1. Progress Report on the Ultra-fast Harmonic Kicker Cavity Design and Beam Dynamic Simulation Yulu Huang 1,2 H. Wang 1, R. A. Rimmer 1, S. Wang 1 1.Thomas Jefferson National Accelerator Facility, Newport News, VA,23606 2.Institute of Modern Physics,Chinese Academy of Science, Lanzhou, Gansu,730000

2. Outline 2  Fast Kicker Requirements for the JLEIC  Kicker Waveform  Challenges and Solutions  Beam Dynamics Tracking for One Kicker Scheme  Beam Dynamics Tracking for Two Kicker Scheme  Kicker Cavity Design  Prototype Cavity Progress  Multi-Cavity Kick-Drift Model Tracking  Conclusion  Acknowledgement

3. 3 Kicker Requirements for the JLEIC  Electron cooling is essential for achieving high luminosity. High energy bunched electron cooling is part of multi-phased cooling scheme of JLEIC  To achieve very high current (~1.5A) for bunched beam cooling in the future high luminosity upgrade, a circulator ring was proposed to reuse the electron bunches  Electrons circulate 10~30 turns in the circulator ring, beam current and bunch repetition frequency in the ERL can be reduced by a factor of 10~30  One or two ultra-fast kickers are required for this circulator ring

4. Challenges and Solutions 4 ~ns ~10 of ns Few kV Few mrad  Pulsed power supplies, especially with these characteristics are beyond state of the art.  An alternative driving method is summing simple cosine waves at sub- frequencies of the final beam repetition frequency to generate a continuous waveform.

5. Kick Waveforms to Kick Every 10 th Bunch 5 10 Harmonics+DC offset9 Harmonics+DC offset

6. One Kicker Scheme Tracking 6 P [MeV/c]55 ε x, ε y [nm] 10 β x, β y [m] 10 σ s [cm] 3 σ Δ p/p 3e-4 f [MHz]476.3 n10 V kick [kV]55 Incoming bunch Outgoing bunch kicker Monitor  One kicker scheme tracking with ELEGANT was following Amy Sy ’s presentation in the COOL2015 workshop.  Circulator ring approximated with 1 turn linear transfer matrix  Kicker waveform generated using a series of zero-length RF deflectors with appropriate frequencies, phases, and amplitudes  One monitor was put after the kicker  One bunch recirculates for 10 turns One kicker tracking scheme and tracking parameters obtained from Amy Sy x x’ x -1 mrad

7. One Kicker Tracking Result 7 Flat-Top Zero-Gradient Equal-AmplitudeLeast-Modes Kicked in Kicked out

8. Emittance Growth During Recirculation 8  For zero-Gradient scheme, negligible emittance growth seen during recirculation due to the near-zero residual voltage  For other three schemes, larger emittance growth seen due to the larger residual voltage gradient (the wave slopes)

9. Two Kicker Scheme Tracking 9 Incoming bunch Outgoing bunch Kicker 1 Monitor 1 Kicker 2 Recirculating bunch (180 degree Betatron phase advance in x-x’ plane) Pi Matrix x x’ x -1 mrad 1 mrad x’ ~0 mrad x x x’ x Monitor 2 Monitor 3 Single particle in the recirculating bunch The residual kick due to the waveform slope can be canceled Kicker 2 180 phase advance (x 0,x’ 0 ) (x 0,x’ 0 -) (-x 0,-x’ 0 +) Kicker 1 (-x 0,-x’ 0 )

10. 10 Two Kicker Tracking Result Flat-Top Zero-GradientEqual-AmplitudeLeast-Modes Monitor 1 Monitor 2 Monitor 3 Kicked in Kicker 2 Kicked out New bunch Kicked in 180 degree rotate Kicker 1

11. 11 Bunch Rotated after the Pi Matrix Monitor 2 Monitor 3 180 degree Betatron phase advance in x-x’ plane

12. 12 Emittance Growth During Recirculation  Negligible emittance growth during recirculation for all schemes due to the cancelation of the kicker-Pi Matrix-kicker scheme  Flat-Top scheme has minimum emittance growth due to the uniform kick when the bunch was kicked in  If the emittance tolerance increase, harmonic modes can be reduced to half with Least- Modes scheme

13. Kicker Cavity Model 13 5 harmonics 47.63MHz  1,3,5,7,9 3 harmonics 47.63MHz  2,6,10 1 harmonics 47.63MHz  4 1 harmonics 47.63MHz  8 Frequency (MHz) (kV) Flat-Top (kV) Zero- Gradient (kV) Equal- Amplitude(kV) Least- Mode(kV) #1 47.6313.7119.95.511 142.8910.5327.75.511 238.155.5035.5 333.410.633.35.5 428.67-2.4321.15.5 #2 95.2612.4628.85.511 285.782.9174.45.5 476.3-3.0115.5 #3190.528.1296.65.511 #4381.04-1.2092.25.5 DC7.7685.5 Total kick voltage=55kV

14. Shunt Impedance and Power 14 Mode (MHz) Flat-Top Kick Voltage (kV) CST Trans. Shunt Impedance (Ω) Dissipated Power (W) 47.63 13.711 7.53E624.98 95.26 12.462 1.08E714.38 142.89 10.532 3.95E628.05 190.52 8.1290 1.15E75.73 238.15 5.5030 2.92E610.39 285.78 2.9170 4.08E62.08 333.41 0.6300 1.86E60.21 381.04 -1.2090 8.64E60.17 428.67 -2.4320 1.13E65.23 476.3 -3.0110 1.56E65.81 DC 7.768 Total 55 3.18E791.55 Shunt Impedance and Dissipated power is calculated for copper

15. Half-Scale Prototype Cavity 15  Half scale prototype cavity with 5 harmonic modes (fundamental f=95.26MHz)  Engineering drawings were already finished  All materials are already delivered 32 inch ~6 inch ~2 inch 5 Stub tuners for 5 harmonic modes (tuner positions are optimized) Beam pipe One loop coupler port for 5 modes 4 Straight slope tapers on the inner conductor (Taper positions are optimized)

16. Multi-Cavity Kick-Drift Model 16 X’X’ X 1 mrad Incoming bunch Outgoing bunch Single particle in the Recirculating bunch (-x 0 -(3x’ 0 +3 1 +2 2 + 3 )Drift, -x’ 0 + 1 + 2 + 3 + 4 ) (x 0,x’ 0 ) (x 0 +(3x’ 0 +3 1 +2 2 + 3 )Drift, x’ 0 - 1 - 2 - 3 - 4 ) (-x 0 -x’ 0 Drift,-x’ 0 ) K21+Dr+K22+Dr+K23+Dr+K24 K11+Dr+K12+Dr+K13+Dr+K14 180 betatron phase advance Not fully cancelation Residual emittance growth is depending on the Drift, but still a very small value 180 degree phase advance

17. 17 Monitor 3Monitor 2 Monitor 1 Monitor 2 Monitor 3 Multi-Cavity Kick-Drift Tracking Same bunch, but in different time scale

18. 18 Monitor 1 Monitor 3 Monitor 2 Monitor 1 Monitor 2 Monitor 3 Multi-Cavity Kick-Drift Tracking

19. 19 Emittance Growth During Recirculation Initial Normalized Emittance

20. Conclusions 20  An Ultra-fast, high repetition rate kicker concept was developed.  Several kick waveforms were discussed with the beam dynamics tracking in ELEGANT.  A series harmonic kicker cavities with great power efficiency were designed to generate such kind of kick waveform. Beam dynamics tracking is also studied for this multi-cavities scheme.  An half scale prototype cavity is under manufacture.  A 3-D bead-pull system is set up for the future bench test

21. Acknowledgement 21 Acknowledge to Jiquan Guo for the helpful discussions during this work ! Acknowledge to Amy Sy for the help on ELEGANT tracking!