1. Feedback Simulations with Amplifier Saturation, Transient and Realistic Filtering Mauro Pivi, Claudio Rivetta, Kevin Li Webex CERN/SLAC/LBNL 13 September 2012

2. Simulation Code Development Realistic single-bunch feedback system have been implemented in 3 simulation codes: Head-Tail, C-MAD, WARP. At SLAC (by Rivetta, Pivi, Li): –Feedback implemented firstly in C-MAD –Developed and tested then translated in HeadTail

3. Plans for codes utilization The feedback system is simulated with: HeadTail which comes with different options for the SPS: electron cloud, TMCI and advanced impedances model for the SPS. For benchmarking, C-MAD parallel code: electron cloud instability, Intra-Beam Scattering IBS. Allows uploading the full SPS lattice from MAD for increased realistic simulations.

4. HeadTail-CMAD codes comparison Initial beam offset of 2 mm, no electron cloud Feedback Bandwidth 200MHz turns Vertical beam position (m) HeadTail CMAD

5. Following simulation results For our feedback simulations, here: –To reduce the statistical noise, used bunch slices with same constant charge (rather than slices with constant distance). –Kicker bandwidth 500MHz, cloud density of 6e11 e/m 3, gain = 15 (equivalent to Kevin’s 0.5) –Bunch extent: ±4  z (as feedback input matrices)

6. Feedback system design Saturation in the Receiver: ± 250mV Saturation in the Amplifier: defined by DAC ± 200mV Corresponds to kicker signal: ± 4e-5 eV-sec/m

7. Feedback system and electron cloud: reference simulation run *equivalent to 0.5 for Kevin parametervalue Kicker bandwidth500 MHz Cloud density6×10 11 e/m 3 Feedback gain15* Emittance evolutionVertical displacement - each slice Rivetta, Pivi turns Set high electron cloud density

8. Momentum signal delivered by kicker is within saturation limits ± 4e-5 ev-sec/m Central bunch slice # 32: DAC Voltage is within the saturation values ± 200mV Central bunch slice # 32: kicker signal Rivetta, Pivi Feedback system and electron cloud: reference simulation run

9. Rivetta, Pivi (above) Vertical slice positions (central) ADC Voltage at Receiver, well within saturation ± 250mV (below) Yout=fir(Yin) in Volts Each of 64 bunch slices is shown Feedback system and electron cloud: reference simulation run

10. Next Set Amplifier saturation (or DAC saturation) Introduce a transient in the bunch

11. Set Amplifier saturation and beam with initial offset parametervalue Kicker bandwidth500 MHz Cloud densityno cloud Set: No electron cloud Amplifier saturation corresponds to saturation limits for DAC ± 200 mV “Transient” or initial beam offset 500 um Rivetta, Pivi Without electron cloud, the feedback damps the oscillation The question was: with an electron cloud, will it still dump? Vertical displacementKicker signal constrained See also Claudio presentation:

12. Set Amplifier Saturation and beam with initial offset *equivalent to 0.5 for Kevin parametervalue Kicker bandwidth500 MHz Cloud density6×10 11 e/m 3 Feedback gain15* EmittanceVertical displacement - each slice Set: Turn electron cloud ON Saturation limits for DAC ± 200 mV “Transient” or initial beam offset of 500 um (representing position jitter) Rivetta, Pivi turns

13. Set Amplifier saturation (DAC  200 mV), and a beam with initial offset 500um Rivetta, Pivi Constrained kicker saturation limits ± 4e-5 eV-sec/m DAC Control Voltage when saturation is set to ± 200mV Bunch slice # 32: kicker signal Effective Damping of emittance and vertical motion with DAC saturation limits

14. Rivetta, Pivi (above) Vertical slice positions (central) ADC Voltage at Receiver, well within saturation ± 250mV Each of 64 bunch slices is shown Set Amplifier saturation (DAC  200 mV), and a beam with initial offset 500um

15. Shift of beam signal due to realistic Filter Even more shift at kickershift at filter processing measured See also Claudio presentation: Note: All previous simulations (also Kevin’s) did not include a realistic Filter yet, but an ideal one.

16. turns We included a realistic filter in the feedback system Not compensating the signal shift internally in the feedback results in an unstable beam. Shift of beam signal due to realistic Filter Beam unstable! Emittance Vertical displacement - each slice kicker signal exceeds saturation limits

17. Including a realistic filter results in a shift (+ distortion) of the beam signal by ~ +7 slices Beam unstable We compensated by shifting back the beam signal at kicker by shifting -7 slices Transparent process for beam: all internal processing inside feedback system Compensation of shifted beam signal due to Filter

18. compensate shift at kickershift at filter processing measured See also Claudio presentation: Compensation of shifted beam signal due to Filter Rivetta, Pivi

19. Compensation of shifted beam signal due to Filter *equivalent to 0.5 for Kevin parametervalue Kicker bandwidth500 MHz Cloud density6×10 11 e/m 3 Feedback gain15* Emittance growthVertical displacement - each slice turns Rivetta, Pivi

20. Compensation of shifted beam signal due to Filter Momentum signal delivered by kicker is within saturation limits of ± 4e-5 ev-sec/m Rivetta, Pivi Effective damping of emittance and beam motion

21. Simulation plan M. Pivi, C. Rivetta, K. Li, SLAC/CERN Support for proof of principle prototype design final design LHC Long Shutdown

22. What we didn’t include, in these simulations Although the codes have full features capabilities In these results we are not showing issues: –Noise: both in the receiver and amplifier –Limitations in the bunch sampling –Other processing algorithms –Realistic SPS lattice Step by step adding more physics and more reality into simulations

23. Summary Successful implementation of a realistic single- bunch feedback system into codes and very promising initial results Preliminary studies to include: -Amplifier Saturation (DAC) -Beam transient -Compensation of shift due to realistic Filtering Simulation plan to support the feedback prototype, the final design and construction

24. Code comparison (M. Pivi et al. SLAC) (G. Rumolo et al. CERN) (J-L Vay et al. LBNL)