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, Institute of Modern Physics,Chinese Academy of Science, Lanzhou, Gansu,730000

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 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

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.

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

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

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

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)

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 phase advance (x 0,x’ 0 ) (x 0,x’ 0 -) (-x 0,-x’ 0 +) Kicker 1 (-x 0,-x’ 0 )

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

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

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) # # # # DC Total kick voltage=55kV

Shunt Impedance and Power 14 Mode (MHz) Flat-Top Kick Voltage (kV) CST Trans. Shunt Impedance (Ω) Dissipated Power (W) E E E E E E E E E E65.81 DC Total E Shunt Impedance and Dissipated power is calculated for copper

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)

Multi-Cavity Kick-Drift Model 16 X’X’ X 1 mrad Incoming bunch Outgoing bunch Single particle in the Recirculating bunch (-x 0 -(3x’ )Drift, -x’ ) (x 0,x’ 0 ) (x 0 +(3x’ )Drift, x’ ) (-x 0 -x’ 0 Drift,-x’ 0 ) K21+Dr+K22+Dr+K23+Dr+K24 K11+Dr+K12+Dr+K13+Dr+K 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 Monitor 3Monitor 2 Monitor 1 Monitor 2 Monitor 3 Multi-Cavity Kick-Drift Tracking Same bunch, but in different time scale

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

19 Emittance Growth During Recirculation Initial Normalized Emittance

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

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