1. The IR lattice design and optimization of the dynamic aperture for the ring Yiwei Wang, Huiping Geng, Yuan Zhang, Sha Bai, Dou Wang, Tianjian, Jie Gao Institute of High Energy Physics (IHEP, Beijing) CEPC workshop IHEP, 11-12 Sep 2015 Yiwei Wang23-27 Sep 20151

2. Outline CEPC layout Lattice design of the Interaction region Optimization of the dynamic aperture Summary Yiwei Wang23-27 Sep 20152

3. CEPC layout P.S. IP1 IP4 IP3 IP2 D = 17.3 km ½ RF RF ½ RF RF One RF station: 650 MHz five-cell SRF cavities; 4 cavities/module 12 modules, 8 m each RF length 120 m C = 54 km IP1 and IP3 for CEPC Yiwei Wang323-27 Sep 2015

4. CEPC parameters Yiwei Wang23-27 Sep 20154 ParameterUnitValueParameterUnitValue Beam energy [E]GeV120Circumference [C]m54752 Number of IP[N IP ] 2SR loss/turn [U 0 ]GeV3.11 Bunch number/beam[n B ] 50Bunch population [Ne] 3.79E+11 SR power/beam [P]MW51.7Beam current [I]mA16.6 Bending radius [  ] m6094 momentum compaction factor [  p ] 3.36E-05 Revolution period [T 0 ]s1.83E-04Revolution frequency [f 0 ]Hz5475.46 emittance (x/y)nm6.12/0.018  IP (x/y) mm800/1.2 (3.0) Transverse size (x/y) mm 69.97/0.15  x,y /IP 0.118/0.083 Beam length SR [  s.SR ] mm2.14 Beam length total [  s.tot ] mm2.88 Lifetime due to Beamstrahlungmin lifetime due to radiative Bhabha scattering [  L ] min52 RF voltage [V rf ]GV6.87RF frequency [f rf ]MHz650 Harmonic number [h] 118800 Synchrotron oscillation tune [ s ] 0.18 Energy acceptance RF [h]%5.99 Damping partition number [J  ] 2 Energy spread SR [  .SR ] %0.132 Energy spread BS [  .BS ] %0.119 Energy spread total [  .tot ] %0.177nn 0.23 Transverse damping time [n x ]turns78Longitudinal damping time [n  ]turns39 Hourglass factorFh0.658Luminosity /IP[L]cm -2 s -1 2.04E+34

5. Interaction region design As shown in beam-beam simulation, the luminosity are almost the same when  y* increased from 1.2 mm to 3 mm. For the first try, we just refit the final transformer. – the parts other than FT are almost kept L*=1.5m  y*=1.2mm Yiwei Wang23-27 Sep 20155 L*=1.5m  y*=3mm

6. Design principle of final doublet constraint R22=0, R44=0 at the exit of QF1 – point to parallel image on both x and y planes – The real design just adjust the gradient a bit (less than 10%) L*dl1 l2 QD0 QF1 L*, d, G1, G2  y,  x, R, B1, B2  y*,  x*, ay, ax l1, l2 our main concern

7. Optimization of final doublet L*=1.5m, G1=G2 When G>200T/m –  y decrease slowly with the increase of G – B increase almost linearly with G and independent of the space between QD0 and QF1 Seems possible to reduce the gradient from 300T/m to 200T/m –  y slightly increased from -148 to -149 and B significantly decreased from 6.4 to 4.5 T with ay (7.88*10^-8 m  rad) used in the pre-CDR – With a more optimistic ay (5.33*10^-8 m  rad), B could be further reduce to be 3.9 T – need to check with a full IR lattice. At present we still work with G=300T/m L*=1.5m, G1=G2

8. Local chromaticity correction Add additional sextupoles next to the main one* – Compensate the finite length effect (Lsext=0.3m) Yiwei Wang23-27 Sep 20158 *A.Bogomyagkov et al. http://arxiv.org/abs/0909.4872 k=1, S1/S2=-0.1 Adjust the phase advances between the final doublet and the sextupoles to minimize second order chromaticity – QD0 and VS1 – QF1 and HS1

9. Local chromaticity correction (cont.) Yiwei Wang23-27 Sep 20159

10. Lattice of the whole ring Close the whole ring – matching linear lattice function Yiwei Wang23-27 Sep 201510 Dispersion suppressor and FODO cell in the ARC

11. Tune vs. momentum deviation Adjust the tune to be.08/.22 ( x/ y) – determined by beam- beam study match Q’ to be ~0.5 with the sextupoles in the ARC – Currently only 2 family of sextupoles in the ARC Good region of ±1% in Dp/p Yiwei Wang23-27 Sep 201511

12. Dynamic aperture for the ring without radiation damping, error of the magnets Synchrotron motion included Tracking with 3 times of damping time Coupling factor  =0.003 for emitty – -2% (2  x, 20  y), 2% (1  x, 7  y) Yiwei Wang1223-27 Sep 2015 Result in Pre-CDR

13. Optimization of the dynamic aperture Yiwei Wang23-27 Sep 201513

14. FFS_3.0mm_v0_Feb_2015 FFS_3.0mm_v1_Mar_2015 FFS_3.0mm_v2.2_Sep_2015 Remove 2 quads in FT Additional sext at 1 st image point Reduce  y in CCY Remove 2 quads Yiwei Wang23-27 Sep 201514

15. Beta and tune vs. deltap v1v2.2v0 Upper for FFS only and lower for the whole ring – Tune vs. deltap on vertical plane become very flat – Qx’ for FFS should be optimized in next step Yiwei Wang23-27 Sep 201515

16. Tune vs amplitude Tune shift with amplitude: – d(Qx)/d(Ex) d(Qy)/(dEy) d(Qy)/d(Ex) – v0: -2.555503E+04 4.563207E+06 -8.407153E+04 – v1: -2.687453E+04 1.265348E+06 -8.279601E+04 – V2.2: -2.614945E+04 1.260286E+06 -8.044155E+04

17. Vertical dynamic aperture vs. deltap v0 -> v1: DA increased significantly for on-momentum and small off-momentum v1 -> v2.2: DA increased significantly for large off-momentum Yiwei Wang23-27 Sep 201517 X0=0.001  x 02-21

18. Dynamic aperture for both planes Yiwei Wang23-27 Sep 201518 v1 v0 DA for off momentum increased significantly effect from additional sextupole can be ease by further increasing dispersion v2.2

19. Summary A preliminary designs got for the CEPC interaction region Optimization to get a reasonable dynamic aperture for the whole ring – Reduce the chromaticity contribution for CCS and IT; Remove 2 quadrupoles in FT to reduce high order chromaticity; Additional sextupole at 1 st image point to further reduce high order chromaticity – DA increased significantly for both on- and off- momentum particles – Further optimization is possible Qx’ for FFS should be optimized break down of –I matrix 2 nd order dispersion … Yiwei Wang23-27 Sep 201519

20. Acknowledge Yunhai Cai, Xiaohao Cui, Yingshun Zhu, Yuanyuan Guo, Tianjian Bian, Feng Su, Ming Xiao, Zhe Duan, Gang Xu, Jie Gao, Qing Qin, Demin Chou, Kazuhito Ohmi, Yoshihiro Funakoshi, Yukiyoshi Ohnishi, A. Bogomyagkov, Luis Eduardo Medina Medrano Thanks for your kind help and beneficial discussion! Yiwei Wang23-27 Sep 201520

21. Thank you for your attention ! Yiwei Wang23-27 Sep 201521

22. reserved Yiwei Wang23-27 Sep 201522

23. Comparison of  y*=1.2 mm and 3 mm Yiwei Wang23-27 Sep 201523  y*=1.2mm  y*=3mm

24. Comparison of  y*=1.2 mm and 3 mm With the real ring DA for off momentum: – For  y*=1.2mm, the DA is almost zero for off momentum 2% – For  y*=3mm, the DA has been extended to 2% region: -2% (2  x, 20  y), 2% (1  x, 7  y)  y*=1.2mm  y*=3mm Yiwei Wang23-27 Sep 201524