H. Wang1, R. A. Rimmer1, S. Wang1, J. Guo1 Ultra-Fast Harmonic Resonant Kicker Design for the MEIC Electron Circular Cooler Ring (Update after ERL 2015 Workshop) Yulu Huang1,2 H. Wang1, R. A. Rimmer1, S. Wang1, J. Guo1 1.Thomas Jefferson National Accelerator Facility , Newport News, VA,23606 2.Institute of Modern Physics ,Chinese Academy of Science, Lanzhou, Gansu,730000

Motivation and Concept Electron cooling is essential for achieving high luminosity for MEIC High energy bunched electron cooling is part of multi-phased cooling scheme for MEIC To achieve very high current for bunched beam cooling in the future high luminosity upgrade, we adopt a circulator ring to reuse the electron bunches An ultra-fast kicker (less than 2.1 ns ,476.3MHz) is required for this circulator ring We start an R&D proposal to develop such a kicker Our approach is to generate a series harmonic modes with RF resonant cavities Every 25th bunch will be kicked while all the other bunches un-kicked with the designed prototype cavities

MEIC Multi-Phased Electron Cooling Reduce/maintain emittance High Luminosity! same velocities same 𝜸 factor   Phase Function Proton kinetic energy (Gev/u) Electron kinetic energy (MeV) Cooler type Booster 1 Assisting accumulation of injected positive ions 0.11 ~ 0.19 0.062 ~ 0.1 DC 2 Emittance reduction 1.09 Collider ring 3 Suppressing Intra-Beam Scattering and maintaining emittance during stacking of beams 7.9 4.3 Bunched Beam Cooler (ERL) 4 Suppressing Intra-Beam Scattering and maintaining emittance during collision 100 55

Single Turn ERL Cooler Scheme in MEIC Baseline Design ion bunch electron bunch Cooling section solenoid SRF Linac dump Gun/booster 0.2 A injection, 55 MeV,476.3MHz

High Luminosity Upgrades Need High Current! (1.5A) ion bunch electron bunch circulator ring Cooling section solenoid Fast kicker SRF Linac dump Gun/booster Electrons circulate 25 Turns in circulator ring 1.5A, 55MeV, 476.3MHz Periodically kick 1 in every25 bunches Ultra-fast ,2.1 ns 55kV(1 mrad kick angle) 0.06A, 55MeV, 19.052MHz(476.3/25) (bunch repetition frequency)

Ideal Kick Voltage Pulse Shapes How to generate such a pulse? DC? pulse rise time challenge repetition frequency RF? broad-band system many harmonics needed

FFT of the Kick Voltage Pulse Demonstrated 10 turns need 10 harmonics Prototype a simplified version with 1 kick every 10th bunch FFT Reconstruct the square pulse with first 10 modes Flat top kick can be got by adjusting the pulse width before FFT Head tail difference can be canceled by a 1800 betatron phase advance between two kickers

Could we used less modes to produce more un-kicked bunches? Concept update from Jiquan: 5 modes for 10 un-kicked bunches Mathematic solution By Truncated FFT?

Could we used less modes to produce more un-kicked bunches? Concept update from Jiquan: 12 modes for 24 un-kicked bunches mode # 1 2 3 4 5 6 7 8 9 10 11 12 Mode amp 2.2 4.4 phase

How to Generate Harmonic Modes? beam beam Quarter wave resonator with loading capacitor Electric Field Deflection Fix the cavity length, the gap distance, and the outer conductor radius Taper the inner conductor (change Z0)to make the frequencies to be harmonics. l≈(2n+1)λ/4 Cavity Length related with Frequency

Cavity Model for 10 Modes 5 harmonics 47.63MHz1,3,5,7,9 ξ= 𝑎(𝑖𝑛𝑛𝑒𝑟 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑟𝑎𝑑𝑖𝑢𝑠) 𝑏(𝑜𝑢𝑡𝑒𝑟 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑟𝑎𝑑𝑖𝑢𝑠) g is the end gap(beam pipe diameter)

Cavity Model (Update) for 12 modes 6 harmonics 19.052MHz1,3,5,7,9,11 3 harmonics 19.052MHz2,6,10 2 harmonics 19.052MHz4,12 1 harmonics 47.63MHz8 No more cavity is needed for 12-mode operation for the 25-turns CCR option Cavity picture is not updated yet 3.93 m

Boundary Conditions Plot Electric Field Along The Red Curve In the 5 Modes Cavity Just odd-integer multiples of the fundamental mode can be generate in one cavity!

M Cavities Needed for N Harmonics Cavity #1 Cavity #2 Cavity #3 Cavity #4 Cavity #5 2𝑛+1 𝑓 0 𝑁 2𝑛+1 2𝑓 0 𝑁 2𝑛+1 4𝑓 0 𝑁 2𝑛+1 8𝑓 0 𝑁 2𝑛+1 16𝑓 0 𝑁 𝐻𝑒𝑟𝑒 𝑓 0 𝑖𝑠 𝑡ℎ𝑒 𝑏𝑢𝑛𝑐ℎ 𝑟𝑒𝑝𝑒𝑡𝑖𝑡𝑖𝑜𝑛 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑖𝑛 𝑡ℎ𝑒 𝐶𝑜𝑜𝑙𝑒𝑟 𝑟𝑖𝑛𝑔(476.3MHz). n=0,1,2,… Relationship between Cavity number and Harmonics number: 𝟐 𝑴 −𝟏≤𝑵 If we use 4 cavities, the max Harmonic we can get is 15 If we use 5 cavities, the max Harmonic we can get is 31

Flat Top for the Kicked Bunch We can adjust the square pulse width b to get a flat top kick b/2 Consider a normalized square pulse with width b, in one period [-b/2,2𝜋-b/2],it can be expanded to a Fourier series in the following form : Here s is the harmonic number, x is the distance variable For a flat top along +/-3𝜎 of 2cm bunch length, consider 10 harmonic modes, the fundamental mode is 47.63MHz. We can solve the equation F(10, b, 0.06)=F(10, b, 0) (The head and tail voltage is equal to the center voltage.) Flatness of the flat top Even larger b means better flatness, but larger b also means larger amplitude of each mode thus more power needed, and a wider pulse also have the effect on the unkicked bunch. So far initial beam dynamic simulation (A. Sy) indicates the flatness <0.01 is acceptable!

Shunt Impedance and Power Mode (MHz) FFT Kick Voltage (kV) CST Trans. Shunt Impedance (Ω) Dissipated Power (W) 47.63 13.711 7.13E6 26.37 95.26 12.462 1.14E7 13.62 142.89 10.532 4.09E6 27.12 190.52 8.1290 1.35E7 4.89 238.15 5.5030 3.14E6 9.64 285.78 2.9170 6.09E6 1.40 333.41 0.6300 2.65E6 0.15 381.04 -1.2090 1.65E7 0.09 428.67 -2.4320 2.40E6 2.46 476.3 -3.0110 4.57E6 1.98 DC 8.2760   Total 55.508 3.56E7 87.72 Two to Three orders of magnitude lower than a strip-line kicker The kick voltage (amplitude with phase) is come from the FFT result Transverse shunt impedance with TTF is calculated with CST Microwave Studio. (Cavity model is simplified, straight line taper with no blending is used to achieve the target frequency for each mode, beam pipe is not optimized )

Compensated for the un-kicked bunch Shaoheng and Jiquan Use 180o phase shift in optic design in kick plane between two kickers Head-tail residuals cancel out after 10 (25) turns Need multi-turn tracking simulation to confirm Negative kick Zero kick Positive kick X’ X Negative kick Zero kick Positive kick X’ X

Input Loop Coupler Design 30mm in length, 46mm in width Fundamental mode has a lowest coupling strength but requires the highest power.1360mm is selected, the fundamental mode is critically coupled, and the higher modes are slightly over-coupled

Cavity Tuning Need Estimation Operation Frequency (MHz) Q0 For 300K Copper 𝛽 Bandwidth (kHz) Designed Frequency with Taper (kHz) Error Frequency by Design (kHz) Five Modes Cavity 47.63 8586 ≈1 ≈11.09 47.62991 -0.09 142.89 14689 ≥1 ≥19.46 142.8915 0.15 238.15 18973 ≥25.10 238.153 3 333.41 22472 ≥29.67 333.4117 1.7 428.67 25536 ≥33.57 428.6718 1.8 Three Modes Cavity 95.26 12002 ≈16.04 95.26267 2.67 285.78 20784 ≥27.50 285.7868 6.8 476.3 27056 ≥35.21 476.3087 8.7 One Mode Cavity 190.52 15298 ≈24.91 190.5267 6.7 381.04 19435 ≈39.21 381.0361 3.9 Bandwidth is calculated for one-coupler system ∆ 𝑓 𝑛 = 𝑓 𝑛 𝑄 0𝑛 (1+ 𝛽 𝑛 ) Fundamental mode in each cavity is critical coupled, higher modes in the 5 modes and 3 modes cavities is over coupled. With an optimized taper design, harmonic frequencies without the tuner tunings can be designed within the bandwidths of operation modes. Two feedbacks from IPAC2015 and ERL 2015 have been well communicated

Stub Tuner Design Mistuning due to manufacturing tolerance can be returned by stub tuners inserted into the cylinder wall. Extra power loss on stub tuners Might be doubled the RF power consumption 5 mm in height, 20 mm in diameter 3 Modes Cavity 3 Tuner Needed 5-stub tuners design on 5-mode cavity is in progress Number of Tuners = Number of Modes

Analytical Calculation to Confirm the CST Simulations Transit Time Factor Characteristic Impedance of the transmission line Surface Resistance 𝜂 is the vacuum wave impedance

Transverse Strip-line RF Kicker for PEP-II at SLAC Port1 Port2 Port4 Port3 180o phase shift Frequency f (MHz) Kick Voltage V (kV) Voltage Phase (rad) Impedance RT2 (Ω) Power PK (kW) 47.63 13.711 15076.6 6.235 95.26 12.462 9859.0 7.876 142.89 10.532 4373.1 12.682 190.52 8.129 934.4 35.360 238.15 5.503 0.016 9.403E5 285.78 2.917 422.3 10.074 333.41 0.63 806.4 0.246 381.04 1.209 𝜋 613.7 1.191 428.67 2.432 183.0 16.160 476.3 3.011 2.833E5 DC offset 8.256   Total 55.488 3.324E4 89.824 for 1 mrad kick angle

Conclusions An Ultra-fast , high repetition rate(2.1ns,476.3MHz) kicker was conceptual developed. It’s great power efficiency, just 87.72W. Cost-effective, just copper cavities in room temperature. Cavity RF design and Concept design of the stub tuner and loop coupler is done. Beam dynamics tracking is being study. Mechanical design, HOM damping will be studied. Prototype Cavity will be made Bench RF Measurement Future beam experiment?