1. Radiation Damping S.A. Bogacz, G.A. Krafft, S. DeSilva and R. Gamage
Jefferson Lab and Old Dominion University
USPAS, Fort Collins, CO, June 13-24, 2016

2. Outline Beam dynamics with synchrotron radiation:
Discuss the effect of synchrotron radiation on the (linear) motion of particles in storage rings.
Define action-angle variables for describing symplectic motion of a particle along a beam line.
Derive expressions for the damping times of the vertical, horizontal and longitudinal emittances.
Introduce the synchrotron radiation integrals (Sand’s Integrals).
Discuss the effects of quantum excitation, and derive expressions for the equilibrium horizontal and longitudinal beam emittances in an electron storage ring.
M. Sands, “The physics of electron storage rings, an introduction” SLAC
A. Wolski, University of Liverpool and the Cockcroft Institute, CAS 2009,
USPAS, Fort Collins, CO, June 13-24, 2016

3. Outline – cont. Equilibrium emittance and storage ring lattice design
Emittance preserving lattices :
The natural emittance for different types of lattice - Examples:
FODO
Double Bend Achromat (DBA)
Theoretical Minimum Emittance (TME)
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4. Coordinate system
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5. Longitudinal coordinate
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6. Energy deviation
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7. Canonical variables
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8. Symplectic matrices U
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9. Twiss parameters and the particle action
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10. Cartesian variables and action-angle variables
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11. Action and Emittance
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12. Action and Radiation
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13. Radiation damping of vertical emittance
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14. Radiation damping of vertical emittance
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15. Radiation damping of vertical emittance
USPAS, Fort Collins, CO, June 13-24, 2016

16. Radiation damping of vertical emittance
USPAS, Fort Collins, CO, June 13-24, 2016

17. Radiation damping of vertical emittance
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18. Synchrotron radiation energy loss
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19. Synchrotron radiation energy loss
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20. The first synchrotron radiation integral
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21. Damping of horizontal emittance
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22. Horizontal-longitudinal coupling
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23. Damping of horizontal emittance
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24. Radiation damping of horizontal emittance
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25. Appendix A: Damping of horizontal emittance
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26. Appendix A: Damping of horizontal emittance
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27. Appendix A: Damping of horizontal emittance
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28. Appendix A: Damping of horizontal emittance
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29. Appendix A: Damping of horizontal emittance
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30. Appendix A: Damping of horizontal emittance
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31. Damping of synchrotron oscillations
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32. Damping of synchrotron oscillations
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33. Damping of synchrotron oscillations
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34. Damping of synchrotron oscillations
USPAS, Fort Collins, CO, June 13-24, 2016

35. Damping of synchrotron oscillations
USPAS, Fort Collins, CO, June 13-24, 2016

36. Damping of synchrotron oscillations
USPAS, Fort Collins, CO, June 13-24, 2016

37. Damping of synchrotron oscillations
USPAS, Fort Collins, CO, June 13-24, 2016

38. Damping of synchrotron oscillations
USPAS, Fort Collins, CO, June 13-24, 2016

39. Damping of synchrotron oscillations
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40. Summary: synchrotron radiation damping
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41. Quantum excitation
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42. Quantum excitation of horizontal emittance
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43. Quantum excitation of horizontal emittance
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44. Appendix B: Quantum excitation of horizontal emittance
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45. Appendix B: Quantum excitation of horizontal emittance
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46. Appendix B: Quantum excitation of horizontal emittance
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47. Appendix B: Quantum excitation of horizontal emittance
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48. Quantum excitation of horizontal emittance
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49. Quantum excitation of vertical emittance
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50. Quantum excitation of synchrotron oscillations
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51. Quantum excitation of synchrotron oscillations
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52. Natural energy spread
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53. Summary: Radiation Damping
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54. Summary: Synchrotron radiation integrals
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55. Summary: Sand’s Integrals
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56. Summary
So far we have:
discussed the effect of synchrotron radiation on the (linear) motion of particles in storage rings;
derived expressions for the damping times of the vertical, horizontal and longitudinal emittances;
discussed the effects of quantum excitation, and derive expressions for the equilibrium horizontal and longitudinal beam emittances in an electron storage ring.
USPAS, Fort Collins, CO, June 13-24, 2016