1. CEPC Partial Double Ring Lattice Design and DA Study
SU Feng GAO Jie WANG Dou WANG Yiwei
Li Yongjun BIAN Tianjinan BAI Sha DUAN Zhe GENG Huiping ZHANG Yuan XU Gang XIAO Ming
Key Laboratory of Particle Acceleration Physics and Technology
Institute of High Energy Physics
Chinese Academy of Sciences

2. Out line CEPC PDR Lattice Layout CEPC PDR DA without FFS
CEPC PDR DA with FFS
New FODO cell ： 90/90 non-interleave
NSGAII & DA Optimization
DA Study Strategy and Next Steps
Summary

3. CEPC Partial Double Ring Layout
SU Feng
IP1_ee
IP3_ee
IP2_pp
IP4_pp
3.2Km RF
1/2RF
IP1_ee/IP3_ee, 3.2Km
IP2_pp/IP4_pp, m
4 Short Straights, 141.6m
4 Medium Straights, 566.4m
4 Long Straights, 849.6m
2 Short ARC, 24*FODO, m
4 Medium ARC, 112*FODO, m
4 Long ARC, 124*FODO, m
C=59044m
Bypass
about 42m

4. CEPC Bypass at IP2/4
566.4m s
12Lc
24Lc
L=42m s
Cell length=47.2m

5. CEPC Partial Double Ring Layout
For CEPC 120GeV beam:
Max. deflection per separator is 66μrad.
Using Septum Dipole after separator to acquire 15 mrad
CEPC Partial Double Ring Layout B1 B2 B3 B4
15mrad
Full crossing angle 30mrad
Separator
Version 1.0
sufeng
1642m 12
62.5urad
4.5m IP
507.1m
614.4m
307.2m
7.852m
54m
Septum Dipole

6. New PDR1.0.1
90/90
12cell

7. Dipole Strength PDR1.0.1 without FFS
Angle(mrad)
L(m)
Rho(m)
Brho(E0/c)(T/m)
B(T)
Ek(KeV)
KeV/m B0
3.205
19.6
400
31.956
BSepL
4.5
-72000
53.2
11.822
BSeptumL
-4.25 3
5426.4
1808.8
BMatch1L
1.277
4.9
0.1042
BMatch2L
-7.656
1496.2
76.337
BMatch3L
-3.621
36.104 B2
1.5
14.956 B3
-1.5
BMatch3R
3.621
0.0740
BMatch2R
7.656
0.1562
BMatch1R
-1.277
BSeptumR
4.25
BSepR
0.0625
72000

8. New ARC FODO 90/90 non-interleave
SF1
SD1

9. SF2
SD2
SF1
SD1
SF3
SD3
SF4
SD4
SF6
SD6
SF5
SD5

10. ARC1.2.1-bypass-PDR1.0.1-without FFS (90/90)
X：0.53mm
Y：0.012mm
Before optimization：2 group sexts

11. ARC1.2.1-bypass-PDR1.0.1-without FFS (90/90)
X：0.53mm
Y：0.012mm
100

12. NSGA-II & DA Optimization
Objective
Variable
SF1.K2
SF2.K2
SF3.K2
SF4.K2
SF5.K2
SF6.K2
SD1.K2
SD2.K2
SD3.K2
SD4.K2
SD5.K2
SD6.K2
'npop': 500,
'ngen': 100,
'nobj': 30,
'nvar': 12,
200CPU
T1=40min
T2=70h

13. DA Study Strategy and Next Steps
1. Nonlinear driving term:
habcde , a+b+c+d+e=3 , 1st order nonlinear driving term
a+b+c+d+e=4 , 2nd order nonlinear driving term
1st order chromaticity: h11001, h00111
2nd order chromaticity: h11002, h00112
Tune with amplitude: h11110, h22000, h00220 ……
For NSLS-II, up to 2nd order nonlinear driving terms are suppressed by 9 families of sextuples per cell. Tune with amplitude coefficients were used as extra constraints. For CEPC, which terms are more important and have strong contribution on dynamic aperture, and how to define these constraints need further studies. Which term is more important and has strong contribute to dynamic aperture and need more constraints？（now 0< h11002 and h00112 real part <4000， the second order chromaticity is very large while the first order is small as 3/3, and tune with amplitude coefficients are already small. We need to make sure which coefficient needs extra constraints.）

14. DA Study Strategy and Next Steps
2. population & generation：To keep enough population at each generation is a key condition to produce good solutions through cross-over and mutation. Since CEPC ring scale is quite big, it is very time-consuming to using large population. Limited by the parallel computer cluster at NSLS-II, we only used 500 populations per generation. We need to numerically determine the amount of population once computation resource is available. Now the time for one computation of 100 generation with 500 populations per generation is about 80h.
NSLS-II
CEPC （now） 没有好解
4000 or more ？ Long time

15. DA Study Strategy and Next Steps
3. Tune footprint, Tune space, Working point choice: Now the CEPC working point is (0.08, 0.22), and the second order chromaticity is negative. Tune will approach to the resonance line for the off-momentum particles, then energy acceptance is too small to have a decent lifetime. Frequency map analysis needs to be implemented. A tune scan may be helpful to localize a better range for tune. We need to analyse the tune footprint, choose a space to fit it in. We should consider whether the work point is good or not. Maybe the injection work point can be another choose for large enough DA, and after injection, we rump the work point to (0.08, 0.22) for the high luminosity requirement. It seems that the linear lattice design is isolated from nonlinear beam dynamics, which should be considered in a consistent way. Some iteractions are needed.
4.Energy acceptance： Thus far 2% energy acceptance is expected, but FODO lattice itself has a very small energy acceptance. How to enlarge the energy spread for FODO lattice need to be studied before blindly launching optimization process. （PETRA III 1.5%）

16. DA Study Strategy and Next Steps
5. Error tolerance:
The error tolerance for the magnets in the lattice is not considered yet. Optimization with random magnet imperfections is needed.
6. Thin lens & thick lens:
Now the calculation is treating the elements as thin lens. If the real elements have real length, it need to integrate the whole length. How will the difference be?
degree FODO cell compare and choose:
We need to compare the FODO cell with different phase advance to choose the better design for DA. In design PETRA-3 ring, we found this has a significant impact on DA.
8. How to divided the sextupoles groups?
How many group should the sextupoles to be divided? This needs to try. Now the configuration of the sextupoles layout is arbitrary. How to group sextupoles, and if any symmetry can help to minimize driving terms, or provide extra knobs is not clear.
9. Converge of sexts: A strong evidence to have a good DA is that, at the end of optimization, the sextupole strengthes should be seen to converge to several ranges in parameter space. So far, we didn’t see any convergence for first try.

17. DA Study Strategy and Next Steps
10. A new approach, using square matrix Jordan form to optimization tools, which proposed by Li-Hua Yu has been tested successfully at NSLS-II. The tools are still under benchmark and optimization, which is not ready for other users. The main idea was explained to Feng Su. We want to start a close collaboration with IHEP CEPC team once we are ready.
11. A necessary computation environment: Since our codes is parallel, we strongly recommend that IHEP should set up a necessary computation environment in the near future.

18. Next to do 一、计算环境，服务器： Acc-ap 不忙时可以提供一定运算（焦毅 张源 段哲）
计算中心云计算（目前700核，可用多少不清楚）：下午去找程耀东老师谈
二、DA 优化：
三、Latt-cepc.python code 改进：
四、……

19. Thank You !

20. ARC1.2.1-bypass-PDR1.0.1-without FFS (90/90)
X：0.53mm
Y：0.012mm 96