A CCELERATOR L ABORATORY of T SINGHUA U NIVERSITY Haisheng Xu ( 许海生 ), Wenhui Huang, Chuanxiang Tang 清华大学工程物理系 Department of Engineering.

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A CCELERATOR L ABORATORY of T SINGHUA U NIVERSITY Haisheng Xu ( 许海生 ), Wenhui Huang, Chuanxiang Tang 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

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

TTX – Layout

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

TTX – Next A small ring!

TTX – Next

Observation of Nonlinear Resonances ! Observation of Nonlinear Resonances !

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

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

Analytical Analysis

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

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

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

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

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

MINI BETA x y Mini-beta Design Courtesy of Tenghui Rui

Summary

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