l 15 radiationdamping rev1 - casa.jlab.org
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Thomas Jefferson National Accelerator Facility1Lecture 15 − 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 Facility2Lecture 15 − Radiation Damping
Outline
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.
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. 1970A. 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
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Thomas Jefferson National Accelerator Facility3Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Coordinate system
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Thomas Jefferson National Accelerator Facility4Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Longitudinal coordinate
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Thomas Jefferson National Accelerator Facility5Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Energy deviation
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Thomas Jefferson National Accelerator Facility6Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Canonical variables
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Thomas Jefferson National Accelerator Facility7Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Symplectic matrices
U U
U
U
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Thomas Jefferson National Accelerator Facility8Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Twiss parameters and the particle action
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Thomas Jefferson National Accelerator Facility9Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21,
2013
Cartesian variables and action-angle variables
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Thomas Jefferson National Accelerator Facility10Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Action and Emittance
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Thomas Jefferson National Accelerator Facility11Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Action and Radiation
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Thomas Jefferson National Accelerator Facility12Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Radiation damping of vertical emittance
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Thomas Jefferson National Accelerator Facility13Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Radiation damping of vertical emittance
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Thomas Jefferson National Accelerator Facility14Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Radiation damping of vertical emittance
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Thomas Jefferson National Accelerator Facility15Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Radiation damping of vertical emittance
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Thomas Jefferson National Accelerator Facility16Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Radiation damping of vertical emittance
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Thomas Jefferson National Accelerator Facility17Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Synchrotron radiation energy loss U0
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Thomas Jefferson National Accelerator Facility18Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Synchrotron radiation energy loss
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Thomas Jefferson National Accelerator Facility19Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
The first synchrotron radiation integral
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Thomas Jefferson National Accelerator Facility20Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of horizontal emittance
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Thomas Jefferson National Accelerator Facility21Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Horizontal-longitudinal coupling
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Thomas Jefferson National Accelerator Facility22Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of horizontal emittance
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Thomas Jefferson National Accelerator Facility23Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Radiation damping of horizontal emittance
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Thomas Jefferson National Accelerator Facility24Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix A: Damping of horizontal emittance
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Thomas Jefferson National Accelerator Facility25Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix A: Damping of horizontal emittance
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Thomas Jefferson National Accelerator Facility26Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix A: Damping of horizontal emittance
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Thomas Jefferson National Accelerator Facility27Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix A: Damping of horizontal emittance
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Thomas Jefferson National Accelerator Facility28Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix A: Damping of horizontal emittance
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Thomas Jefferson National Accelerator Facility29Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix A: Damping of horizontal emittance
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Thomas Jefferson National Accelerator Facility30Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility31Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility32Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility33Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility34Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility35Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility36Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility37Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility38Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Damping of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility39Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Summary: Synchrotron radiation damping
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Thomas Jefferson National Accelerator Facility40Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Quantum excitation
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Thomas Jefferson National Accelerator Facility41Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Quantum excitation of horizontal emittance
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Thomas Jefferson National Accelerator Facility42Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Quantum excitation of horizontal emittance
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Thomas Jefferson National Accelerator Facility43Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix B: Quantum excitation of horizontal emittance
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Thomas Jefferson National Accelerator Facility44Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix B: Quantum excitation of horizontal emittance
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Thomas Jefferson National Accelerator Facility45Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix B: Quantum excitation of horizontal emittance
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Thomas Jefferson National Accelerator Facility46Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix B: Quantum excitation of horizontal emittance
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Thomas Jefferson National Accelerator Facility47Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Equilibrium horizontal emittance
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Thomas Jefferson National Accelerator Facility48Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Quantum excitation of vertical emittance
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Thomas Jefferson National Accelerator Facility49Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Quantum excitation of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility50Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Quantum excitation of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility51Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Natural energy spread
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Thomas Jefferson National Accelerator Facility52Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Summary: Radiation Damping
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Thomas Jefferson National Accelerator Facility53Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Summary: Synchrotron radiation integrals
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Thomas Jefferson National Accelerator Facility54Lecture 15 − Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Summary: Sand’s Integrals
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Thomas Jefferson National Accelerator Facility55Lecture 15 − 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