1. JLEIC 200 GeV ion beam formation options
Jiquan Guo

2. Schemes proposed earlier
ion sources
SRF Linac with warm front end
~285MeV H-
~100MeV Pb67+
8GeV H+
2GeV Pb67+
<=100GeV H+
<=40GeV Pb82+
Multi-turn injection
Bucket-to-bucket transfer
Booster with DC cooler
H- Strip
Collider ring with BB/DC cooler
Pb Strip
285MeV linac, 8 GeV single booster, 100GeV ion collider,
may scale to 200GeV by increasing booster to 11 GeV p / 3GeV Pb
285MeV linac, 8 GeV small booster, 25GeV fullsize booster/stacker, 200GeV ion collider, as listed in the pCDR-65 HE appendix

3. Major bottlenecks for ion bunch formation
Max/min field ratio of magnets
For each ring, ratio of ~10 is reasonable, >20 is risky but possible. PS ~12, RHIC typical 8.6 (97.3Tm vs 837Tm), RHIC low energy 43 (19.3Tm, TUPAS103 PAC07)
The higher ramp ratio for each ring, the less boosters are needed
DC cooling
Cooler electron energy of ~4.3MeV (7.9GeV/u ion) proven for non magnetized beam, assumed low risk for magnetized beam
GSI-FAIR and HI-Mainz are developing higher voltage DC cooler (targeting 8MV, or ~15GeV/u ion)
Space charge effect
Laslett tuneshift
Bottleneck at the booster stages with lowest energy (injected from linac or a smaller booster), especially shorter bunch length; or the stages when beam is DC cooled.
For boosters with given aperture (and geometric emittance), bunching factor, and Laslett tuneshit, the total charge can be stored in the ring is proportional to β2γ3/rc, and independent of the booster circumference.
Linac energy determines how many booster cycles needed for the first booster
Laslett tuneshift limited at 0.15 for our schemes, but could increase to up to 0.3 in extreme cases
Δ𝜈 𝑠𝑐,𝑦, 𝐺𝑎𝑢𝑠𝑠𝑖𝑎𝑛 =− 𝑟 𝑐 𝑁 𝑏𝑢𝑛𝑐ℎ 4𝜋𝛽 𝛾 2 𝜖 𝑛, 𝑦 𝜖 𝑛, 𝑥 𝜖 𝑛, 𝑦 𝐶 𝑟𝑖𝑛𝑔 2𝜋 𝜎 𝑠

4. Examples of Laslett tuneshift bottleneck
150MeV proton injected into booster 1, 6σt=40mm with betatron~14m. Beam captured to h=1 RF bucket, Gaussian beam with 6σz=circumference,
Laslett tuneshift limited at 0.15, total protons in the ring 6.77×1011, total charge 0.109μC
Takes 52 cycles to accumulate 3.52×1013 protons or 5.642μC in the collider ring assuming 100% transfer. Achieves 0.75A beam current in the 2256m collider ring
285MeV proton injected into booster 1, 6σt=40mm with betatron~14m. Beam captured to h=1 RF bucket, Gaussian beam with 6σz=circumference,
Takes 26 cycles to accumulate 3.52×1013 protons or 5.642μC in the collider ring assuming 100% transfer. Achieves 0.75A beam current in the 2256m collider ring
total protons in booster 1.35×1012, total charge 0.218μC, Laslett tuneshift 0.13
2.04 GeV Pb82+ injected into the fullsize booster or collider ring (2.04 GeV Pb67+ has the same rigidity as 8 GeV proton)
Normalized emittance 1.5μm (6σt=40mm with betatron~14m at 100 MeV in booster 1)
26 long bunches, 6σz=circumference/28, 8.6×109 particles in each bunch, 0.4A in the ring. Laslett tuneshift reaches 0.15
needs to lower collider beam current to 0.25A if beam energy lowered to 1.47 GeV
8 GeV proton cooled in fullsize booster or collider ring
26 long bunches (0.109μC 6.77×1011 particles ea), 0.75A beam current, 6σz=circumference/28
When εn reduced to 0.8μm, Laslett tuneshift reaches 0.147

5. Low energy 3 boosters scheme
Proton Pb
Inj
Ext (col)
Linac
Energy (MeV)
150 41
Charge state -1
+67
Booster 1
(race track)
1500
247
Bρ (T-m)
1.839
7.5
2.904
Ramp ratio
4.08 +1
Circumference (m)
80 (max BL 47 Tm)
Booster cycles 52 54
Booster 2
Energy (GeV)
1.5 6
0.247
1.467
22.93
3.06
483 (max BL 216 Tm)
Booster 3 11
3.85
39.7
18.739
2.12
+82
2255 (Max BL 374 Tm)
Collider ring
670.2
16.88

6. Bunch formation process for the proposed 3 booster scheme
Accumulate in booster 1 at 150MeV (p) or 41 MeV (Pb67+) in coasting beam, with possible DC cooling keeping the emittance
Capture to RF bucket, accelerate to top energy 1.5 GeV (p) or 247 MeV (Pb67+),
Compress to bunch length ~6.7m rms, 95% bunch length 28m
extract from booster 1, inject into booster 2 in ~40m buckets, ramp back booster 1 to injection
repeats step 1-4 for cycles
ramp booster 2 to 6 GeV (p) or GeV (Pb67+)
Extract from booster 2, strip Pb67+ to Pb82+, inject into booster 3 in ~80m buckets, ramp back booster 2 magnets. Booster 3 DC cooling kept on to maintain emittance.
repeat step 5-7 for 5-6 cycles (total cycles for booster 1) to fill all the desired buckets in booster 3
Ramp booster 3 to 11 GeV (p) or 3.85 GeV (Pb82+). Perform DC cooling at 8GeV (p), (or 11 GeV if technology available), 3.85 GeV Pb82+, to space charge limit. Perform factor of 128 bunch splitting to 476MHz buckets
Extract from booster 3, inject into collider

7. 2 boosters scheme Proton Pb Inj Ext (col) Linac Energy (MeV) 150 41
Charge state -1
+67
Booster 1
(f8)
6000
1467
Bρ (T-m)
1.839
22.93
2.904
Ramp ratio
12.47 +1
Circumference (m)
564 (max BL 216 Tm)
Booster cycles 52 54
Booster 2
(fullsize)
Energy (GeV) 6 16
1.467
5.80
56.4
18.739 3
+82
2255 (Max BL 374 Tm)
Collider ring
670.2
11.88

8. Two boosters (with a full size booster)
More schemes
Scheme
Single booster
Two boosters (with a full size booster)
Two boosters
1st booster shape
Figure-8
racetrack
Linac energy for p (MeV)
285
150
1st booster ext energy (GeV)
p: *
D+: 6.1
Pb 67+: 3.65
p: 8;
D+: 2.45;
Pb 67+: 2.08
D+: 3.55;
p: 2, D+: 0.74, Pb 67+: 0.361
1st booster ramp ratio (max)
17.76
10-16 5
2nd booster shape
N/A
2nd booster ext energy (GeV)
p 25; D+ 12; Pb
P: , D: 6.1, Pb67+: 3.65
2nd booster ramp ratio 4
3.58
Ion collider ring max ramp ratio
17.63
7.75
Final DC cooling
GeV in main ring
>=8 GeV in fullsize booster
γt transition
In collider ring (p avoidable if DC cooling at 13GeV)
Only Pb82+ in collider ring
pro
space charge injected into the full size ring lowest
Duty factor enhance by stacking, no γ-transition for most ions
Duty factor , no γ-transition for most ions
Con
high energy DC cooling for proton
D+/Pb space charge in fullsize booster inj stage (can take ~ A)
*3.65GeV Pb67+ has the same rigidity as 13 GeV Proton; 3.65 GeV Pb82+ has the same rigidity as 10.5 GeV proton
2.08 GeV Pb67+ has the same rigidity as 8 GeV proton