1. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 1 Simulation of E-Cloud driven instability and its attenuation using a feedback system in the CERN SPS* J.-L. Vay, J. M. Byrd, M. A. Furman, R. Secondo, M. Venturini - LBNL, USA J. D. Fox, C. H. Rivetta - SLAC, USA; W. Höfle - CERN, Switzerland *WEOBRA02

2. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 2 The problem  Transverse instability observed in SPS beams due to electron clouds  Interaction between e-cloud and beam leads to large transverse oscillations  Feedback system was proposed to control the beam transverse motion  We use the Particle-In-Cell framework Warp-Posinst to investigate dynamics of instability as well as feasibility and requirements of feedback Pipe e-e- gas e-e- bunch 1 bunch 2

3. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 3 Our simulation framework encompasses the Warp and Posinst PIC codes 2-D slab of electrons 3-D beam s proc 1 2 N/2 N/2+1 N-1 N Station n n+1 n+N/2-1 n-N/2 n+N-2 n+N-1 Warp quasistatic model similar to HEADTAIL, PEHTS, QuickPIC. parallellized using pipelining Mesh refinement provides higher efficiency Secondary emission from Posinst: - enables self-consistent multi-bunch calculations. Example: - 2 bunches separated by 25 ns in SPS 36 35 Beam ions Electrons Beam direction side view top view side view

4. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 4 Physics of electron interaction with bunches Beam direction 1. Electrons injected here from Posinst dump Beam density (x10 15 ) at t=0 (bunches 35-36 = buckets 176-181) chamber wall 3D view

5. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 5 Physics of electron interaction with bunches 2. Electrons are focused by bunch chamber wall 3D view Electron density (x10 12 m -3 ) at turn 500 (bunches 35-36 = buckets 176-181)

6. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 6 Physics of electron interaction with bunches 3. High-density spikes eject electron jets chamber wall 3D view Electron density (x10 12 m -3 ) at turn 500 (bunches 35-36 = buckets 176-181)

7. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 7 Physics of electron interaction with bunches 4. Secondary emission from impact of e- jets on walls chamber wall 3D view Electron density (x10 12 m -3 ) at turn 500 (bunches 35-36 = buckets 176-181)

8. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 8 Physics of electron interaction with bunches 5. Electrons fill the chamber chamber wall 3D view Electron density (x10 12 m -3 ) at turn 500 (bunches 35-36 = buckets 176-181)

9. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 9 Physics of electron interaction with bunches 6. Electrons interact with next bunch chamber wall 3D view Electron density (x10 12 m -3 ) at turn 500 (bunches 35-36 = buckets 176-181)

10. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 10 Electrons after 500 turns chamber wall Electron density (x10 12 m -3 ) at turn 500 (bunches 35-36 = buckets 176-181) 3D view

11. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 11 Bunches 35 and 36 after 500 turns chamber wall Beam density (x10 15 m -3 ) at turn 500 (bunches 35-36 = buckets 176-181) 3D view

12. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 12 Fractional tune Comparison with experimental measurements  Separation in two parts, core and tail, with tune shift in tail higher than in core  Similar tune shift for the core of the beam but higher with simulations for tail  More experimental results at poster WEPEB052, J. D. Fox et al, “SPS Ecloud instabilities - Analysis of machine studies and implications for ecloud feedback”, Wednesday, May 26, 16:00-18-00. ExperimentWarp-Posinst Bunch 36, Turn 0-100Bunch 119, Turn 100-200 headtailheadtail Fractional tune Z slice Nominal fractional tune=0.185

13. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 13 Comparison with experimental measurements - 2  Both expt. and sim. show activity level inversely proportional to frequency  Interesting difference: instability grows in simulation but is already there at turn 0 in experiment ExperimentWarp-Posinst Turn Freq. [GHz] Spectrum bunch 35 Spectrum bunch 36

14. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 14 Bunches transverse internal structure has fairly long wavelength component Can a feedback system resolving the bunch control the instability? What characteristics are needed, (amplitude, frequency range, noise level, delay, …)? m -3

15. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 15 Simulated feedback model E f is set from estimated velocity offset v y : predicts y’(t)=v y /v z from records of centroid offsets at two previous turns y i-1 (t) and y i (t) using linear maps, ignoring longitudinal motion and effects from electrons EfEf LfLf vzvz z y  v y = (q/  m) E f L f /v z Kick in transverse velocity E f = g  v y (  m/q) v z / L f  g  i -1 i i +  with In following results,  =1. (for  =0, same as Byrd PAC95 and Thompson et PAC09) SPS

16. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 16 Emittance history with feedback on/off, with gains g=0.1 and 0.2 Feedback very effective at damping instability. Better with g=0.2 for bunch 36. Run with bunch 35 frozen. Effect of bunch 35 on 36 is weak.

17. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 17 Tests with finite bandwidth Runs with 5 different digital filters with cutoffs (-3 dB) around 250, 300, 350, 450 and 575 MHZ. With these filters, cutoff>450 MHz needed for maximum damping. cutoff

18. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 18 Multi-bunch simulations: beware of electron injection procedure. Run of bunch (36,37) gives same emittance histories as (35,36). Single bunch runs with electron load (a)Uniform (b)Random refreshed at each time step (c)Random using load from t=0 => Bunch 36 experienced more noise than 35 because of random secondary electron generation. Why is emittance of 36 >> 35? Is it because raises by ~8%? Source of inconsistency?

19. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 19 Summary and future work  Beam-ecloud self-consistent simulations are now within reach, allowing detailed understanding of the dynamics and control of beam instability via feedback systems.  Improvements to Warp-Posinst quasistatic model mesh refinement, secondary emission, gas ionization, better feedback model.  Multi-bunch simulations are now possible (thanks in part to parallelism).  Good qualitative and semi-quantitative agreement with experiment.  Modeling of bunches 35 and 36 in SPS at 26 GeV show effective damping from simulated feedback, provided that bandwidth cutoff>450 MHz.  Care must be exercised with interpretation due to statistical implications of electrons injection procedures.  A lot more work is needed, including: implementation of planed feedback n-tag prediction, filtering, etc; better control of numerical noise issue in simulations, eventually using as proxy to emulate real machine noise; replace smooth focusing with linear optics, etc.

20. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 20 Backups

21. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 21 Physics of electron interaction with bunches Beam direction 1. Electrons injected here from Posinst dump Electron density (x10 12 ) at t=0 (bunches 35-36 = buckets 176-181) 2. Electrons are focused by bunch 3. High-density spikes eject electron jets 4. Secondary emission from impact of e- jets on walls 5. Electrons fill chamber and interact with next bunch chamber wall

22. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 22 Example: application to SPS @ 120 GeV

23. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 23 SPS - W=120 GeV Electron density at station 0 Buckets 95-100Buckets 345-350

24. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 24 Larger 3D view of electron density at t=0 (buckets 95-100) Beam direction Electrons injected here from Posinst dump

25. IPAC10, Kyoto, Japan, May 23-28, 2010 E-cloud feedback simulations - Vay et al. 25 Added model for kicker E L vzvz  v y = (q/  m) E L/v z Kick in transverse velocity Kick is at fixed station and is on/off on turn basis. From betatron tune , can infer induced maximum displacement  y=   v y /v z Example:  SPS at injections (26 GeV)  L = 37.5 cm   = 71.87  For a field of 10 kV/m, the beam maximum displacement is ~10  m. z y