1. JLEIC electron ring with damping wigglers
Jiquan Guo, Fanglei Lin
Sept 12, 2019

2. Why damping wiggler?
For storage rings with fixed trajectory and bending radius
Energy loss per turn 𝑈 0 ∝ 𝐸 4 , Damping time 𝜏 𝐷 ∝ 𝐸 𝑈 0 ∝ 𝐸 −3
JLEIC e-ring covers 3-12 GeV
Without wigglers, damping time will have a range with a factor of 64
U0 at 12GeV needs to be minimized to increase beam current
τD need to be reduced at 3 GeV to improve collective instabilities (include beam-beam), injection time, etc.
Currently the damping time with dipoles and spin rotator at 3GeV is 475ms, which is not short enough, but could be reduced with damping wigglers
eRHIC proposes to use wiggling dipoles at low energy (comparably lower wiggler field)
We currently plan to use higher field monolithic wigglers for 3-6 GeV cases

3. Effects to be considered for damping wiggler
Higher SR power: to be kept in the admin limit and RF system limit
Emittance: Depends on the dispersion at the location of the wiggler and the bending angle of each pole of the wiggler. Usually wigglers can reduce emittance.
Energy spread: will increase if wiggler field is stronger than arc dipole (likely to be the case for JLEIC, more severe if a superconducting high field wiggler is chosen to shorten the total wiggler length)
RF voltage: higher energy spread required higher voltage
Moderately increased RF voltage can help increasing the stability in the RF system at low energy
Too much RF voltage increase may require additional SRF cavities
How to dump the SR power? Location of the wiggler?
Other effects in beam dynamics:
Shorter polarization lifetime (not worse than the case of 7 GeV w/o wiggler) due to S-T
Edge focusing needs to be compensated

4. JLEIC e-ring parameters w/o wigglers
Energy (GeV) 3 5 61 7 10 12
Energy loss per turn U0 (MeV)
0.098
0.759
1.575
2.92
12.15
25.2
Trans. Damping Time (ms)
475
103 59
37.4
12.8
7.42
Beam current (A)
3.6
3.3
0.82
0.39
Total SR power (MW)
0.30
2.73
5.20
8.75
9.84
Energy spread (10-4)
2.47
4.12
4.95
5.77
8.25
9.90
Normalized Horizontal emittance (µm) 18 85
148
234
683
1180
Normalized Vertical emittance (µm)
1.3
6.0
10.4
16.6
48.3
83.5
Bunch length (cm)2
1.0
0.74
0.7
0.6 1
1.2
VRF, peak (MV)
0.742
6.26
12.10
26.10
29.81
41.25
Combined Syn. Phase (deg)
7.6
7.0
7.5
6.4
24.1
37.6
Bucket height/energy spread ratio
18.0
24.6
25.8
30.5
14.0
9.1
Number of cavities (PEP-II+SRF)
1+0
8+0
16+0
16+12
Vcav (PEP-II/SRF, MV)
0.742/NA
0.783/NA
0.756/NA
0.719/1.22
0.719/1.55
0.790/2.71
PRF, FWD/Cav (PEP-II/SRF, kW) 3
374/NA
429/NA
406/NA
355/357
404/394
391/422
New column added
Adjusted bunch length to keep the cavity voltage high enough (PEP-II MV, SRF >1MV) for transient minimization and possibly counteracting other instabilities.
Assuming optimal detuning to minimize RF power; not including any overhead, assuming 600kW klystron power per cavity, 40-50% overhead for WG loss, feedback, etc.

5. JLEIC e-ring parameters with wigglers for 3-5GeV (reduce damping time to ~6GeV no wiggler equivalent)
Energy (GeV) 3 5 6
Wiggler B (T) (square wave)
No wiggler
1.4
2.0
1.1
Wiggler length (m) 32 16
Energy loss per turn U0 (MeV)
0.098
0.827
0.759
1.399
1.575
Trans. Damping Time (ms)
475
56.5
103
55.7 59
Beam current (A)
3.6
3.3
Total SR power (MW)
0.30
2.98
2.73
5.04
5.20
Energy spread (10-4)
2.47
9.11
10.8
4.12
8.11
4.95
Bunch length (cm)
1.0
1.13
1.22
0.74
1.03
0.7
VRF, peak (MV)
0.742
7.85
9.48
6.26
12.49
12.10
Syn. Phase (deg)
7.6
6.1
5.0
7.0
6.4
7.5
Bucket height/energy spread ratio
18.0
16.3
15.3
24.6
17.8
25.8
Number of cavities (PEP-II) 1 10 12 8
Vcav (PEP-II, MV)
0.785
0.790
0.783
0.781
0.756
PRF, FWD/Cav (PEP-II, kW)
374
387
344
429
403
406
Further reduction of damping time to ~30ms is possible with 3-3.6A beam current, requiring more SRF cavities, doubling the beam power for 5-6GeV cases, and double wiggler length.
Assumes square wave wiggler field profile for simpler spreadsheet calculation.

6. Courtesy of Rui Li