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Thomas Jefferson National Accelerator Facility
1 Lecture 16 Radiation Damping
Radiation Damping
USPAS, Fort Collins, CO, June 10-21, 2013
Alex Bogacz, Geoff Krafft and Timofey Zolkin
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Thomas Jefferson National Accelerator Facility
2 Lecture 16 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,
http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf
USPAS, Fort Collins, CO, June 10-21, 2013
Operated by JSA for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
3 Lecture 16 Radiation Damping
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)
USPAS, Fort Collins, CO, June 10-21, 2013
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4 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Coordinate system
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5 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Longitudinal coordinate
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6 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Energy deviation
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7 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Canonical variables
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8 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Symplectic matrices
U U
U
U
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9 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Twiss parameters and the particle action
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10 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21,
2013
Cartesian variables and action-angle variables
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11 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Action and Emittance
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12 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Action and Radiation
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13 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Radiation damping of vertical emittance
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14 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Radiation damping of vertical emittance
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15 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Radiation damping of vertical emittance
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16 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Radiation damping of vertical emittance
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17 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Radiation damping of vertical emittance
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18 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Synchrotron radiation energy loss
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19 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Synchrotron radiation energy loss
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20 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
The first synchrotron radiation integral
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21 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of horizontal emittance
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22 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Horizontal-longitudinal coupling
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23 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of horizontal emittance
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24 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Radiation damping of horizontal emittance
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25 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix A: Damping of horizontal emittance
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26 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix A: Damping of horizontal emittance
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27 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix A: Damping of horizontal emittance
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28 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix A: Damping of horizontal emittance
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29 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix A: Damping of horizontal emittance
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30 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix A: Damping of horizontal emittance
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31 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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32 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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33 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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34 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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35 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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36 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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37 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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38 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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39 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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40 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Summary: synchrotron radiation damping
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41 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Quantum excitation
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42 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Quantum excitation of horizontal emittance
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43 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Quantum excitation of horizontal emittance
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44 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix B: Quantum excitation of horizontal emittance
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45 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix B: Quantum excitation of horizontal emittance
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46 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix B: Quantum excitation of horizontal emittance
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47 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix B: Quantum excitation of horizontal emittance
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48 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Quantum excitation of horizontal emittance
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49 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Quantum excitation of vertical emittance
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50 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Quantum excitation of synchrotron oscillations
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51 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Quantum excitation of synchrotron oscillations
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52 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Natural energy spread
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53 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Summary: Radiation Damping
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54 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Summary: Synchrotron radiation integrals
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55 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Summary: Sand’s Integrals
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56 Lecture 16 Radiation Damping
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 10-21, 2013
