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Radiation Damping - Low emittance...
Transcript of Radiation Damping - Low emittance...
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Thomas Jefferson National Accelerator Facility
http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf1
Radiation Damping - Low emittance
lattices
USPAS, Hampton, VA, Jan. 17-28, 2011
Alex Bogacz ,Geoff Krafft and Hisham Sayed
Operated by JSA for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf2
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, Hampton, VA, Jan. 17-28, 2011
Operated by JSA for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf3
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, Hampton, VA, Jan. 17-28, 2011
Operated by JSA for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf4USPAS, Hampton, VA, Jan. 17-28, 2011
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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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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Thomas Jefferson National Accelerator Facility
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Damping of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility
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Damping of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility
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Damping of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility
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Damping of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility
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Damping of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility
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Damping of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility
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Damping of synchrotron oscillations
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Thomas Jefferson National Accelerator Facility
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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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Thomas Jefferson National Accelerator Facility
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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: synchrotron radiation integrals
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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
Operated by JSA for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf57USPAS, Hampton, VA, Jan. 17-28, 2011
S-R integrals - Re-cap
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S-R integrals - Re-cap
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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
Operated by JSA for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf60USPAS, Hampton, VA, Jan. 17-28, 2011
Calculating the natural emittance in a lattice
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FODO lattice - natural emittance
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FODO lattice - natural emittance
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FODO lattice - natural emittance
1
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FODO lattice - natural emittance
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Thomas Jefferson National Accelerator Facility
http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf65USPAS, Hampton, VA, Jan. 17-28, 2011
FODO lattice - natural emittance
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Thomas Jefferson National Accelerator Facility
http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf66USPAS, Hampton, VA, Jan. 17-28, 2011
FODO lattice - natural emittance
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Thomas Jefferson National Accelerator Facility
http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf67USPAS, Hampton, VA, Jan. 17-28, 2011
FODO lattice - natural emittance
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Thomas Jefferson National Accelerator Facility
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FODO lattice - natural emittance
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Thomas Jefferson National Accelerator Facility
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FODO lattice - natural emittance
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Thomas Jefferson National Accelerator Facility
http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf70USPAS, Hampton, VA, Jan. 17-28, 2011
FODO lattice - natural emittance
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Thomas Jefferson National Accelerator Facility
http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf71USPAS, Hampton, VA, Jan. 17-28, 2011
DBA lattice - natural emittance
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DBA lattice - natural emittance
1
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http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf73USPAS, Hampton, VA, Jan. 17-28, 2011
DBA lattice - natural emittance
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Thomas Jefferson National Accelerator Facility
http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf74USPAS, Hampton, VA, Jan. 17-28, 2011
DBA lattice - natural emittance
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Thomas Jefferson National Accelerator Facility
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DBA lattice - natural emittance
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Thomas Jefferson National Accelerator Facility
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DBA lattice - natural emittance
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Thomas Jefferson National Accelerator Facility
http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf77USPAS, Hampton, VA, Jan. 17-28, 2011
TME lattice - natural emittance
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Thomas Jefferson National Accelerator Facility
http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf78USPAS, Hampton, VA, Jan. 17-28, 2011
TME lattice - natural emittance
Operated by JSA for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf79USPAS, Hampton, VA, Jan. 17-28, 2011
TME lattice - natural emittance
Operated by JSA for the U.S. Department of Energy
Thomas Jefferson National Accelerator Facility
http://cas.web.cern.ch/cas/Germany2009/Lectures/PDF-Web/Wolski-1.pdf80USPAS, Hampton, VA, Jan. 17-28, 2011
TME lattice - natural emittance
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Thomas Jefferson National Accelerator Facility
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Summary: FODO, DBA and TME lattices
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Design for low emittance lattices
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Summary
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Summary cont.