF /7.45/5.6 SPEAR /.4/.6 NSLSII /.8/ 8. SUPERKEKBI /6.4/6 8.7 SUPERKEKBII /8.3/4 3.7 ILC K/6K 4.5/.8/./ PEPX /8.43/ ρ i,eff /γ 4

41 Effect of frequenc spread of HOM (BBU) Constant Wake of ion-cloud ω W( z) = We iz Qc ωi z sin( ) c Z t ( ω) = Wt Q ω + iq ( ω ) i Frequenc spread model: modes with equal frequenc variation ω ω ω i ω/ω= ω/ω=.5 [Yokoa,? ]

42 Tpes of beam ion instabilit[] Single bunch train: Fast ion Instabilit (FII) zero frequenc spread (next page) With large frequenc spread Uniform beam filling pattern Multi-bunch train beam filling pattern The maximum exponential growth rate ρ i, eff λi = 3σ ( σ + σ ) x ρ ρ t τ ~ ( t) e a =.5 a =. (.5 a re cβ Q ( aρ ) a τ γ Is the average ion densit seen b all bunches ) = ρ / ρ Is the maximum ion densit seen b all the bunches Q : tpicall ~8, can be smaller than 4

43 Quasi-exponential growth Regime I (FII, Zero Frequenc spread case) ω il c << t τ c Regime II Region I ~ ( s, z) s z ~ ( s, z) = I z = β Λ 4 z ~ ( s, z) β Λ s exp z β Λ = z s exp l t τ c Amp (σ) Regime I τ c = cr β Nn e γ b Wˆ ( l) = r cβ e γ ρ i, eff Fast instabilit onl when the amplitude is small than the beam size! ωiz c Turns (/) FII, simulation ( T. Raubenheimer, F. Zimmermann, PRE V5, 5487, 995) 43

44 Single bunch train instabilit Theor of FII Zero frequenc spread (w.o optics), Quasi-exponential growth ( T. Raubenheimer, F. Zimmermann, PRE V5, 5487, 995) ~ z t cr ( eβ Nnb s, z) exp = Wˆ ( l) l τ c τ c γ With frequenc spread due to optics, exponential growth [G. Stupakov, KEK Proceedings 96-6, 43 (996)] r cβ λ e i e, FII 3 γσ ( σ + σ x ) τ ω / ω i = i r cβ e γ ρ i, eff ωiz c Multi-Bunch-train instabilit τ a = ρ / ρ r cβ e ρq γ (.5 a ) Both Optics effect beam a= for an even beam filling pattern; a=.5 for a single bunch train beam filling pattern 44

45 Comparison of simulation with analsis ( bunch train) Analsis Using the total wake (Q=8) Optics effect is included C ωi ( s) z 4 ωi, ( s) λi ( s) Q c ωi ( s) z Wring ( z) = e sin( ) ds 3 c λ σ ( s)( σ ( s) + σ ( s)) c e τ=.859 ms x x f = 9.759(MHz), W 5 x = m -, Q=4.99 τ=.394(ms) Data Fitting X,Y (σ) - -4 Simulation Tau=.8ms Wake (m - ) - Tau=.3ms Calculated wake 3 4 Time (ms) S (m) One train, 5mA, 8 bunches, CO onl.5ntorr

46 Can a slower feedback suppress the instabilit? A bunch-b-bunch feedback with a damping rate slower than the exponential growth rate ma limit the oscillation amplitude in the exponential growth region (.~sigma ) b suppressing the linear oscillation. τ=3turn Y(σ) Y(σ) Turn Feedback damping time turn. It is turned on around 5th turn when the instabilit is alread developed. (file:ocs_767nb3devefdbk_amp) Turn 46

47 /5/ Slide 47