1. Ion bunch formation options for 400GeV JLEIC
Jiquan Guo

2. 400GeV JLEIC ion ring Two possible dipole technology
With ~8.4T dipoles (proven LHC technology),
Collider ring circumference increases by ~50% compared to 6T 200GeV design
Optimization in the figure-8 crossing angle may slightly reduce the circumference.
Assume we can design the ring with circumference m (Nh=42x256=10752, 50% increase from 2256m).
With the more aggressive 12T technology for dipoles
The ring circumference can be approximately same as the previous 200 GeV 6T dipole design of ~2336m
The two different circumference options imply different ion beam formation parameters.

3. Requirements for JLEIC bunch formation process
Capable to deliver high current, high repetition rate, low emittance ion beam in the ion collider ring within reasonable time (reasonable booster cycles)
Simplify the process, minimize the number of booster stages if possible
Reasonable ramp ratio of each ring
Max/min dipole field ratio of is desired.
A full size ring with DC-cooler, either the collider ring or a large booster, can maintain the ion beam emittance during stacking, until the beam is ramped to a much higher energy (IBS becomes weak)
A full size booster ring allows most bunch formation process to be finished while the collider ring is running for physics, increasing the collider’s duty factor
DC cooler technology
Ek, ion=7.9GeV/u DC cooler is considered proven. Higher DC voltage for electron beam implies higher risk but possible. 7.9GeV/u was chosen in the previous versions of JLEIC designs.
Space charge tune shift, especially at each stage of beam injection into a larger ring, or when the bunch is cooled/compressed, will be the major bottleneck of bunch formation process.
The measures reducing Laslett tuneshift include reducing the collider ring size, decreasing beam current or increasing the transverse/longitudinal size (which are undesired), or higher injection/cooling energy (brings higher risk for DC cooler and higher booster magnet cost)

4. JLEIC 400GeV 12T ion ring beam formation
ion sources
SRF Linac
Low Energy Booster with DC cooler
Fullsize high energy booster/ stacker with DC cooler
MeV H-
40-100MeV Pb67+
~8GeV H+
~2GeV Pb67+
~27GeV H+
~10GeV Pb82+
Multi-turn injection
Bucket-to-bucket transfer
H- Strip
Pb Strip
ion injector chain for 400 GeV ion ring
Collider ring with BB cooler
~400GeV H+
~160GeV Pb82+
For the 400GeV ion ring of 2336m, the major bunch formation parameters (number of cycles, particle number in the booster, etc) can be quite similar to the 200GeV case.
The main difference is the higher extraction energy of the HEB of 27GeV (~0.83T dipole with same packing factor), which is also good for the heavy ion DC cooling. More bunch splitting can be moved to the HEB.
Raising HEB to 38GeV (<1.2T dipole), HEB can be used as a collider ring for 22-38GeV/u ions (or <22GeV) without gear change
Linac energy can be chosen at MeV in the initial phase (at the cost of doubling the booster cycles), then upgrade to 300MeV later
LEB can choose a slightly (~20%) higher extraction rigidity to improve heavy ion performance

5. 2336m 400GeV JLEIC, 170MeV linac, 8GeV DC cooler and LEB extraction, 27GeV HEB extraction
Proton D Pb
Number of LEB cycles 54 28
Collider beam current(A)
0.75
0.67
0.25
Linac Ek (MeV/u)
170 95
50 (Pb67+)
LEB inj Bρ (T-m)
1.97
2.87
3.19
LEB particles at injection (1010) (η=90%) 75 67
0.59
LEB inj emittance (µm, 6σt=40mm)
2.00
1.47
1.05
LEB inj capture Laslett Tuneshift (σz=C/6)
0.148
0.131
0.101
LEB ext Ek (GeV) 8
3.60
2.08
LEB ext Bρ (T-m)
29.65
LEB ramp ratio
15.1
HEB inj Bρ (T-m)
24.23
HEB inj particle per bunch (1010, λ=80m) 68 60
0.27x2
HEB inj Laslett tuneshift
0.063
0.150
0.151
HEB DC cooling energy (GeV)
HEB DC cooled emittance (µm)
0.85
0.38
0.11
HEB cooled Laslett tuneshift
0.149 (σz=λ/6)
0.146 (σz=λ/6)
HEB ext/split Ek (GeV/u)
26.72
12.92 10
HEB split Laslett tuneshift (σz=λ/8)
0.020
0.081
0.132
HEB ext Bρ (T-m)
92.21 (~0.83T, increases to 1.17T at 38GeV)
HEB ramp ratio
3.81 (increases to 5.36 with 38GeV HEB)
Collider ring ramp ratio
14.5 (reduces to 10.3 with 38GeV HEB)

6. Larger 400GeV ion ring with ~8T dipoles
With constant Ib, Laslett tune shift is proportional to circumference. With larger circumference of HEB/collider ring, space charge will be worse in HEB injection/cooling stages. Possible solutions:
Decrease ion collider beam current (of course not desired)
Increase LEB/HEB magnetic rigidity, increase the HEB injection and DC cooling energy of Pb/D. Keep larger p emittance (minimal DC cooling, limited by DC cooling energy of 8GeV) from HEB, rely on BB cooling
Increase HEB DC cooling energy for proton to Ek~10GeV, increase HEB rigidity and D/Pb DC cooling energy
Increase HEB Laslett tune shift threshold from 0.15 to 0.2 or more
HEB extraction energy (Ek) options (22-48GeV/c):
~22GeV/c: Pb Ek 8GeV/u (fully utilize 8GeV DC cooler), collider ring ramp ratio ~18
~28GeV/c: Pb Ek 10GeV/u (fully utilize 10GeV DC cooler if technology permits), collider ramp ratio 14.5
~48GeV/c: Collider ramp ratio ~8, can use HEB as a low energy collider, with doglegs down to the 400GeV collider IR (avoid the gear change issue for 27-47GeV/u proton and He3). For example, HEB circumference w/ two IP bypass chicanes is set at m, w/ one bypass chicane and one IP m, w/ two IPs m. We can move HEB magnets to extend the “no gear change” energy range to lower than 27GeV/u

7. 10GeV DC cooler and LEB extraction, 27GeV HEB extraction
Proton D Pb
Number of LEB cycles 40 20
Collider beam current(A)
0.75
0.4
Linac Ek (MeV/u)
300
170
106 (Pb67+)
LEB inj Bρ (T-m)
2.70
3.91
4.71
LEB particles at injection (1010)
155 (transfer η 85%)
153 (transfer η 87%)
2.02 (transfer η 85%)
LEB inj emittance (µm, 6σt=40mm)
2.73
2.00
1.55
LEB inj capture Laslett Tuneshift (C=6σz)
0.146
0.150
LEB ext Ek (GeV) 10
4.60
LEB ext Bρ (T-m)
36.35
LEB ramp ratio
13.5
HEB inj Bρ (T-m)
29.70
HEB inj particle per bunch (1010, λ=80m)
132
0.86x2
HEB inj Laslett tuneshift
0.044
0.117
HEB DC cooling energy (GeV)
HEB DC cooled emittance (µm)
0.80
0.40
0.225
HEB cooled Laslett tuneshift
0.150 (σz=λ/6)
0.15 (σz=λ/8)
HEB ext/split Ek (GeV/u)
26.72
12.92
HEB split Laslett tuneshift (σz=λ/8)
0.031
0.124
HEB ext Bρ (T-m)
92.21
HEB ramp ratio
3.11
Collider ring ramp ratio
14.50

8. 8GeV DC cooler (LEB 10GeV, HEB 27GeV), larger DC cooled emittance
Proton D Pb
Number of LEB cycles 40 20
Collider beam current(A)
0.75
0.4
Linac Ek (MeV/u)
300
170
106 (Pb67+)
LEB inj Bρ (T-m)
2.70
3.91
4.71
LEB particles at injection (1010)
155 (transfer η 85%)
153 (transfer η 87%)
2.02 (transfer η 85%)
LEB inj emittance (µm, 6σt=40mm)
2.73
2.00
1.55
LEB inj capture Laslett Tuneshift (C=6σz)
0.146
0.150
LEB ext Ek (GeV) 8
4.60
LEB ext Bρ (T-m)
29.65
36.35
LEB ramp ratio
13.5
HEB inj Bρ (T-m)
29.70
HEB inj particle per bunch (1010, λ=80m)
132
0.86x2
HEB inj Laslett tuneshift
0.066
0.117
HEB DC cooling energy (GeV)
HEB DC cooled emittance (µm)
1.20
0.60
0.25
HEB cooled Laslett tuneshift (σz=λ/6)
HEB ext/split Ek (GeV/u)
26.72
12.92 10
HEB split Laslett tuneshift (σz=λ/8)
0.021
0.083
0.134
HEB ext Bρ (T-m)
92.21
HEB ramp ratio
3.11
Collider ring ramp ratio
14.50

9. 300MeV linac, 8GeV DC cooler, 8GeV LEB, 27GeV HEB, larger Laslett tuneshift threshold (0.20)
Proton D Pb
Number of LEB cycles 40 20
Collider beam current(A)
0.75
0.36
Linac Ek (MeV/u)
300
170
106 (Pb67+)
LEB inj Bρ (T-m)
2.70
3.91
4.71
LEB particles at injection (1010)
155 (transfer η 85%)
1.82 (transfer η 85%)
LEB inj emittance (µm, 6σt=40mm)
2.73
2.00
1.55
LEB inj capture Laslett Tuneshift (C=6σz)
0.146
0.153
0.136
LEB ext Ek (GeV) 8
3.60
2.08
LEB ext Bρ (T-m)
29.65
LEB ramp ratio
11.0
HEB inj Bρ (T-m)
24.23
HEB inj particle per bunch (1010, λ=80m)
132
0.77x2
HEB inj Laslett tuneshift
0.066
0.175
0.199
HEB DC cooling energy (GeV)
HEB cooled emittance (µm)
0.90
0.45
0.17
HEB cooled Laslett tuneshift (σz=λ/6)
0.200
HEB ext/split Ek (GeV/u)
26.72
12.92 10
HEB split Laslett tuneshift (σz=λ/8)
0.028
0.110
0.178
HEB ext Bρ (T-m)
92.21
HEB ramp ratio
3.81
Collider ring ramp ratio
14.50

10. Other changes
To keep e-ring injection scheme to inject ½ ring each bunch train, collider ring C<=2739m (Nh=34*256=8704), so the injected bunch train will be <=1289m. Otherwise we might face problems like multiturn BBU in the ~1300m CEBAF, etc
for larger rings, can be solved by ¼ ring bunch train injection. Injection time and top-off frequency may also increase
single bunch swap might be a solution if the CEBAF energy spread can be controlled to 0.2% for a 6.3nC bunch
Raise e- energy to ~14GeV and reduce ion energy to GeV to keep ion ring size small (<2800m) and dipole magnets under 8.4T.
LEB circumference is not critical so far, although multiple of 80.25m is preferred
For the case of larger circumference, 300MeV linac is preferred for less injection cycles (~40 cycles for 0.75A proton) and possible smaller ramp ratio for LEB.
LEB to HEB transfer efficiency reduced to a more conservative 85-90% in this estimate

11. Preferred scheme(s)
2336m rings, 170MeV linac (upgradable to 300MeV), LEB 8.9GeV/c (8GeV Ek), HEB 27.7GeV/c (10GeV/u Ek Pb). 8GeV/u DC cooler.
Raising HEB extraction energy to ~38GeV is also an option
3383m rings, 300MeV linac, LEB 10.9 GeV/c (10GeV Ek proton), HEB 27.7GeV/c (10GeV/u Ek Pb). Start with 8GeV/u DC cooler, with larger HEB extraction emittance and/or higher DC cooled Laslett tuneshift. Upgrade DC cooler to 10GeV/u or more if technology permits
3383m rings, 300MeV linac, LEB 10.9 GeV/c (10GeV Ek proton), HEB 48GeV/c (18GeV/u Ek Pb). Start with 8GeV/u DC cooler. Upgrade DC cooler to up to higher energy in the future. Use HEB as collider ring for <48GeV/c ions (share SRF and IR with the 400GeV collider ring), avoid gear change for at least 27-47GeV/u by utilizing the IR bypass chicanes.