1. CEPC pretzel scheme study
H. Geng, Y. Zhang, J. Gao, Y. Wang, D. Wang, G. Xu, Q. Qin, W. Chou, N. Wang, Y. Peng, X. Cui, Z. Duan, S. Bai, F. Su
Beihang University, Beijing, China
CEPC-SPPC Study Group Meeting
September 2-3, 2016

2. Outline Introduction on pretzel scheme
DA optimization with downhill simplex method
DA optimization with MODE
Combination with FFS
Summary

3. Intro. on pretzel scheme
In single ring collider, pretzel orbit is used to avoid the beam collision at positions except for the IPs
Beam with off-center pretzel orbit will see extra fields in magnets, which will break the periodicity of lattice, and will significantly reduce the DA
In CEPC, the pretzel orbit has been designed for 50 bunches
Every 12-FODO cells were regrouped as a super-period in the arc, to correct the betatron aberration

4. Layout of the ring FODO cell length: 47.2 m (60/60degrees)
ARC length:5852.8m
Short straight: 18 FODO cells, 849.6m
Long straight: 34 FODO cells, m
Circumference: km
For 50 bunches:
Every nearest parasitic collision points will have a phase advance of 4Pi.

5. DA results before adding pretzel
Pure standard FODO cells, plus matching section adjusting working points
DA: (30sx,450sy) for ±2% momentum spread

6. DA with pretzel (no FFS)
DA tracking is done with SAD
240 turns (or 3 times transverse damping time ) is tracked
The DA is (5sx*50sy) at ± 2.0% momentum spread
DA: (5sx,50sy) for ±2% momentum spread

7. DA optimization with Downhill Simplex method
In Oide’s code
Sextupoles are adjusted
DA is the only optimization objective
Target modifications
Quadrupoles are adjusted (to be done)
DA, closed orbit, dispersion function, phase advance are the optimization objectives

8. Modifications Weight Objective function Dispersion Phase advance
Closed orbit DA

9. Results No significant improvement found !
DA: (5sx,50sy) for ±2% momentum spread
DA: (5sx,100sy) for ±2% momentum spread

10. A Multi-Objective coDE (MODE)
DA result directly from SAD matching (use 0.3% coupling)
Horizontal:
dp/p
dp/p

11. Results
DA result after optimization (about 3-4days), use 13 families of sextupoles
Horizontal:
dp/p
dp/p

12. Constraints have been set for orbit, dispersion etc.
Beta, dispersion function and orbit of the optimized lattice

13. Check DA at different direction
Not all directions are equally improved
Other directions can be further optimized…

14. Combination with FFS
One version of FFS (which has been optimized for the ring without pretzel orbit) is inserted to the lattice with pretzel
The betatron and dispersion functions of the FFS are shown in the left plot
The whole lattice of the ring is shown in the right plot
Courtesy of Yiwei Wang, by*=3mm

15. Emittance change No pretzel orbit/FFS ex=6.8 nm , sp/p=0.13%
With pretzel orbit
ex=7.9 nm , sp/p=0.13%
Increased by 16%
With pretzel orbit, and FFS
ex=21.1 nm , sp/p=0.17%
Increased by 167%
The contribution of FFS is too big, but should be managable by tuning the bending magnet strength in FFS.

16. DA with pretzel and FFS No DA after combining with pretzel and FFS
Further optimization needed

17. Summary
Downhill simplex method and a multi-objective code MODE has been used to optimize DA
The DA for lattice with pretzel reached dp/p
and dp/p
The FFS has be inserted to the lattice with pretzel orbit
Further optimization will be carried out……

18. Thank you !