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Review of the two-stream instability: beam and Ion instability

Review of the two-stream instability: beam and Ion instability. Lanfa Wang, SLAC. 3 rd Low Emittance Ring Workshop, Oxford University, 8-10 July 2013. Electron beam and ion-cloud. Two-stream instabilities. Positron/proton beam and electron cloud. (schematic). C ontents.

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Review of the two-stream instability: beam and Ion instability

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  1. Review of the two-stream instability: beam andIoninstability Lanfa Wang, SLAC 3rd Low Emittance Ring Workshop, Oxford University, 8-10 July 2013

  2. Electron beam and ion-cloud Two-stream instabilities Positron/proton beam and electron cloud (schematic) Low Emittance'13 L. Wang

  3. Contents Low Emittance'13 L. Wang • Reviews of Observations • Reviews of theories in linear regime • Beam ion instability in nonlinear regime • Mitigations • Summary • I apologize for many works which couldn't be mentioned here!

  4. Reviews of Observations

  5. Early Observation of vertical beam size blow-up in ELETTRA C. J. Bocchetta, et. al. 1153, EPAC94, 1994 96% 100% 75% Before beam current threshold After threshold ELETTRA Beam current effect (Beam energy 1.1 GeV) Beam filling pattern effect Low Emittance'13 L. Wang

  6. First Direct Observations--ALS, with Helium added, 1997 (J. Byrd et al., PRL, 79 (1997), 79 Single bunch train with 26% gap, Nb=240, 240mA ALS y~30m Nominal 0.25nTorr He added Vertical sideband Vertical emittance growth a factor of 2–3 increase in the vertical beam size Low Emittance'13 L. Wang

  7. head Pohang Light Source (1998) 0.4ntorr 0.7mA Ion pumps off 0.64mA • J. Y. Huang, et al., Phys. Rev. Lett. 81, 4388 (1998) • Single bunch train 250 bunches (46% gap), 180mA • No beam ion instability observed at normal condition (although a instability is expected). • Instability observed with injection of Helium • Bunch size blowup of ~ 2yand the oscillation amplitude of ~ 0.75 y. • Suppression of the FBII was also demonstrated in the presence of the multiple gases or an extra clearing gap in the bunch train. tail 0.2ntorr He 0.61mA 3.34ntorr He 0.52mA 3.34ntorr He 0.6mA 3.34ntorr He 0.6mA Non-monotonic growth Low Emittance'13 L. Wang

  8. KEK ATF N. Terunuma1, et.al. EPAC08 Bunch 12 Bunch 3 Bunch 1 Bunch 15 Bunch 5 Low Emittance'13 L. Wang

  9. SSRF with nominal vacuum 2010 (Bocheng Jiang, et. al. NIMA 614, 2010) amplitude of bunch centroid from BPM Question: Is it true emittance growth? • Single bunch train with bunch Number 450, 37.5% gap (0.54s) • Beam current: 200mA • Vertical emiittance: 27.3pm • Horizontal emittance 3.9nm y=0.61 y=0.61 y=2.04 y=2.04 Vertical beam size measured from the interferometer Low Emittance'13 L. Wang

  10. Observation in SPEAR3 (L. Wang, et. al. MOPS090, IPAC11) (courtesy Dmitry Teytelman) Beam spectrum, 200mA, single bunch train Vertical amplitude along the single bunch train 6 bunch train Vacuum pressure effect (by turning off vacuum pump) Coupling effect, Singe bunch train 192mA Low Emittance'13 L. Wang =2.0 in all cases

  11. Resistive wall Instability (RW) in SEPAR3 Recent experiment in SPEAR3 shows an instability (resistive wall type) threshold with chromaticity about 0.9 with 4 and six bunch train, 500mA beam The resistive wall impedance (1) (2) Six bunch train =0.9 RW Uniform filling =5.4 RW only Ion effect is hard to see Vertical low sideband: stronger vertical instability (1) uniform filling pattern (2) multiple bunch train filling with low chromaticity Low Emittance'13 L. Wang

  12. Summary of the Observations Low Emittance'13 L. Wang • (Vertical) Coupled bunch instability • (Vertical) Beam Emittance growth • The growth in amplitude and beam size is always small, order of beam size • The growth in amplitude and beam size along the bunch is not necessarily monotonic • Remain Questions: • Why the predicted instability is much faster? ( 1ms vs. 16ms in PLS) • Can we explain the non-monotonic growth in the experiment? (Note that Linear theory shows faster growth for the tail bunches)

  13. Reviews of theories in linear regime

  14. Ion distribution (steady status) [P.F. Tavares, CERN PS/92-55 (LP) (1992), also L. Wang, PRSTAB14, 084401 (2011) ] • The ion-cloud has sharp peak near center, non-Gaussian • Ion dimension is smaller than the electron bunch and simply decided by the electron bunch 1D theory The distribution at x0 is =0.577215 Low Emittance'13 L. Wang

  15. First prediction of Fast Ion Instability (FII),1995 • T.O. Raubenheimer and F. Zimmermann, Phys. Rev. E52, No. 5, 5487 (1995). • Single bunch train • Single gas species • Linear space charge force • Constant beam size • Good model for FODO lattice Nonlinear 1sigma • Quasi-exponential growth Bunch Spacing Bunch population N Linear regime Mass number e-bunch size Bunch number Ion density Simulation Low Emittance'13 L. Wang

  16. FII with the variation of beam size (beam optics), 1996 (Gennady Stupakov, KEK Proceedings 96-6) • Single bunch train • Single gas species • Linear space charge force • Variation of the beam size (optics effect) • good for weak instability and lattice with large frequency spread Exponential growth Calculated oscillation frequency of CO+ along the SPEAR3 ring, 500mA Note that it doesn’t apply when i is close to zero (constant beam size); Low Emittance'13 L. Wang

  17. Comparison with analysis Wake field Model (Nonlinear space charge force), 2007- 2011 • The nonlinear space charge force is included. The Q of the wake represents the nonlinearity of the E-force. Typically, it is below 10. • The wake has good linearity when the bunch offset is smaller than the beam size where the fastest instability occurs L. Wang, Y. Cai, and T. O. Raubenheimer, PAC2007 E. Kim and K. Ohmi, Japanese Journal of Applied Physics 48 (2009) 086501 L. Wang, Y. Cai and T. O. Raubenheimer, H. Fukuma. PRSTAB 14, 084401, 2011 Low Emittance'13 L. Wang

  18. FII with nonlinear space charge force, 2009 (E. Kim and K. Ohmi, Japanese Journal of Applied Physics 48 (2009) 086501) • Single bunch train • Single gas species • Constant beam size (no beam optics) • with nonlinear space charge force (Q in the wake field) • When Q=0, got similar solution as Tor and Frank, • When Q is finite and short distance (time)?, the exponential growth rate per revolution of the tail bunch with the train length Note that the ion cloud is assumed to be the same dimension as the electron bunch in their study! Low Emittance'13 L. Wang

  19. How can we get good model to compare with the experiments? Low Emittance'13 L. Wang A realistic model should include the following in one analysis: The nonlinear space charge force The real beam optics (variation of the beam size) The realistic vacuum (multiple gas species, variation along the ring, important to compare with observations) The chromaticity … Note All these factors provide damping to the beam ion instability.

  20. An accurate model with nonlinear space charge, realistic beam optics and multiple gas species vacuum, 2012, 2013 The total wake function of ions along the whole ring Impedancedirectly relate to beam optics and vacuum, and growth rate Impedance of ion cloud in ILC DR with KCS configuration. The total pressure is 0.5nTorr. The partial pressure is 48%, 5%, 16%,14% and 17% for H2, CH4, H2O, CO and CO2 gas, respectively. SLAC-PUB-15353: L. Wang, J. Safranek, T. O. Raubenheimer, M.Pivi, 2012 SLAC-PUB-15638, L. Wang, J. Safranek, Y. Cai, J. Corbett, B. Hettel, T. O. Raubenheimer, J. Schmerge and J. Sebek, 2013, submitted to PRSTAB Low Emittance'13 L. Wang

  21. Compassion with simulation and experiment SLAC-PUB-15638, 2013 When the beam is evenly filled along the ring, the exponential growth rate • The fast growth time is 2.72 ms and 3.18 msfrom analysis and simulation. • Experimentally, the growth time is close to, but slightly shorter than radiation the damping time of 5.0ms analysis Simulation SPEAR3, Six bunch train, 500mA. P=0.37nTorr Low Emittance'13 L. Wang

  22. Summary of Damping factors • Damping mechanism • Nonlinear space charge force • Beam optics • Multiple gas species Linear force only Non-Linear space charge force With realistic Optics Q~4 (SPEAR3) ~2 (ILC DR) Q~10 Q~ broad broader Sharp spectrum Multiple gas species Much broader Ion induced impedance in ILC Damping ring Low Emittance'13 L. Wang

  23. Beam ion instability in nonlinear regime

  24. Instability at nonlinear regime • Theory (S. A. Heifets, SLAC Report No. SLAC-PUB-7411, 1997) A linear Growth at saturation (Y>beam size) Tr is the revolution period • Simulation • Experiment • The amplitude of beam ion instability saturates at order of beam sigma although the instability can be very fast in the linear regime. • Slow growth with amplitude beating which can be well explained! Low Emittance'13 L. Wang

  25. Mitigations

  26. Mitigations • Natural Damping mechanism • Nonlinear space charge force; • Beam optics; • Multiple gas species ; Frequency spread along the bunch trains(weak) Low Emittance'13 L. Wang • Mitigations • Better Vacuum: heavy ions are more important, large cross section, more stable. • Beam filling pattern (almost free): • long bunch train gap (most existing light source use it); • multiple bunch train with short gap (very effective for low emittance, high beam current machine, future ultra low emittance machine ); • longer bunch spacing (work in some case, such as APS, high bunch charge with longer bunch pacing) • Chromaticity • Clearing electrode (not recommended) Suitable for small ring only due to impedance contribution (a)Eva S. Bozokiand Henry Halama, NIMA A307 (1991) 156-166) (b) M. Zobov, Journal of Instrumentation 2, P08002 (2007) • Beam Shaking (not recommended): E. Bozoki and D. Sagan, Nucl. Instrum. Meth. A340, 259(1994) • Feedback

  27. Filling pattern effect: Observation in SPEAR3 (L. Wang, et. al. MOPS090, IPAC11) Now SPEAR3 using 4-6 bunch train and a slightly larger chromaticity to completely suppress the instability!! Beam filling pattern effect, 500mA, vertical chromaticity 2 SPEAR3 beam filling pattern Low Emittance'13 L. Wang

  28. Multiple bunch train effect in SPEAR3: Theory andSimulation Simulation and analyses can predict the multiple bunch train effect! Both agree well with the observation (SLAC-PUB-15638) Instability driven by H2 is damped by radiation damping in most case! CO CO2 H2O Simulation H2 CO2 H2O Analysis, 0.37ntorr H2 is very weak Radiation damping Low Emittance'13 L. Wang Simulation, single bunch train

  29. Multiple bunch train effect in SPEAR3: Theory andSimulation Simulation and analyses can predict the multiple bunch train effect! Both agree well with the observation (SLAC-PUB-15638) Instability driven by H2 is damped by radiation damping in most case! CO CO2 H2O Simulation H2 CO2 H2O Analysis, 0.37ntorr H2 is very weak Radiation damping Low Emittance'13 L. Wang Simulation, single bunch train

  30. Chromaticity effect in SPEAR3: experiment and analysis (L. Want, et. al. SLAC-PUB-15638) The effective impedance of a bunched beam is given by single bunch train, 500mA Analysis Low Emittance'13 L. Wang

  31. Bunch-by-bunch Feedback Test in SPEAR3 (courtesy Dmitry Teytelman) The feedback is initially turned off and turned on around 20ms. Close to uniform filling, total beam current of 448mA Noise in the feedback: Noise in the pickup or amplifier may be transferred to the kicker, which then induces some jitter on the beam. The net result of the feedback is that the beam will reach certain rms oscillation amplitude which is determined by the feedback damping and noise • (A. W. Chao and G. V. Stupakov, KEK Proceedings 97-17, 110 (1997)) Low Emittance'13 L. Wang

  32. Summary and discussion (1/2) Low Emittance'13 L. Wang • Many observations included normal machine condition • The instability can be well explained using Impedance model, which includes nonlinear space charge, realistic beam optics, multiple gas species vacuum and chromaticity; • There are reasonable good agreements in SPEAR3: growth rate, filling pattern effect, beam spectrum (frequency), etc. • The beam ion instability is broad band due to the beam opticsand multiple gas species in the vacuum. It is essential to includes both of them in analysis and simulation • (Most of ) the experiment results are in saturation regime: small amplitude in the order of beam size and non-monotonic growth along the bunch train!

  33. Summary and discussion (2/2) Low Emittance'13 L. Wang • Some issues need to be addressed • There is a difficulty to separate the coupled instability and emittance growth in the experiment if average method is used. • The initial experiment shows feedback works to suppress the instability amplitude to sub-sigma, However, more studies are required to look at the noise level. • While the coupled instability is well studied, the emittance growth is not studied much, which is a concern for Ultimate Storage Ring, such as PEPX.

  34. Acknowledgements Low Emittance'13 L. Wang • thanks to Y. Cai, A. Chao,J. Corbett, H. Fukuma, K. Ohmi, M. Takao , T. Raubenheimer, J. Safranek, J. Sebek, Ryutaro Nagaoka, Dmitry Teytelman, SSRL operators • Thanks Riccardo, Susanna and Yannis

  35. Beam ion instability in Ultra Small emittanceRing--- A special case

  36. Beam Ion Instability in the Ultimate Storage Ring--PEPX Y. Cai, et. al.,Synchrotron Radiation News, Vol.26,37, 2013 • The growth time is order of 1ms! • Theory doesn't work in this case y=1.89ms x=3.35ms USR x=1.34ms No hori instability Multiple bunch train filling: 10 bunch train 200mA Vacuum: total pressure 0.4nTorr, H2(20%),CH4(20%),H2O(20%),CO(20%),CO2(20%) FEL Low Emittance'13 L. Wang

  37. CSR Spectra & cancellation of emittance growth Lanfa Wang, SLAC 3rd Low Emittance Ring Workshop, Oxford University, 8-10 July 2013

  38. Contents Low Emittance'13 L. Wang • Characteristics of CSR Spectra • Long CSR wake • Towards full 3D model • Cancellation of emittancegrowth due to CSR • Summary

  39. Spectra at NSLS-VUV Ring G. L. Carr, S. L. Kramer, N. Jisrawi, L. Mihaly, and D. Talbayev, PAC’01, p377 Low Emittance'13 L. Wang

  40. Comparison with simulation (D. Zhou, IPAC12 talk, MOOBB03) Low Emittance'13 L. Wang

  41. The VUV spectrum also is explained by the theory Robert Warnock and John Bergstrom, PAC11, WEP119 Toroidal Vacuum Chamber R. L.Warnock and P. Morton, SLAC-PUB-4562; Part. Accel. 25, 113 (1990). Low Emittance'13 L. Wang

  42. Another explanation of the resonance D. Zhou, et al., Jpn. J. Appl. Phys. 51 (2012) 016401. B • Outer wall reflection causes the modulation • The spike in impedance induces long wake tail C s=AC+CB-arc(AB) xb A p.l. L=0.5m L=2m L=8m Low Emittance'13 L. Wang

  43. CSR Spectrum from CLS Robert Warnock and John Bergstrom, PAC11, WEP119 The spectrum is repeatable Note that the frequencies of the peaks is more important than the amplitude Low Emittance'13 L. Wang

  44. CSR spectrum at CLS measurement • Indeed, the spikes in CLS can’t be explained by a single magnet mode, and even the torus model (long magnet); • Besides the geometry of the cross section of the beam pipe; The realistic layout of the ring, including straight section, is crucial. Torus Model, only magnets With straight section, realistic layout but a constant cross section Low Emittance'13 L. Wang

  45. “Long Range” (~meter) CSR Wake

  46. Wake filed measured by EO detector and Interbunch communication at ANKA • The “long range” wake cause multiple bunch effect • Multiple bunch effect observed: ANKA & CLS: Increasing the charge in preceding bunch enhances the radiation. Strong evidence of interbunch cooperation! • VitaliJudin, Lowemittance’11 • Robert Warnock,5th Microwave instability workshop, 2013 N. Hiller, et. al. IPAC13, MOPME014 Low Emittance'13 L. Wang

  47. Long range Wake in Super-KEKB DR The spikes in the impedance (interference) causes “long range” wake Single bend; 1/32 of the ring 6/32 of the ring; 16/32 of the ring; L. Wang, H. Ikeda, K. Oide K. Ohmi and D. Zhou, IPAC13, TUPME017 D. Zhou, et al., Jpn. J. Appl. Phys. 51 (2012) 016401. Low Emittance'13 L. Wang

  48. CSR impedance with realistic geometry Similar as the geometry impedance, the CSR impedance depends on the geometry of the whole beam pipe.

  49. New CSR code with arbitrary cross section of the pipe Required for Self-consistent computation Initial field at the beginning of the bend magnet After the bend magnet Agoh, Yokoya, PRSTAB 054403,2004 G. Stupakov, PRSTAB 104401, 2009 K. Oide, PAC09 D. Zhou, JJAP (2012) 016401. Low Emittance'13 L. Wang

  50. Example of fields Low Emittance'13 L. Wang

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