1. Radiation Damping - Low emittance lattices
Alex Bogacz
USPAS, Hampton, VA, Jan , 2011

2. Outline Beam dynamics with synchrotron radiation.
The effects of synchrotron radiation on the (linear) motion of particles in storage rings.
The synchrotron radiation integrals.
Damping times of the vertical, horizontal and longitudinal emittances.
Quantum excitation and the equilibrium horizontal and longitudinal beam emittances in an electron storage ring.
Equilibrium emittance and storage ring lattice design.
The natural emittance in different types of lattice (FODO, DBA, TME…).•
Emittance reduction in an achromat by "detuning" from the zero-dispersion conditions.
USPAS, Hampton, VA, Jan , 2011

3. Outline – content Beam dynamics with synchrotron radiation:
Define action-angle variables for describing symplectic motion of a particle along a beam line.
Discuss the effect of synchrotron radiation on the (linear) motion of particles in storage rings.
Derive expressions for the damping times of the vertical, horizontal and longitudinal emittances.
Discuss the effects of quantum excitation, and derive expressions for the equilibrium horizontal and longitudinal beam emittances in an electron storage ring.
Emittance preserving lattices - Examples:
FODO, DBA, TME…
A. Wolski, Academic Lectures, University of Liverpool , 2009
USPAS, Hampton, VA, Jan , 2011

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
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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
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16. Radiation damping of vertical emittance
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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. Damping of synchrotron oscillations
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26. Damping of synchrotron oscillations
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27. Damping of synchrotron oscillations
USPAS, Hampton, VA, Jan , 2011

28. Damping of synchrotron oscillations
USPAS, Hampton, VA, Jan , 2011

29. Damping of synchrotron oscillations
USPAS, Hampton, VA, Jan , 2011

30. Damping of synchrotron oscillations
USPAS, Hampton, VA, Jan , 2011

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. Summary: synchrotron radiation damping
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35. Quantum excitation
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36. Quantum excitation of horizontal emittance
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37. Quantum excitation of horizontal emittance
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38. Quantum excitation of horizontal emittance
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39. Quantum excitation of vertical emittance
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40. Quantum excitation of synchrotron oscillations
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41. Quantum excitation of synchrotron oscillations
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42. Natural energy spread
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43. Summary: radiation damping
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44. Summary: synchrotron radiation integrals
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45. Summary: synchrotron radiation integrals
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46. Radiation Damping - Re-cap
So far we:
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, Hampton, VA, Jan , 2011

47. S-R integrals - Re-cap
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48. S-R integrals - Re-cap
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49. Lattice Examples Practical implementations: FODO
DBA (double-bend achromat)
multi-bend achromat, including the triple-bend achromat (TBA)
TME (theoretical minimum emittance)
USPAS, Hampton, VA, Jan , 2011

50. Calculating the natural emittance in a lattice
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51. FODO lattice - natural emittance
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52. FODO lattice - natural emittance
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53. FODO lattice - natural emittance
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54. FODO lattice - natural emittance
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55. FODO lattice - natural emittance
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56. FODO lattice - natural emittance
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57. FODO lattice - natural emittance
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58. FODO lattice - natural emittance
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59. FODO lattice - natural emittance
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60. FODO lattice - natural emittance
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61. DBA lattice - natural emittance
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62. DBA lattice - natural emittance
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63. DBA lattice - natural emittance
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64. DBA lattice - natural emittance
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65. DBA lattice - natural emittance
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66. DBA lattice - natural emittance
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67. TME lattice - natural emittance
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68. TME lattice - natural emittance
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69. TME lattice - natural emittance
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70. TME lattice - natural emittance
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71. Summary: FODO, DBA and TME lattices
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72. Design for low emittance lattices
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73. Summary
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74. Summary cont.
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75. Appendix A: Damping of horizontal emittance
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76. Appendix A: Damping of horizontal emittance
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77. Appendix A: Damping of horizontal emittance
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78. Appendix A: Damping of horizontal emittance
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79. Appendix A: Damping of horizontal emittance
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80. Appendix A: Damping of horizontal emittance
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81. Appendix B: Quantum excitation of horizontal emittance
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82. Appendix B: Quantum excitation of horizontal emittance
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83. Appendix B: Quantum excitation of horizontal emittance
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84. Appendix B: Quantum excitation of horizontal emittance
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