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1Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Radiation Damping
S.A. Bogacz, G.A. Krafft, S. DeSilva and B. Dhital
Jefferson Lab and Old Dominion University
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2Lecture 12 - Radiation Damping
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-121. 1970
A. Wolski, University of Liverpool and the Cockcroft Institute, CAS 2009,
USPAS, San Diego, CA, January 13-24, 2020
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3Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Coordinate system
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4Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Longitudinal coordinate
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5Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Energy deviation
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6Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Canonical variables
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7Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Symplectic matrices
U U
U
U
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8Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Twiss parameters and the particle action
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9Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Cartesian variables and action-angle variables
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Action and Emittance
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Action and Radiation
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12Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Radiation damping of vertical emittance
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Radiation damping of vertical emittance
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Radiation damping of vertical emittance
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15Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Radiation damping of vertical emittance
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Radiation damping of vertical emittance
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17Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Synchrotron radiation energy loss
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18Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Synchrotron radiation energy loss
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19Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
The first synchrotron radiation integral
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Damping of horizontal emittance
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21Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Horizontal-longitudinal coupling
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22Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Damping of horizontal emittance
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23Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Radiation damping of horizontal emittance
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24Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Appendix A: Damping of horizontal emittance
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25Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Appendix A: Damping of horizontal emittance
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26Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Appendix A: Damping of horizontal emittance
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27Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Appendix A: Damping of horizontal emittance
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Appendix A: Damping of horizontal emittance
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Appendix A: Damping of horizontal emittance
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Damping of synchrotron oscillations
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31Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Damping of synchrotron oscillations
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Damping of synchrotron oscillations
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Damping of synchrotron oscillations
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Damping of synchrotron oscillations
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Damping of synchrotron oscillations
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Damping of synchrotron oscillations
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Damping of synchrotron oscillations
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38Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Damping of synchrotron oscillations
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39Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Summary: synchrotron radiation damping
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40Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Quantum excitation
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41Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Quantum excitation of horizontal emittance
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Quantum excitation of horizontal emittance
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Appendix B: Quantum excitation of horizontal emittance
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Appendix B: Quantum excitation of horizontal emittance
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Appendix B: Quantum excitation of horizontal emittance
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Appendix B: Quantum excitation of horizontal emittance
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47Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Quantum excitation of horizontal emittance
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48Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Quantum excitation of vertical emittance
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49Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Quantum excitation of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility
50Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Quantum excitation of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility
51Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Quantum excitation of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility
52Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Quantum excitation of synchrotron oscillations
-Let us calculate:
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53Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Quantum excitation of synchrotron oscillations
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54Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Natural energy spread
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55Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Summary: Radiation Damping
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56Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Summary: Synchrotron radiation integrals
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57Lecture 12 - Radiation Damping USPAS, San Diego, CA, January 13-24, 2020
Summary: Sand’s Integrals
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Thomas Jefferson National Accelerator Facility
58Lecture 12 - Radiation Damping
Summary
In this lecture 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, San Diego, CA, January 13-24, 2020