1. A CCELERATOR L ABORATORY of T SINGHUA U NIVERSITY Haisheng Xu ( 许海生 ), Wenhui Huang, Chuanxiang Tang haishengxu@gmail.com 清华大学工程物理系 Department of Engineering Physics, Tsinghua University The 12 th Symposium on Accelerator Physics Intrinsic Nonlinearity of Dipole Magnets in Small Rings Aug. 14, 2014

2. A CCELERATOR L ABORATORY of T SINGHUA U NIVERSITY Outline Introduction to TTX Introduction to TTX Intrinsic nonlinearity in small rings Intrinsic nonlinearity in small rings  Analytical analysis;  Simulation; Status of the small ring for TTX Status of the small ring for TTX Tsinghua Thomson scattering X-ray source

3. TTX – Layout

4. Yingchao Du et.al., Rev. Sci. Instrum 84, 053301 (2013) TTX – Status

5. TTX – Next A small ring!

6. TTX – Next

7. Observation of Nonlinear Resonances ! Observation of Nonlinear Resonances !

8. Analytical Analysis We carry out the analytical analysis in Frenet-Serret coordinate system. The Hamiltonian can be expressed as

9. Analytical Analysis Consider an accelerator with ideal dipoles and quadrupoles, there are transverse magnetic field only. The vector potential can be expressed as Different !!! Linear Part Nonlinear Part Intrinsic

10. Analytical Analysis

12. Simulation – Particle Tracking By adjusting the quadrupoles’ strength simultaneously, the betatron tunes can be varied in a large range.

14. Varying bending radius of dipoles, we can obtain resonance strength both analytically and by particle tracking.

15. Four stable islands; Rectangular shape distortion of the phase trajectories of particles in the central region;

16. Baseline Design H.S. Xu, W.H. Huang, C.X. Tang, and S.Y. Lee, Phys. Rev. ST Accel. Beams, 2014, 17:070101 [Editors’ Suggestion]

17. MINI BETA ParametersValue Betax/Betay at IP (m)0.194 / 0.489 Dispersion at IP (m)1.00e-3 Tune ( x / y ) 1.40 / 1.40 Chromaticity (  x /  y ) -1.10 / -1.10 Horizontal damping partition number (J x )0.999 Momentum compaction factor (  c ) 0.280 Mini-beta Design Courtesy of Tenghui Rui

18. MINI BETA x y 0.031.37371.3711 0.021.38111.3800 0.011.38981.3896 01.4000 -0.011.41191.4117 -0.021.42531.4254 -0.031.43951.4425 Mini-beta Design Courtesy of Tenghui Rui

19. Summary

20. The 12 th Symposium on Accelerator Physics A CCELERATOR L ABORATORY of T SINGHUA U NIVERSITY Thanks谢谢