Feedback Simulations with Amplifier Saturation, Transient and Realistic Filtering

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 HeadTail CMAD Vertical beam position (m) turns • Initial beam offset of 2 mm, no electron cloud • Feedback Bandwidth 200MHz

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/m3, gain = 15 (equivalent to Kevin’s 0.5) • Bunch extent: ±4 sz (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 • Set high electron cloud density *equivalent to 0.5 for Kevin turns Emittance evolution Vertical displacement - each slice Rivetta, Pivi

8. Feedback system and electron cloud: reference simulation run Central bunch slice # 32: kicker signal 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 Rivetta, Pivi

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

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

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

12. Set Amplifier Saturation and beam with initial offset • Set: • Turn electron cloud ON • Saturation limits for DAC ±200 mV • “Transient” or initial beam offset of 500 um (representing position jitter) *equivalent to 0.5 for Kevin turns Emittance Vertical displacement - each slice Rivetta, Pivi

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

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

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

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

17. Compensation of shifted beam signal due to Filter • 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

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

19. Compensation of shifted beam signal due to Filter *equivalent to 0.5 for Kevin turns Emittance growth Vertical displacement - each slice 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 • Effective damping of emittance and beam motion Rivetta, Pivi

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

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) (J-L Vay et al. LBNL) (G. Rumolo et al. CERN)