Radiation Damping S.A. Bogacz, G.A. Krafft, S. DeSilva and R. Gamage

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Presentation transcript:

Radiation Damping S.A. Bogacz, G.A. Krafft, S. DeSilva and R. Gamage Jefferson Lab and Old Dominion University USPAS, Fort Collins, CO, June 13-24, 2016

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, Fort Collins, CO, June 13-24, 2016

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 13-24, 2016

Coordinate system USPAS, Fort Collins, CO, June 13-24, 2016

Longitudinal coordinate USPAS, Fort Collins, CO, June 13-24, 2016

Energy deviation USPAS, Fort Collins, CO, June 13-24, 2016

Canonical variables USPAS, Fort Collins, CO, June 13-24, 2016

Symplectic matrices U USPAS, Fort Collins, CO, June 13-24, 2016

Twiss parameters and the particle action USPAS, Fort Collins, CO, June 13-24, 2016

Cartesian variables and action-angle variables USPAS, Fort Collins, CO, June 13-24, 2016

Action and Emittance USPAS, Fort Collins, CO, June 13-24, 2016

Action and Radiation USPAS, Fort Collins, CO, June 13-24, 2016

Radiation damping of vertical emittance USPAS, Fort Collins, CO, June 13-24, 2016

Radiation damping of vertical emittance USPAS, Fort Collins, CO, June 13-24, 2016

Radiation damping of vertical emittance USPAS, Fort Collins, CO, June 13-24, 2016

Radiation damping of vertical emittance USPAS, Fort Collins, CO, June 13-24, 2016

Radiation damping of vertical emittance USPAS, Fort Collins, CO, June 13-24, 2016

Synchrotron radiation energy loss USPAS, Fort Collins, CO, June 13-24, 2016

Synchrotron radiation energy loss USPAS, Fort Collins, CO, June 13-24, 2016

The first synchrotron radiation integral USPAS, Fort Collins, CO, June 13-24, 2016

Damping of horizontal emittance USPAS, Fort Collins, CO, June 13-24, 2016

Horizontal-longitudinal coupling USPAS, Fort Collins, CO, June 13-24, 2016

Damping of horizontal emittance USPAS, Fort Collins, CO, June 13-24, 2016

Radiation damping of horizontal emittance USPAS, Fort Collins, CO, June 13-24, 2016

Appendix A: Damping of horizontal emittance USPAS, Fort Collins, CO, June 13-24, 2016

Appendix A: Damping of horizontal emittance USPAS, Fort Collins, CO, June 13-24, 2016

Appendix A: Damping of horizontal emittance USPAS, Fort Collins, CO, June 13-24, 2016

Appendix A: Damping of horizontal emittance USPAS, Fort Collins, CO, June 13-24, 2016

Appendix A: Damping of horizontal emittance USPAS, Fort Collins, CO, June 13-24, 2016

Appendix A: Damping of horizontal emittance USPAS, Fort Collins, CO, June 13-24, 2016

Damping of synchrotron oscillations USPAS, Fort Collins, CO, June 13-24, 2016

Damping of synchrotron oscillations USPAS, Fort Collins, CO, June 13-24, 2016

Damping of synchrotron oscillations USPAS, Fort Collins, CO, June 13-24, 2016

Damping of synchrotron oscillations USPAS, Fort Collins, CO, June 13-24, 2016

Damping of synchrotron oscillations USPAS, Fort Collins, CO, June 13-24, 2016

Damping of synchrotron oscillations USPAS, Fort Collins, CO, June 13-24, 2016

Damping of synchrotron oscillations USPAS, Fort Collins, CO, June 13-24, 2016

Damping of synchrotron oscillations USPAS, Fort Collins, CO, June 13-24, 2016

Damping of synchrotron oscillations USPAS, Fort Collins, CO, June 13-24, 2016

Summary: synchrotron radiation damping USPAS, Fort Collins, CO, June 13-24, 2016

Quantum excitation USPAS, Fort Collins, CO, June 13-24, 2016

Quantum excitation of horizontal emittance USPAS, Fort Collins, CO, June 13-24, 2016

Quantum excitation of horizontal emittance USPAS, Fort Collins, CO, June 13-24, 2016

Appendix B: Quantum excitation of horizontal emittance USPAS, Fort Collins, CO, June 13-24, 2016

Appendix B: Quantum excitation of horizontal emittance USPAS, Fort Collins, CO, June 13-24, 2016

Appendix B: Quantum excitation of horizontal emittance USPAS, Fort Collins, CO, June 13-24, 2016

Appendix B: Quantum excitation of horizontal emittance USPAS, Fort Collins, CO, June 13-24, 2016

Quantum excitation of horizontal emittance USPAS, Fort Collins, CO, June 13-24, 2016

Quantum excitation of vertical emittance USPAS, Fort Collins, CO, June 13-24, 2016

Quantum excitation of synchrotron oscillations USPAS, Fort Collins, CO, June 13-24, 2016

Quantum excitation of synchrotron oscillations USPAS, Fort Collins, CO, June 13-24, 2016

Natural energy spread USPAS, Fort Collins, CO, June 13-24, 2016

Summary: Radiation Damping USPAS, Fort Collins, CO, June 13-24, 2016

Summary: Synchrotron radiation integrals USPAS, Fort Collins, CO, June 13-24, 2016

Summary: Sand’s Integrals USPAS, Fort Collins, CO, June 13-24, 2016

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 13-24, 2016