1. Collective effects in CEPC
Na Wang, Yudong Liu, Saike Tian, Hongjuan Zheng, Dianjun Gong, Jun He, Institute of High Energy Physics, China
Kazuhito. Ohmi, KEK, Japan
2016/11/7
International workshop on High Energy Circular Electron Positron Collider Nov. 6-8, 2017, IHEP

2. Motivations
The collective instabilities can induce beam quality degradation or beam losses, and finally restrict the machine performance. A thorough evaluation of the coupling impedance and collective effects is required.
Calculate the impedance for various vacuum components in the ring, and suggest possible modifications on hardware designs.
Rough impedance requirement
Impedance modeling
Investigate possible collective effects that may affect the beam quality, give the intensity threshold or growth rate of the instability, and provide possible remedies.
Impedance driven single bunch instabilities
Impedance driven coupled bunch instabilities
Electron cloud in the positron ring
Fast beam ion instability in the electron ring

3. Scenarios of collective effect studies
Parameter
Symbol, unit
Higgs W Z
Beam energy
E, GeV
120 80
45.5
Circumference
C, km
100
Beam current
I0, mA
17.7
90.3
83.8
Bunch number nb
286
5220
10900
Bunch Population Ne
12.91010
3.61010
1.61010
Natural bunch length
l0, mm
2.7
3.0
3.7
Emittance (horz./vert.)
x/y, nm
1.21/0.0036
0.54/0.0018
0.17/0.0029
RF frequency
frf, MHz
650
Natural energy spread
e0
9.8E-4
6.6E4
3.7E4
Momentum compaction p
1.14E5
Betatron tune
x/y
355.08/355.22
Synchrotron tune s
0.064
0.04
0.018
Synchrotron damping time
x/y/z, ms
48/48/24
162/162/81
871/871/436

4. Impedance requirement
For different operation scenarios, the design of Z shows the most critical restriction for both broadband and narrowband impedances.
In the following, the instability issues of H and Z will be discussed.
Parameter
Symbol, unit
Higgs W Z
Beam energy
E, GeV
120 80
45.5
Beam current
I0, mA
17.7
90.3
83.8
Bunch number nb
286
5220
10900
Bunch current
Ib, mA
0.062
0.017
0.0077
Bunch Population Ne
12.91010
3.61010
1.61010
Threshold of broadband ZL
|ZL/n|eff, mΩ
9.4
10.8
5.3
Threshold of broadband ZY
κy, kV/pC/m
73.0
108.9
62.7
Threshold of narrowband ZL
3.2
0.08
3.9E-3
Threshold of narrowband ZY
2.1
9.3E-3

5. Impedance calculations
Main sources:
Resistive wall, RF cavities, Flanges, BPMs, Bellows, Pumping ports, Electro-separators, IP chambers, Transitions.
Impedance components
Number
Resistive wall -
RF cavities
366
Flanges
20000
BPMs
1450
Bellows
12000
Pumping ports
5000
Electro-separators 2
IP chambers 22
Transitions
164

6. Impedance budget Broadband impedance threshold: Threshold Higgs W Z
Components
Number
R, kΩ
L, nH
Z||/n, mΩ
kloss, V/pC
ky, kV/pC/m
Resistive wall -
15.3
866.8
16.3
432.3
23.0
RF cavities
336
11.2
-72.9
-1.4
315.3
0.41
Flanges
20000
0.7
145.9
2.8
19.8
BPMs
1450
0.53
6.38
0.12
13.1
0.3
Bellows
12000
2.3
115.6
2.2
65.8
2.9
Pumping ports
5000
0.01
1.3
0.02
0.4
0.6
IP chambers 2
0.2
0.8
6.7
Electro-separators 22
1.5
-9.7
41.2
Taper transitions
164
1.1
25.5
50.9
0.5
Total
32.9
1079.7
20.6
945.4
32.1
Broadband impedance threshold:
Threshold
Higgs W Z
|ZL/n|eff, mΩ
9.4
10.8
5.3
κy, kV/pC/m
73.0
108.9
62.7
Longitudinal wake at the nominal σz = 3mm

7. Bunch lengthening and microwave instability
Macro-particle simulations are performed with the code Elegant
The threshold bunch intensity is 67 nC for H, which is about three times higher than the design current (20.6 nC). The bunch length is increased by 30% at the design intensity.
For Z, the energy spread start to increase at very low intensity (0.8 nC). At design bunch intensity of 2.6 nC, the bunch length is increased by 40% and the energy spread is increased by ~2% at the design intensity.
Higgs Z

8. Transverse mode coupling instability
The threshold for the transverse mode coupling instability is estimated using both analytical formula and Eigen mode analysis.
The threshold intensity is about 2~3 times of the design value for both H and Z, therefore we still have some safety margins to avoid the instability.
Higgs
Higgs Z
Design bunch intensity [nC]
20.6
2.6
TMCI threshold_analytical [nC] 47 5
TMCI threshold_EigenMode [nC] 65 8

9. Transverse frequency shift
The transverse working points are (355.08, ), which is slightly above integer in the horizontal plane.
Since tune shift due to transverse impedance is negative, the beam could become unstable at lower beam current (or lower impedance) than that for the transverse mode coupling instability.
The effective impedance for =0.08 is:
Zeff=4.3M/m for Higgs
Zeff=17.3M/m for Z
These are much higher than the impedance budget of 0.65M/m, so the beam should be stable from the integer resonances.

10. Transverse resistive wall instability
The coupled bunch instability can be driven by the resonance at zero frequency of the transverse resistive wall impedance.
For H, the growth time for the most dangerous instability mode is 280ms => much slower than the transverse radiation damping. So the beam should be safe from the resistive wall coupled bunch instability.
For Z, the growth time for the most dangerous instability mode is 23ms => faster than the radiation damping of 871ms.
An effective transverse feedback system is needed to damp the instability. Z

11. CBI due to RF HOMs
Hundreds of 2-cell superconducting RF cavities will be used.
With a sophisticated HOM coupler design and a efficient feedback system, all the transverse modes below cutoff can be well damped, and the monopole mode of TM011 still above the threshold.
When consider the whole RF system, HOM frequency spread can further relax the instability. With a frequency spread of 0.1MHz and 1MHz, the growth time of the TM011 can be increased to 20 ms and 80 ms, respectively. Z Z

12. Electron cloud Yudong Liu
For different SEY and bunch spacing, the electron cloud density are simulated.
For H
The threshold value of the volume density of electron cloud for the head-tail instability:
For H: ρe,th=8.2×1011[m-3]
For Z: ρe,th=1.1×1011[m-3]
A SEY lower than 1.6 and bunch spacing longer than 25ns is needed.
With NEG coating, SEY can be as low as 1.1~1.3.
For Z
With SEY=1.6 and bunch spacing=25ns, the CBI instability growth time is ~ 3ms.
Transverse feedback system is required.

13. Beam-ion instability Ion trapping
Instability can be excited by residual gas ions trapped in the potential well of the electron beam.
With uniform filling pattern, the ions with a relative mass larger than A will be trapped.
Higgs Z
The ions will not be trapped by Higgs beam.
The ionized species with mass greater than 5 can be trapped for Z. A cleaning gap is required to avoid the ion trapping.

14. Fast beam ion instability
Transient beam instability excited by the beam generated ions accumulated in a single passage of the bunch train.
The phase angle between adjacent bunches are Lsepωion/c0
Higgs Z H Z
Lsepωion/c0 23 3
ρion,ave[m-3]
Over focused
1.2×1011
τ [ms] - 26

15. SaikeTian, Kazuhito Ohmi
Simulation of Z with wake-strong model
τy = 7 ms σy
The growth time indicates the time duration of maximum amplitude growth of beam from 0.1σ to 1.0σ.
Transverse feedback system is required to damp the instability. σx

16. Summary
An impedance model is developed for the CEPC collider. Based on the impedance model, the potential instability issues for the operation scenario of Higgs and Z are investigated.
Bunch lengthening of 30% and 40% are expected for Higgs and Z, and the energy spread will be increase by 2% for Z.
Transverse broadband impedance is about 2~3 times lower than the instability threshold, so that we still have some safety margin to avoid the transverse single bunch instability.
Coupled bunch instability can be excited by the transverse resistive wall, HOMs of the RF cavities and the two stream effects for Z. Transverse and longitudinal feedback systems are required.

17. Thank you for your attention!