1. CEPC Main Ring Cavity Design with HOM Couplers
Hongjuan Zheng, Jie Gao, Zhenchao Liu, Jiyuan Zhai

2. Outline CEPC main ring cavity RF design parameters
5 cell cavity with waveguide HOM couplers
Eigenmode analysis
Damping Results
Summary

3. Large Riris is good for the cell-to-cell coupling.
The iris ellipse ratio (b/a) is determined by the local optimization of the peak electric field.
Small alpha decreases the Hp/Eacc value while increasing the cell-to-cell coupling.
The parameter d is used to balance the Ep/Eacc and Hp/Eacc value.

4. 650 MHz superconducting cavity cell shape parameters
Mid-cell
Left end cup
Right end cup
L/ mm
115
114
113
Riris/ mm 78
84.5
A/ mm
94.4
92.1 91
B/ mm
a/ mm 20
13.8
13.7
b/ mm
22.1
21.1
20.3
D/ mm
206.6
alpha/ (˚)
2.24
16.7
16.4
The asymmetric end cell design is better to extract the HOMs.

5. CEPC Main Ring Cavity RF Design Parameters
Unit
Main Ring
Cavity frequency
MHz
650
Number of cells - 5
Cavity effective length m
1.154
Cavity iris diameter mm
156
Beam tube diameter
170
Cell-to-cell coupling
3 %
R/Q Ω
514
Geometry factor
268
Epeak/Eacc
2.4
Bpeak/Eacc
mT/(MV/m)
4.23
Cavity longitudinal loss factor k∥ HOM *
V/pC
1.8
Cavity transverse loss factor k⊥*
V/pC/m
Acceptance gradient
MV/m 20
Acceptance Q0
4E10
* collider bunch length 2.65 mm

6. CEPC Main Ring 5-Cell Cavity
Electromagnetic fields and electromagnetic radiation pressure on the surface. Fields and power normalized to E0T = 1 MV/m.
Ez -- field on axis
field flatness %
P: electromagnetic radiation pressure

7. JLab Waveguide HOM Coupler
Monopole Spectrum
Dipole Spectrum

8. CEPC Main Ring 5-Cell Cavity
5-cell cavity with two asymmetrical end groups + JLab HOMs waveguide couplers
Higher Order Modes:
HOM power for 2 beam is 3.63kW/cavity
Qe as low as possible
Identification of dangerous modes
HOM couplers:
The structure of waveguide HOM coupler
is simple.
Cutoff is natural rejection filter for fundamental mode.
HOM power can be dissipated in loads located at ambient temperature.
High power handling capability.

9. Influence of HOM Waveguide Couplers on Field Flatness
Do the waveguide HOM couplers influence the field flatness of the fundamental mode?
Only 0.11% difference - so the HOM waveguide couplers can be assumed have no influence on fundamental mode.

10. Eigenmode Analysis
Two separate eigenmode simulations for just a single cell, with periodic boundary conditions (PBC), were computed. 34 modes up to 1.8 GHz were calculated.
Results:
0 mode and π mode frequency for every passband.
Number of modes within one passband depends on number of cells in the cavity.
The cell to cell coupling factor is
For small kcc values there is a danger that if that given mode is excited by the beam, it will propagate and decay very slowly.
650MHz

11. Eigenmode Analysis
Eigenmode analysis results of a single cell combined with external quality factors of the 5 cell cavity were obtained.
Phase advance 0°
Phase advance 180°
mode
f/GHz
Z=(R/Q)’*Qe
Z= (R/Q)’*Qe
type
kcc 1
0.630
1.21E+11
0.650
9.15E+13
TM M1
0.0303
2,3
0.759
1.91E+3
4,5
0.887
2.46E+5
TE D1
0.1551
0.946
1.03E+1
0.877
8.00E+2
TM D2
-0.075 8
1.182
1.79E+2
1.130
5.02E+2
TM M2 9
1.213
2.7E-2 11
1.218
1.43E-3
TE M3
0.0045
10,11
1.238
1.63E+4
16,17
1.361
1.67E+3
TM D3
0.0948 14
1.331
8.48E+1 18
1.400
2.76
TM M4
0.0506
17,18
1.479
5.93E+6
19,20
1.509
2.15E+4
TE D4
0.0202
27,28
1.652
1.56E+5
29,30
1.661
4.26E+3
TM D5
0.0057 35
1.802 31
1.665
2.69E+1
0 - mode
π - mode

12. Phase advance 0°
Phase advance 180°
mode
f/GHz
Z=(R/Q)’*Qe
Z= (R/Q)’*Qe
type
kcc 1
0.630
1.21E+11
0.650
9.15E+13
TM M1
0.0303
2,3
0.759
1.91E+3
4,5
0.887
2.46E+5
TE D1
0.1551
0.946
1.03E+1
0.877
8.00E+2
TM D2
-0.075 8
1.182
1.79E+2
1.130
5.02E+2
TM M2 9
1.213
2.7E-2 11
1.218
1.43E-3
TE M3
0.0045
10,11
1.238
1.63E+4
16,17
1.361
1.67E+3
TM D3
0.0948 14
1.331
8.48E+1 18
1.400
2.76
TM M4
0.0506
17,18
1.479
5.93E+6
19,20
1.509
2.15E+4
TE D4
0.0202
27,28
1.652
1.56E+5
29,30
1.661
4.26E+3
TM D5
0.0057 35
1.802 31
1.665
2.69E+1

13. Phase advance 0°
Phase advance 180°
mode
f/GHz
Z=(R/Q)’*Qe
Z= (R/Q)’*Qe
type
kcc 1
0.630
1.21E+11
0.650
9.15E+13
TM M1
0.0303
2,3
0.759
1.91E+3
4,5
0.887
2.46E+5
TE D1
0.1551
0.946
1.03E+1
0.877
8.00E+2
TM D2
-0.075 8
1.182
1.79E+2
1.130
5.02E+2
TM M2 9
1.213
2.7E-2 11
1.218
1.43E-3
TE M3
0.0045
10,11
1.238
1.63E+4
16,17
1.361
1.67E+3
TM D3
0.0948 14
1.331
8.48E+1 18
1.400
2.76
TM M4
0.0506
17,18
1.479
5.93E+6
19,20
1.509
2.15E+4
TE D4
0.0202
27,28
1.652
1.56E+5
29,30
1.661
4.26E+3
TM D5
0.0057 35
1.802 31
1.665
2.69E+1

14. 650 MHz Cavity Impedance Budget
To keep the beam stable, the radiation damping time should be less than the rise time of any of the oscillation modes.
In the resonant condition, the threshold shunt impedances are

15. Considering the whole RF system, there will be finite tolerances in the cavity construction.
For small frequency spread, this will result in an “effective” quality factor Q of the whole RF system [1].
[1] Impedance and collective effects of CEPC, N. Wang, H. J. Zheng, Y. W. Wang, D. Wang, 55th ICFA Advanced Beam Dynamics Workshop on High Luminosity Circular e+e- Colliders – Higgs Factory (HF2014)

16. Monopole Modes Damping Results
The cutoff frequency of the beam tube for TM01 mode is GHz.
Qe for fundamental mode is 4E11.
For f<2 GHz, all of the monopole modes damping results are under the longitudinal impedance threshold.
The Qe for most of monopole modes is below 103, a few of them is about 105.
If the Q0 for the monopole modes is The HOM power loss on cavity is only a few milliwatts.

17. Dipole Modes Damping Results
The cutoff frequency of the beam tube for TE11 mode is 1.04 GHz.
For f<2 GHz, most of the dipole modes damping results are under the longitudinal impedance threshold.
We didn’t take into account the spread in the resonance frequencies of different cavities. If the frequency spread is 0.5 MHz, the impedance threshold can increase 1~2 orders of magnitude. So, the design can meet the damping requirements.

18. Same Order Modes (SOMs) Damping
f (MHz)
R/Q (Ω)
Qlimit
Qinput coupler
PSOM (W)
PSOM-res (W)
π/5
0.02
4.5E+9
1.2E+07
1.3E-5
268.9
2π/5
5.4E+11
3.3E+06
8.7E-7
0.6
3π/5
0.341
2.6E+8
1.7E+06
9.31E-3
638.9
4π/5
0.078
1.1E+9
1.2E+06
2.92E-4
105.8
Use the input coupler as the SOM coupler.
The external quality factor (Qe) of the input coupler for the fundamental mode is 2.2106.
The damping for the SOMs by the input coupler is very efficient!
The analysis results show that the total SOM power is quite small when we consider the real cavity passband modes frequencies and the bunch time spacing of the collider. Even assuming resonant excitation, the total SOM power is about 1 kW and with the input coupler damping, the power dissipated on the cavity wall is negligible (~ 0.1 W).

19. Summary
5 cell cavity with waveguide HOM coupler can meet the damping requirements.
There is no trap mode until 2GHz.
The damping for the SOMs by the input coupler is very efficient
Other problem？

20. Thank you for your attention !