Radiation Damping - Low emittance lattices

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Presentation transcript:

Radiation Damping - Low emittance lattices Alex Bogacz USPAS, Hampton, VA, Jan. 17-28, 2011

Outline Beam dynamics with synchrotron radiation. The effects of synchrotron radiation on the (linear) motion of particles in storage rings. The synchrotron radiation integrals. Damping times of the vertical, horizontal and longitudinal emittances. Quantum excitation and the equilibrium horizontal and longitudinal beam emittances in an electron storage ring. Equilibrium emittance and storage ring lattice design. The natural emittance in different types of lattice (FODO, DBA, TME…).• Emittance reduction in an achromat by "detuning" from the zero-dispersion conditions. USPAS, Hampton, VA, Jan. 17-28, 2011

Outline – content 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. Discuss the effects of quantum excitation, and derive expressions for the equilibrium horizontal and longitudinal beam emittances in an electron storage ring. Emittance preserving lattices - Examples: FODO, DBA, TME… A. Wolski, Academic Lectures, University of Liverpool , 2009 USPAS, Hampton, VA, Jan. 17-28, 2011

Coordinate system USPAS, Hampton, VA, Jan. 17-28, 2011

Longitudinal coordinate USPAS, Hampton, VA, Jan. 17-28, 2011

Energy deviation USPAS, Hampton, VA, Jan. 17-28, 2011

Canonical variables USPAS, Hampton, VA, Jan. 17-28, 2011

Symplectic matrices USPAS, Hampton, VA, Jan. 17-28, 2011

Twiss parameters and the particle action USPAS, Hampton, VA, Jan. 17-28, 2011

Cartesian variables and action-angle variables USPAS, Hampton, VA, Jan. 17-28, 2011

Action and Emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Action and Radiation USPAS, Hampton, VA, Jan. 17-28, 2011

Radiation damping of vertical emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Radiation damping of vertical emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Radiation damping of vertical emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Radiation damping of vertical emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Radiation damping of vertical emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Synchrotron radiation energy loss USPAS, Hampton, VA, Jan. 17-28, 2011

Synchrotron radiation energy loss USPAS, Hampton, VA, Jan. 17-28, 2011

The first synchrotron radiation integral USPAS, Hampton, VA, Jan. 17-28, 2011

Damping of horizontal emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Horizontal-longitudinal coupling USPAS, Hampton, VA, Jan. 17-28, 2011

Damping of horizontal emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Radiation damping of horizontal emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Damping of synchrotron oscillations USPAS, Hampton, VA, Jan. 17-28, 2011

Damping of synchrotron oscillations USPAS, Hampton, VA, Jan. 17-28, 2011

Damping of synchrotron oscillations USPAS, Hampton, VA, Jan. 17-28, 2011

Damping of synchrotron oscillations USPAS, Hampton, VA, Jan. 17-28, 2011

Damping of synchrotron oscillations USPAS, Hampton, VA, Jan. 17-28, 2011

Damping of synchrotron oscillations USPAS, Hampton, VA, Jan. 17-28, 2011

Damping of synchrotron oscillations USPAS, Hampton, VA, Jan. 17-28, 2011

Damping of synchrotron oscillations USPAS, Hampton, VA, Jan. 17-28, 2011

Damping of synchrotron oscillations USPAS, Hampton, VA, Jan. 17-28, 2011

Summary: synchrotron radiation damping USPAS, Hampton, VA, Jan. 17-28, 2011

Quantum excitation USPAS, Hampton, VA, Jan. 17-28, 2011

Quantum excitation of horizontal emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Quantum excitation of horizontal emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Quantum excitation of horizontal emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Quantum excitation of vertical emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Quantum excitation of synchrotron oscillations USPAS, Hampton, VA, Jan. 17-28, 2011

Quantum excitation of synchrotron oscillations USPAS, Hampton, VA, Jan. 17-28, 2011

Natural energy spread USPAS, Hampton, VA, Jan. 17-28, 2011

Summary: radiation damping USPAS, Hampton, VA, Jan. 17-28, 2011

Summary: synchrotron radiation integrals USPAS, Hampton, VA, Jan. 17-28, 2011

Summary: synchrotron radiation integrals USPAS, Hampton, VA, Jan. 17-28, 2011

Radiation Damping - Re-cap So far we: 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, Hampton, VA, Jan. 17-28, 2011

S-R integrals - Re-cap USPAS, Hampton, VA, Jan. 17-28, 2011

S-R integrals - Re-cap USPAS, Hampton, VA, Jan. 17-28, 2011

Lattice Examples Practical implementations: FODO DBA (double-bend achromat) multi-bend achromat, including the triple-bend achromat (TBA) TME (theoretical minimum emittance) USPAS, Hampton, VA, Jan. 17-28, 2011

Calculating the natural emittance in a lattice USPAS, Hampton, VA, Jan. 17-28, 2011

FODO lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

FODO lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

FODO lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

FODO lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

FODO lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

FODO lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

FODO lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

FODO lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

FODO lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

FODO lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

DBA lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

DBA lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

DBA lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

DBA lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

DBA lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

DBA lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

TME lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

TME lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

TME lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

TME lattice - natural emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Summary: FODO, DBA and TME lattices USPAS, Hampton, VA, Jan. 17-28, 2011

Design for low emittance lattices USPAS, Hampton, VA, Jan. 17-28, 2011

Summary USPAS, Hampton, VA, Jan. 17-28, 2011

Summary cont. USPAS, Hampton, VA, Jan. 17-28, 2011

Appendix A: Damping of horizontal emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Appendix A: Damping of horizontal emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Appendix A: Damping of horizontal emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Appendix A: Damping of horizontal emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Appendix A: Damping of horizontal emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Appendix A: Damping of horizontal emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Appendix B: Quantum excitation of horizontal emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Appendix B: Quantum excitation of horizontal emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Appendix B: Quantum excitation of horizontal emittance USPAS, Hampton, VA, Jan. 17-28, 2011

Appendix B: Quantum excitation of horizontal emittance USPAS, Hampton, VA, Jan. 17-28, 2011