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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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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
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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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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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Action and Emittance
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Action and Radiation
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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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Radiation damping of vertical emittance
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Radiation damping of vertical emittance
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Synchrotron radiation energy loss
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Synchrotron radiation energy loss
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The first synchrotron radiation integral
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Damping of horizontal emittance
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Horizontal-longitudinal coupling
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Damping of horizontal emittance
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Radiation 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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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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Appendix A: Damping of horizontal emittance
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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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Damping of synchrotron oscillations
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Damping of synchrotron oscillations
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Damping of synchrotron oscillations
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Summary: synchrotron radiation damping
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Quantum excitation
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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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47 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Appendix B: Quantum excitation of horizontal emittance
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Operated by JSA for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
48 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Quantum excitation of horizontal emittance
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Operated by JSA for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
49 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Quantum excitation of vertical emittance
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Operated by JSA for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
50 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Quantum excitation of synchrotron oscillations
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Operated by JSA for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
51 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Quantum excitation of synchrotron oscillations
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Operated by JSA for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
52 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Natural energy spread
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Operated by JSA for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
53 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Summary: Radiation Damping
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Operated by JSA for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
54 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Summary: Synchrotron radiation integrals
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Operated by JSA for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
55 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013
Summary: Sand’s Integrals
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Operated by JSA for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
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