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 2016.4.22

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

CEPC Partial Double Ring Layout SU Feng 2016.1.4 IP1_ee IP3_ee IP2_pp IP4_pp 3.2Km RF 1/2RF IP1_ee/IP3_ee, 3.2Km IP2_pp/IP4_pp, 1132.8m 4 Short Straights, 141.6m 4 Medium Straights, 566.4m 4 Long Straights, 849.6m 2 Short ARC, 24*FODO, 1132.8m 4 Medium ARC, 112*FODO, 5286.4m 4 Long ARC, 124*FODO, 5852.8m C=59044m Bypass about 42m

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

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 2015.12.20 1642m 12 62.5urad 4.5m IP 507.1m 614.4m 307.2m 7.852m 54m Septum Dipole

New PDR1.0.1 90/90 12cell

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 6115.44 400 0.06541 626.349 31.956 BSepL -0.0625 4.5 -72000 -0.00556 53.2 11.822 BSeptumL -4.25 3 -705.822 -0.56667 5426.4 1808.8 BMatch1L 1.277 4.9 3837.12 0.1042 998.249 203.724 BMatch2L -7.656 -2560.08 -0.1562 1496.2 76.337 BMatch3L -3.621 -5412.87 -0.0740 707.647 36.104 B2 1.5 13066.7 0.03061 293.143 14.956 B3 -1.5 -13066.7 -0.03061 BMatch3R 3.621 5412.87 0.0740 BMatch2R 7.656 2560.08 0.1562 619.704 BMatch1R -1.277 -3837.12 -0.1042 BSeptumR 4.25 705.822 0.56667 BSepR 0.0625 72000 0.00556

New ARC FODO 90/90 non-interleave SF1 SD1

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

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

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

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

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.）  

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 4000 100 CEPC 500 100 （now） 没有好解 4000 or more ？ Long time

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%）

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? 7. 90 72 60 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.

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.

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、……

Thank You !

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