1. Choice of harmonic number with the consideration of ion beam formation
Jiquan Guo
9/17/2015

2. Ion beam formation cycles:
Multi-turn strip-injection of up polarized ion from linac to booster (non-polarized for heavy ions)
Capture beam into a bucket (~0.7× booster ring circumference)
Ramp energy (to 7.9GeV proton equivalent) and perform DC cooling in the booster
Compress the bunch length to ~0.7/Nh0× of the collider ring circumference
Bucket-to-bucket transfer beam into collider ring
Repeat step 1-5 for (Nh0/2-1) times
Switch to down polarized ions and repeat step 1-5 for another (Nh0/2-1) times
Ramp collider ring to collision energy, perform bunch splitting to Nh
If needed, manipulate the beam to create extra empty buckets in the gap, as required by beam synchronization. (w/o barrier bucket, bunch splitting needs to be done in steps, and the final harmonic number Nh must be multiple of Nh0, but beam sync requires varying Nh by increment of 1, so sometimes Nh is impossible to be multiple of Nh0)
BB cooler
14 up polarized long bunches
2 empty buckets for gap
14 down polarized long bunches
Desired Nh0 depends on linac energy and target collider ring current (0.5A in baseline)
Nh0=36-40 for
~42MeV/u Pb
Nh0=30-32 for
~130MeV proton or ~55MeV/u Pb
Nh0=16-18 for
~210MeV proton or ~100MeV/u Pb

3. Possible choices of Nh Nh 3600 3584 2266 2256 16 30 40 28 32
Circumference (m)
2266
2256
Nh0 16 30 40 28 32
Occupied long bunches 14 36 26
Gap length (ns, ×2)
472
252
378
470
269
235
Linac Energy (MeV/u) Pb
100 55 42 57 50
Proton
215
125
130
115
Occupied short bunches
3150
3360
3240
3136
3328
Split scheme
×3×3×5×5
×5×4×3×2
×5×3×3×2
×7×25
×27
×7×24
Plenty of options to reduce bunch reprate
Binary split, might be the easiest
Factor of 7 split, might be beneficial for e-ring injection with reduced reprate
~110m longer than 2154m, just enough for the bypass lines