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The Study of Off-momentum Particle Motion with Independent Component Analysis

Weiming Guo Accelerator Physics Group / ASD Advanced Photon Source. The Study of Off-momentum Particle Motion with Independent Component Analysis. Acknowledgements. Katherine Harkay Xiaobiao Huang Michael Borland Jack Albert Chunxi Wang Hairong Shang.

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The Study of Off-momentum Particle Motion with Independent Component Analysis

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  1. Weiming Guo Accelerator Physics Group / ASD Advanced Photon Source The Study of Off-momentum Particle Motion with Independent Component Analysis

  2. Acknowledgements • Katherine Harkay • Xiaobiao Huang • Michael Borland • Jack Albert • Chunxi Wang • Hairong Shang

  3. What is the mechanism of synchrotron sidebands? 0.206 ±0.0083

  4. The current theory of dispersion The transverse motion Hamiltonian Consider only quadrupoles and dipoles, the first order dispersion equation Let , the equation for the dispersion function The boundary condition

  5. The physical picture of dispersion Reference C.O. δ < 0 δ > 0

  6. Analytical solution In vector space The solution of the homogeneous equation M(s|0) is the transformation matrix The solution of the inhomogeneous equation

  7. The dispersion functions

  8. The ID(s) and function

  9. The calculated dispersion function

  10. The calculated ID function

  11. The meaning of the ID term Reference C.O. δ < 0 δ > 0

  12. The higher order terms

  13. Particle simulation with ELEGANT(I) Particle on C.O. with 0.4% momentum offset

  14. The spectrum of 4000 turns

  15. Particle simulation with ELEGANT(II) Particle on C.O. with 10o phase kick

  16. Experiment setup APS storage ring operation parameters We give the beam a phase shift of 0~14o, with width of 200 ms. The equilibrium bunch length is about 2.5o . The horizontal dis- placement is about 0~1.2mm. There are about 280 BPMs can be used for history data taking. We analyzed the data with independent component analysis.

  17. Temporal pattern of dispersion Damping time 1188 turns 1300 turns Synchrotron tune 0.0083

  18. The comparison of the dispersion function

  19. The temporal pattern of second order dispersion

  20. The second order dispersion function

  21. The coupling Mode 0.205 0.1975

  22. The comparison of the ID function

  23. Phase advance comparison

  24. Conclusion • We found the analytical expression of the X-Z coupling term. • The mode is damped in most cases, however we found it in the experiment under the critical conditions. • Both the amplitude and phase advance agree with prediction. • In the analysis of the experiment data, we also found the first and second order dispersion function and they all agree with model value.

  25. The effect of the Chromaticity

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