1. CEPC 动力学孔径优化 in progress
张 源、王毅伟、耿会平、王逗

2. Introduction
Only optimize the sextupole strength in arc (240 variables)
Differential evolution algorithm is used, strategy: local-to-best, population: 8100
CEPC lattice: wangyw-v1
SAD is used to track the dynamic aperture
30 cpu core is used

3. Objective function 𝑥 2 20 2 + 𝑧 2 16 2 =1
𝑥 𝑧 =1
𝑧 for energy deviation in unit of 𝜎 𝑝
𝑥 for transverse amplitude in unit of 𝜎
For z = Range[-15,15,1]
objective function = 0, if aperture boundary is outside the ellipse distance between the boundary and the ellipse, otherwise

4. Optimization result 100turns, DAPWIDTH=15, z=Range[-15,15,1], coupling: 0.3%
One generation ~ 17 hrs

5. Check DA with PhaseX->Pi/2, PhaseY->Pi/2 100turns, DAPWIDTH=15, z=Range[-15,15,1], coupling: 0.3%

6. Check DA for different coupling

7. Check DA for different coupling (2)

8. Check DA for different coupling (3)

9. Check DA with Radiation

10. Check DA with Radiation (2)
Rad Off
Rad On

11. Check DA with Radiation (3)
Rad Off
Rad On

12. Check DA with radiation (4)
Rad Off
Rad On

13. DAPWIDTH=15 vs DAPWIDTH=30 (Max=25𝜎)

14. DAPWIDTH=30 (Max=25𝜎) vs DAPWIDTH=15 (Max=50𝜎)

15. Summary
DA is very sensitive to any phase space variable. We’ve to use very detailed tracking to determine it.
What option is more closer to the “real machine”?