1. Updated MEIC Ion Beam Formation Scheme
Jiquan Guo
Nov

2. Ion Complex (originally presented at fall coll. meeting)
~8GeV H+
~2.7GeV Pb82+
130MeV H-
42MeV Pb61+
<=100GeV H+
<=40GeV Pb82+
ion sources
SRF Linac
Booster with DC cooler
collider ring with BB cooler
Strip
Multi-turn strip injection
Bucket-to-bucket transfer
Major bottleneck: with given aperture, the beam current in the booster ring or collider ring is limited by space charge tune shift, especially at the lowest energy (right after injection from the linac or the booster)
Higher linac/booster extraction energy helps mitigating the SC tune shift and reduces the geometric emittance, but associated with higher cost.
The efficiency of strip injection also has dependence on linac energy.
Need to optimize to reach the performance goal with minimum cost
Coasting beam
bunched beam

3. collider ring with BB cooler collider ring with BB cooler
Ion Complex (updated)
ion sources
SRF Linac
Booster with DC cooler
collider ring with BB cooler
130MeV H-
~42MeV Pb61+
(strip at 8.2MeV)
~8GeV H+
~1.8GeV Pb61+
Multi-turn injection
Strip for H
No strip for ions
Bucket-to-bucket transfer
Ion Strip
<=100GeV H+
<=40GeV Pb82+
Change of ion stripping
Pb tuneshift in booster ↓
collider ring ↑
1.8GeV energy might be too low
H Strip
ion sources
SRF Linac
Booster with DC cooler
collider ring with BB cooler
130MeV H-
~40MeV Pb67+
(strip at ~13MeV
after 2 QWR CMs)
~8GeV H-
~3.3GeV Pb67+ (12 GeV H equivalent)
<=100GeV H+
<=40GeV Pb82+
Multi-turn injection
Strip injection
Pb tuneshift in booster ↓
collider ring →
Optional changes

4. Ion Beam Formation Cycles (original)
Step 7/8. Bucket-to-bucket transfer to the collider ring and BB cooling, repeat times
2. Accumulating coasting beam
4. Accelerate to 7.9GeV and cool
DC cooler
BB cooler
up polarized long bunches
2 empty buckets for gaps
down polarized long bunches
DC cooler
5. Bunch compression
3. Capture to bucket
Eject the used beam from the collider ring, cycle the magnets
Multi-turn 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 to an intermediate energy (~2.0GeV proton), perform DC cooling, ramp to 7.9GeV (proton)
Compress the bunch length to ~0.7/Nh0× of the collider ring circumference (Nh0 is the harmonic # for long bunches)
Bucket-to-bucket transfer the long bunch into collider ring
Repeat step 2-6 for (Nh0/2-1) times, each cycle ~1 min
Switch to down polarized ions and repeat step 1-5 for another (Nh0/2-1) times, total cycles ~Nh0-2
Ramp collider ring to collision energy, perform bunch splitting to harmonic # Nh (~ )
If needed, manipulate the beam to create several extra empty buckets (476 MHz) in the gap, as required by beam synchronization.

5. SC Tune Shift in the Booster at Different Injection Energy
Particle in booster
Pb82+
Pb67+
Pb61+
Booster ring circumference (m)
226.7
Collider ring circumference (m)
2267 (Nh=3600)
Collider ring beam current (A)
0.5
1.0
Collider ring charge (µC)
3.78
7.56
Linac extraction energy (MeV/u) 42 53
100 39 69 58
Booster cycles 36 28
Booster nucleon charge (µC)
0.11
0.14
0.27
Normalized emittance, step 3 (µm)
0.95
1.07
1.47
0.92
1.23
0.96
1.13
Booster SC tune shift, step 3
0.15
6σ aperture, step 3 (mm)
39.8
39.6
39.9
40.0
Step 3 ΔνSC limited at 0.15 (won’t be affected by booster circumference)
Beam stay-clear (6σ aperture) limited at 40mm.
Required linac energy is much lower for Pb61+

6. Ion Collider Ring SC Tune Shift
Particle in booster
Pb82+
Pb67+
Pb61+
Booster ring circumference (m)
226.7
Collider ring circumference (m)
2267 (Nh=3600)
Collider ring beam current (A)
0.5
1.0
Collider ring charge (µC)
3.78
7.56
Booster cycles 28
Booster extraction energy (GeV/u)
2.65
2.46
3.20
2.39
3.39
Equiv H extraction energy (GeV)
7.9
9.25
11.6
10.0
13.5
Booster ring charge (µC)
0.14
0.27
Normalized emittance, end of step 8 (µm)
1.47
0.92
1.23
0.96
1.13
Collider ring SC tune shift, end of step 8
0.12
0.17
0.15
6σ aperture, step 6-8 (mm)
11.7
14.2
11.5
12.0
11.9
11.4
Assume step 8 (after the collider ring is filled) emittance is no larger than step 3(after the booster ring bunch captured in one RF bucket).

7. Upgrade path
With Pb67 from linac and no strip injection to booster, 0.5A beam current requires 40/130MeV linac and 9.25GeV proton equivalent energy for the booster. To upgrade to 1.0A, we need 70/212MeV linac and 11.6GeV booster.
Ramp ratio:
130MeV to 9.25GeV=19.9
212MeV to 11.6GeV=18.8
130MeV to 11.6GeV=24.5?
Design convention is 20X ramp ratio for magnets. Can the static field range ratio be higher?
Increase # of booster bends by 25% when upgrading to 1.0A with linac energy upgrade to 70/200MeV? How about quadrupoles?

8. Pre-split in the booster
27 or 32×24 split scheme in the collider ring needs too many stages and requires too many cavities in the collider ring, may cause problems like impedance budget; some low frequency cavities (especially10-40MHz) might be too big. We might consider pre-split the bunch in the booster
Split coasting/rectangular beam into any Nh is comparably easy; Gaussian beam needs multi-step splitting, 2× or 3× each time; 5× split is very hard to achieve.

9. Pre-split in the booster (option 0)
booster ring
DC cooler
Collider ring
Harmonic number: 10-90
BB cooler
up polarized long bunches
2-90 empty buckets for gaps
down polarized long bunches
Capture/pre-split coasting beam into long bunches, ~0.7C/Nh long ea
10× bucket-to-bucket transfers
Example: booster ring m, collider ring 2268 m, ring circumference ratio 10
booster cycles 10, booster ring Nh=90 (10 as shown), booster cycles 10 (-2×0.5 empty),
collider ring Nh0=90x10=900 (32 as shown), after 2x2 splitting, Nh=3600
No compression, can’t increase booster cycles beyond 10, which limits the total beam current in the collider ring (~0.2A with 42MeV/u Pb61+ or 130MeV proton), unless we increase the linac energy to 285MeV for 0.5A, or 450MeV for 1A collider ring beam current.

10. Pre-split in the booster (option 1): barrier bucket
booster ring
DC cooler
Collider ring
BB cooler
420 up polarized long bunches
60 empty buckets for gaps
420 down polarized long bunches
Compress coasting beam with barrier bucket to C/3 rectangular long bunch
booster ring
DC cooler
28× bucket-to-bucket transfers
×30 split
Nh=90, Nb=30
booster ring m, collider ring 2268 m, ring circumference ratio 10
Long bunch compressed to 1/3 circumference, then perform 30× split (Nh=90)
booster cycles 30 (-2 empty), collider ring Nh0=30×30=900 initially,
after 2×2 splitting, Nh=3600
Only need 2 extra frequencies (119MHz, 238MHz).

11. Pre-split in the booster (option 2): binary splits
booster ring
DC cooler
Collider ring
BB cooler
144 up polarized long bunches
12 empty buckets for gaps
144 down polarized long bunches
After compression, ~0.7C/4 long bunch, switch Nh from 1 to 4
booster ring
DC cooler
36× bucket-to-bucket transfers
2×2×2 split
Nh=32, Nb=8
booster ring 242 m, collider ring 2268 m, ring circumference ratio (300/32)
Long bunch compressed to ~1/3 circumference, then perform 2×2×3 split to 12 bunches (Nh=36)
booster cycles 37.5 (-1 empty), collider ring Nh0=12×25=300 initially,
after 2×2×3 splitting, Nh=3600
Still needs the 6-7 RF frequencies for all the splitting

12. Pre-split in the booster (option 3)
booster ring
DC cooler
booster ring
DC cooler
Harmonic number: 10
After capture, 70%
After compression, 70% / 3
1st transfer
2nd transfer
3rd transfer
One of 10 sections of the collider ring
Length same as the booster ring circumference
Yuhong
Example: booster ring m, collider ring 2268 m, ring circumference ratio 10
booster cycles 10x3 = 30 (minus 2 for the gap)
booster ring Nh=10, collider ring Nh=30x10=300 initially,
after 2x2x3 splitting, HM=3600
How to implement the 3× transfers without disturbing the previously injected beam?
Slip stacking(SPS scheme ~50ns bucket size)? strip injection?

13. SPS Slip stacking Procedure
Argyropoulos
Two super-batches injected into the SPS:
PS batch: 4 bunches spaced by 100 ns
6 PS batches injected into the SPS (batch space of 100ns)
SPS super-batch: 24 bunches spaced by 100 ns (2.3 μs)
The two super-batches are captured by the two pairs of
200 MHz TWC  independent beam controls are needed
fRF variation to accelerate the first batch and decelerate the second
Let the batches slip
Bring them back by decelerating
the first and accelerating the
second
Once the bunches are
interleaved they are
recaptured at average
RF frequency

14. Pre-split in the booster (option 4): slip compression
booster ring
DC cooler
booster ring
DC cooler
Harmonic number: 5
Capture with Nh=5, bunch length compressed to 0.7C/5
After compression, bunch length 0.7C/5/3
booster ring
DC cooler
BB cooler
~75 up polarized long bunches
empty buckets for gaps
~75 down polarized long bunches
Harmonic number: 15
28 Bucket to bucket transfers
Slip compression in the booster
Transfer to collider ring
Example: booster ring 226.8m, collider ring 2268m, ring circumference ratio booster Nh0=5, after slip compression Nh=15
booster cycle 30(-2empty), collider ring long bunch Nh0=5×30=150 (~50ns ea)
after 3×23 splitting, Nh=3600
Can we achieve Nh=90 (30 before compression) in the booster?

15. Summary of Updates
Strip injection of heavy ions into the booster is not practical.
Booster extraction energy of lead ions will be lowered due to lower charge state in the updated scheme, space charge lower in the booster but worse in the collider ring. Needs to be compensated by stronger bending magnets with larger ramping ratio in the booster, or partially by increase linac charge state to 67. Change the booster to racetrack may help w/o increasing cost.
27 bunch split in the collider ring sounds very difficult. We may pre-split in the booster. Several options are available, but either have limitations or need extensive R&D.