Radiation Damping - Thomas Jefferson National...

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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

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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)

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4 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013

Coordinate system

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Longitudinal coordinate

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Energy deviation

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Canonical variables

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Symplectic matrices

U U

U

U

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Twiss parameters and the particle action

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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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16 Lecture 16 Radiation Damping USPAS, Fort Collins, CO, June 10-21, 2013

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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Appendix B: Quantum excitation of horizontal emittance

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Quantum excitation of horizontal emittance

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Quantum excitation of vertical emittance

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Quantum excitation of synchrotron oscillations

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Quantum excitation of synchrotron oscillations

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Natural energy spread

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Summary: Radiation Damping

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Summary: Synchrotron radiation integrals

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Summary: Sand’s Integrals

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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