JLEIC 200 GeV ion beam formation options Jiquan Guo

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

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 2 1+ 𝜖 𝑛, 𝑥 𝜖 𝑛, 𝑦 𝐶 𝑟𝑖𝑛𝑔 2𝜋 𝜎 𝑠

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

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

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 10-12 cycles ramp booster 2 to 6 GeV (p) or 1.467 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 52-54 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

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

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) 285 150-285 150 1st booster ext energy (GeV) p: 10.5-13* 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 82+ 9.3 P: 10.5-13, 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 10.5-13 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 ~0.3-0.4A) *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