1. 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

2. 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

3. 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

4. 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

5. 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, MHz
Periodically kick 1 in every25 bunches
Ultra-fast ,2.1 ns
55kV(1 mrad kick angle)
0.06A, 55MeV, MHz(476.3/25)
(bunch repetition frequency)

6. 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

7. 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 betatron phase advance between two kickers

8. 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?

9. 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

10. 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

11. 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)

12. Cavity Model (Update) for 12 modes
6 harmonics MHz1,3,5,7,9,11
3 harmonics MHz2,6,10
2 harmonics MHz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

13. 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!

14. 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 𝑓 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

15. 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!

16. 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
1.65E7
0.09
428.67
2.40E6
2.46
476.3
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 )

17. 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

18. 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

19. 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
-0.09
142.89
14689 ≥1
≥19.46
0.15
238.15
18973
≥25.10 3
333.41
22472
≥29.67
1.7
428.67
25536
≥33.57
1.8
Three Modes Cavity
95.26
12002
≈16.04
2.67
285.78
20784
≥27.50
6.8
476.3
27056
≥35.21
8.7
One Mode Cavity
190.52
15298
≈24.91
6.7
381.04
19435
≈39.21
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

20. 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

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

22. 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
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

23. 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?