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Review of Single-Bunch Instabilities Driven by an Electron Cloud

Review of Single-Bunch Instabilities Driven by an Electron Cloud. experimental evidence simulation approaches analytical treatments similarities & differences to impedance-driven instabilities synergetic effects countermeasures open issues. Napa Valley April 2004. concerns beam loss

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Review of Single-Bunch Instabilities Driven by an Electron Cloud

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  1. Review of Single-Bunch Instabilities Driven by an Electron Cloud • experimental evidence • simulation approaches • analytical treatments • similarities & differences to impedance-driven instabilities • synergetic effects • countermeasures • open issues Napa Valley April 2004 F. Zimmermann

  2. concerns • beam loss • emittance growth • trajectory change • (turn-by-turn or pulse-to-pulse) F. Zimmermann

  3. single-bunch instability • but in multibunch or multi-turn operation • (in all/most cases e- arealready present • when bunch arrives) • for long proton bunches as in PSR, e- density • increases towards tail of the bunch due to • ‘trailing-edge multipacting’ tail becomes • unstable first • e- cloud can as well drive coupled-bunch • instabilities (talk by K. Ohmi) • also strong possibility of combined coupled-bunch • head-tail instabilities! (talk by D. Schulte) F. Zimmermann

  4. (1) observations F. Zimmermann

  5. INP Novosibirsk, 1965, bunched beam other INP PSR 1967: coasting beam instability suppressed by increasing beam current; fast accumulation of secondary plasma is essential for stabilization; 1.8x1012 in 6 m ‘first observation of an e- driven instability? coherent betatron oscillations & beam loss with bunched proton beam; threshold~1-1.5x1010, circumference 2.5 m, stabilized by feedback (G. Budker, G. Dimov, V. Dudnikov, 1965). V. Dudnikov, PAC2001 F. Zimmermann

  6. Argonne ZGS, 1965 bunched beam, h=8 (J.H. Martin, R.A. Winje, R.H. Hilden, F.E. Mills) oscilloscope traces showing coherent vertical instability. Sweep rate is 0.2 sec/cm; top: signal from vertical pick up; bottom: beam current. growth time 5-100 ms, threshold 2-8x1011 protons distributed over 8 bunches, largest bunches are most unstable; bunches move independently from each other; threshold varies with horizontal position; range or memory of the blow up does not extend for more than 70 feet around the machine; instability suppressed by wideband (100 MHz) transverse damper F. Zimmermann

  7. 10 ms/cm, 0.2 cm amplitude growth at 1.15x1012 protons, bunched beam BNL AGS, 1965 (E.C. Raka) coherent vertical betatron oscillations and beam loss caused by a poor vacuum (>10-5 mm Hg) in a small portion (1/12) of the ring threshold showed weak dependence on pressure; but rise time strongly pressure dependent threshold around 4x1011 protons per pulse; growth rates 20-500 ms for n=8, 9 modes, slow compared with 8 ms synchrotron period, instability suppressed by sextupoles; narrow-band feedback studied also at Orsay pressure dependent instabilities were observed, and attributed to nonlinear fields introduced by electrons (H. Bruck, 1965) F. Zimmermann

  8. Bevatron, 1971, coasting beam (H.A. Grunder, G.R. Lambertson) n=3-10 mode number changed towards smaller values as instability progressed; electron oscillation frequency decreased as beam size grew for 1012 protons/pulse, beam size doubled in 200 ms; clearing field at pick ups decreased oscillation signal by factor 2; instability not very sensitive to octupoles; gas pressure 2x10-6 Torr; feedback stopped growth F. Zimmermann

  9. ISR, coasting proton beam, ~1972 (R. Calder, E. Fischer, O. Grobner, E. Jones) excitation of nonlinear resonances; gradual beam blow up similar to multiple scattering beam induced signal from a pick up showing coupled e-p oscillation; beam current is 12 A and beam energy 26 GeV 2x10-11 Torr, 3.5% neutralization, DQ=0.015 extensive system of electrostatic clearing electrodes F. Zimmermann

  10. PSR instability, 1988 (D. Neuffer et al, R. Macek et al.) beam loss on time scale of 10-100 ms above threshold bunch charge of 1.5x1013, circumference 90 m, transverse oscillations at 100 MHz frequency beam current and vertical oscillations; hor. scale is 200 ms/div. F. Zimmermann

  11. frequency spectrum of oscillation PSR instability cont’d (D. Neuffer et al, R. Macek et al.) beginning of instability, t=0 log. y scale t=100 ms lower frequencies associated with lower intensities, t=300 ms after beam loss 0 1 GHz F. Zimmermann

  12. PSR instability cont’d (R. Macek et al., M. Blaskiewicz et al.) • maximum number of protons scales linearly with rf voltage • & depends only weakly on bunch length! • conditioning over time • increases in pressure & losses have marginal effect • sustained coherent oscillations below loss threshold • intense e- flux on the wall during bunch passage • instability starts at bunch tail instability & e- production combined process! F. Zimmermann

  13. AGS Booster, 1998/99 (M. Blaskiewicz) time 5 beam current [A] y power density 500 ms -500 ms 0.2 GHz coasting beam vertical instability growth time ~3 ms ~100 MHz downward shift as instability progresses F. Zimmermann

  14. KEKB e+ beam blow up, 2000 (H. Fukuma, et al.) IP spot size threshold of fast vertical blow up slow growth below threshold? beam current F. Zimmermann

  15. KEKB e+ beam blow up, 1999 (H. Fukuma, E. Perevedentsev, et al.) KEKB witness bunch experiment: bunch size depends on its charge; current of preceding bunches was kept constant. Blow up has single- bunch characteristics! F. Zimmermann

  16. centroid motion & bunch size & tilt by KEKB streak camera – preliminary, October 2002 [J. Flanagan, H. Fukuma, S. Hiramatsu, H. Ikeda, T. Mitsuhashi] tail bunches blown up, slight evidence for tilt F. Zimmermann

  17. PEP-II e+ beam blow up, 2000 (F.-J. Decker, R. Holtzapple) specific lumi new old single beam blow up due to combined effect of e-cloud and beam-beam x blow up disappeared after change in working point colliding beam F. Zimmermann

  18. CERN SPS with LHC beam, 2000 Intensity of 72-bunch LHC beam in the SPS vs. time. batch intensity (top) and bunch intensity for the first 4 bunches and last 4 bunches (where losses are visible after about 5 ms) of the batch (bottom) (G. Arduini) F. Zimmermann

  19. CERN SPS with LHC beam, since 2000 x: coupled bunch instability; y: single-bunch instability; t~50 turns (K. Cornelis, G. Arduini,…) • suppressed by damper and high chromaticity (x&y), possibly by linear coupling • much improved after scrubbing, but residual blow up may occur • interaction e- cloud & impedance F. Zimmermann

  20. tune vs oscillation amplitude for a bunch in the tail of a train, sliding average over 32 turns; evidencing positive and negative detuning with amplitude and sort of hysteresis; indication of nonlinear coupling between bunches in the tail due to e- cloud [G. Arduini] F. Zimmermann

  21. calculated & measured head-tail phase difference foran LHC bunch train in the SPS start of train additional e- cloud wake field with wavelength of 0.3-0.5 bunch length can reproduce measurement end of train [K. Cornelis, 2002] F. Zimmermann

  22. central frequency 357 kHz, zero span CERN PS, 2001 with LHC beam (R. Cappi, et al.) adiabatic rf gymnastics for shorten the bunch: horizontal instability leading to persistent oscillations w/o loss threshold Nb~4.6x1010 rise time 3-4 ms almost constant above threshold; but onset in time depends on intensity for highest intensity bunches are longer (sz is constant only over last 100 ms) F. Zimmermann

  23. CERN PS, 2001 with LHC beam (R. Cappi, et al.) instability rise time independent of x (up to x~0.5) marginal effect of octupoles introducing HWHM tune spread of 0.5x10-4. Fourier spectrum up to 10 MHz signal at 357 kHz vs. time Nb~5.5x1010 instability visible only in the horizontal plane (due to combined function magnets!?) no regular pattern along the bunch train PS pickup before extraction pickup in transfer line to SPS F. Zimmermann

  24. BEPC e+ beam size blow up study (ZY. Guo et al, APAC04; talk by J.Q. Wang) sy sy Q’ -46% BPM bias -18% sy 0 600 V 0.2 2.0 solenoid -27% w/o BPM bias head tail 0 30 sy octupole -34% with BPM bias head tail 0.0 1.0 A F. Zimmermann

  25. DAFNE e+ ring, 2004 (M. Zobov, C. Vaccarezza, et al.) 90 consecutive bunches + 30 bucket gap Bunches 25, 50, 70, 90 Bunches at the train end:75, 80, 85,90 horizontal instability positive x tune shift probably linked to electron cloud but several open questions F. Zimmermann

  26. what is new after 40 years? similar cures: chromaticity, octupoles, wide-band and/or narrow-band feedback, clearing electrodes, better pumping new cures: TiN or getter coating clear identification as e-cloud, better diagnostics, improved models, computer simulations still lots of questions F. Zimmermann

  27. (2) simulations F. Zimmermann

  28. simulation approaches • Microbunches (K. Ohmi, PEHT; Y. Cai, ECI) • Soft-Gaussian approximation (G. Rumolo, HEADTAIL v.0) • discrete PIC codes (K. Ohmi, PEHTS; HEADTAIL, G. Rumolo; IHEP program) • quasi- continuous PIC codes (QUICKPIC, USC) • codes by M. Blaskiewicz, T.-S. Wang (centroids) • df method for solving Vlasov-Maxwell equations (BEST code, H. Qin, R. Davidson) F. Zimmermann

  29. no synchrotron motion with synchrotron motion after 100 turns no synchr. motion with synchr. motion densities 2, 4, and 10x1011 m-3 TMCI TMCI & HT BBU Q’x,y=4,8 Q’x,y=0,0 PEHT microbunches, multiple air bag model (K. Ohmi, F.Z., PRL 85, 2000 ) F. Zimmermann

  30. ECI microbunch simulation for PEP-II (Y. Cai, ECLOUD’02) slow emittance growth along bunch train below TMCI threshold e-cloud density for each bunch was obtained by fit to independent simulation (M. Pivi) F. Zimmermann

  31. simulation scheme for discrete PIC code (G. Rumolo) F. Zimmermann

  32. e- TMCI instability in PIC code:effect of synchrotron tune & e- density instability is suppressed by higher synchrotron tune; synchrotron tune required scales ~linearly with density PEHTS (K. Ohmi, et al., PAC 2003) F. Zimmermann

  33. scaling with r/Qs (K. Ohmi, et al., PAC 2003) PEHTS this scaling works well for moderate e- densities; for largest densities there is a different type of emittance growth (2 regimes, see talk by E. Benedetto) F. Zimmermann

  34. code comparison: chromaticity dependence for KEKB PEHTS (K. Ohmi) HEADTAIL (G. Rumolo) in PIC code Q’ acts stabilizing, HT-inst. not seen (different from microbunch codes) (G. Rumolo, F.Z.,PRST-AB 5, 121002, 2002) F. Zimmermann

  35. e- density beam density quasi-static plasma code e-cloud instability simulations using the plasma code QUICKPIC CERN-USC collaboration [T. Katsouleas, A. Ghalam, G. Rumolo,…] F. Zimmermann

  36. Contacts Persons for the Comparison of Electron-Cloud Simulations Identified at ECLOUD02 & G. Bellodi, RAL! detailed comparisons between ECLOUD and POSINST Build-up simulations highly successful; 5 results – Mike Blaskiewicz, ECLOUD (F.Z./G. Rumolo), PEI (Ohmi), POSINST (Pivi/Furman), CLOUDLAND (L. Wang); less results for instability simulations! F. Zimmermann

  37. Code Comparison after ECLOUD02 http://wwwslap.cern.ch/collective/ecloud02/ecsim/instresults.html benchmark case for instability simulations round bunch in a round pipe: 1e11 protons uniform electron cloud with density 1e12 m^-3 each bunch passage starts with a uniform cloud chamber radius 2 cm uniform transverse focusing for beam propagation zero chromaticity, zero energy spread no synchotron motion energy 20 GeV beta function 100 m ring circumference 5 km betatron tunes 26.19, 26.24 rms transverse beam sizes 2 mm (Gaussian profile) rms bunch length 30 cm (Gaussian profile, truncated at +/- 2 sigma_z) no magnetic field for electron motion elastic reflection of electrons when they hit the wall F. Zimmermann

  38. 1 mm 1.4 mm ex,y ex,y PEHTS 1 IP, K. Ohmi HEADTAIL 1 IP, G.Rumolo 5 ms 5 ms 0.06 mm Post-ECLOUD02 Instability Code Comparison - below TMCI threshold; QUICKPIC gives a rather different result! ex,y quasi-continuous QUICKPIC A. Ghalam, T. Katsouleas need several/many IPs!? 4 ms http://wwwslap.cern.ch/collective/ecloud02/ecsim/instresults.html F. Zimmermann

  39. discretized QUICKPIC with 1 IP HEADTAIL with 1 IP discretized QUICKPIC with 1 IP HEADTAIL with 1 IP another comparison of QUICKPIC-HEADTAIL for the emittance growth in LHC; here QUICKPIC was discretized to model 1 IP for benchmarking purposes; both codes consider conducting boundary conditions for rectangular pipe. (E. Benedetto, A. Ghalam) no explanation for difference yet. F. Zimmermann

  40. transition between 2 regimes? HEAD- TAIL change from incoherent to coherent emittance growth as # IPs is increased; no clear convergence; example HEADTAIL simulation for LHC at injection; re=6x1011 m-3 (E. Benedetto, 2003) F. Zimmermann

  41. effect of space charge Simulated bunch shape after 0, 250 and 500 turns (centroid and rms beam size shown) in the SPS with an e- cloud density of re=1012 m-3 without (left) and with (right) proton space charge (G. Rumolo, 2001) F. Zimmermann

  42. <y> ey [mm] suppression by chromaticity – no HT in PIC e-cloud & broadband impedance & tune spread Evolution of centroid vertical position of an SPS bunch over 500 turns for three cases: e- cloud & broadband impedance, broadband impedance & tune spread, broadband impedance alone Vertical emittance versus time for three chromaticities.e-cloud, broad- band impedance & space charge. (G. Rumolo, F.Z.,PRST-AB 5, 121002, 2002) simulation results including effects of space charge, broadband impedance and chromaticity F. Zimmermann

  43. e- cloud effects in single-passsystem (LC beam delivery) • e- can build up along bunch train and reach densities up to 1014 m-3 • blow up of IP spot size for densities above threshold of 1011 m-3 • two effects: breakdown of –I in CCS and direct focusing effect at IP phase advance change direct focusing effect (D. Chen, et al., 2003) F. Zimmermann

  44. e- cloud effect in NLC beam delivery IP beam size vs electron density, revealing threshold at 1011 m-3 IP beam size and central electron density 100 m upstream of IP, vs. position along the bunch (D. Chen, A. Chang, M. Pivi, T. Raubenheimer, 2003) F. Zimmermann

  45. (3) analytical treatments F. Zimmermann

  46. interaction of beam and electron cloud • electrons accumulate near beam center (‘pinch’) • tune spread, nonlinear fields, dynamic beta • incoherent growth • electrons follow transverse perturbations • in bunch shape with delay • wake field • resulting net cloud response can drive instabilities • beam break up (t<< Ts) • TMCI or strong head-tail (t~Ts) • head-tail instability (t>>Ts) • exotic plasma instability? (e.g., monopole type) • ‘incoherent growth’? F. Zimmermann

  47. analytical estimates of equilibrium electron density, wake field and coherent tune shift e- density due to space charge and thermal energy [after S. Heifets, ECLOUD’02] e- density due to charge neutralization [F.Z., LHC Project Report 95, 1997] SB and CB wake of e- cloud [K. Ohmi + F.Z., PRL 85, 3821, 2000, G. Rumolo + F.Z., APAC 2001, Beijing] coherent tune shift due to e- cloud [K.O. +S.H. + F.Z., APAC2001, Beijing] F. Zimmermann

  48. analytical estimates for single-bunch instability • adapt FBII theory • (F.Z., CERN-SL-Note-2000-004) BBU (2) 2 particle model with length (K. Ohmi & F.Z.,PRL 85, 3821, 2000) BBU Head-Tail instability TMCI threshold F. Zimmermann

  49. (3) approximate wake by broadband resonator (K. Ohmi, F.Z., E. Perevedentsev, PRE 65, 016502, 2001) Green function wake ~ damped oscillation resonator frequency ~ electron oscillation frequency low Q: nonlinear force, variation of lattice, variation of beam line density shunt impedance F. Zimmermann

  50. then apply standard instability analysis (3a) TMCI threshold ‘for long’ bunches (G. Rumolo et al, PAC2001) implicit equation since Rs/QR and wR depend on Nb! (applying conventional formula from B. Zotter, CERN/ISR-TH/82-10, 1982) (3b) threshold of ‘fast blow up’ (K. Ohmi, F.Z., E. Perevedentsev, PRE 65, 016502, 2001) implicit equation since Zeff and wR depend on Nb! (applying conventional formalism by R.D. Ruth & Wang, IEEE Tr. NS-28 no. 3, 1981; P. Kernel, et al., EPAC 2000 Vienna; D. Pestrikov, KEK Report 90-21, p. 118, 1991) F. Zimmermann

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