June 19, Wednesday: Transverse motion
Transverse Motion
Transverse Motion
Guiding Particles Toward the Ideal Trajectory (J. Kunz)
Guiding Particles Toward the Ideal Trajectory (J. Kunz)
[slides]
- The ideal trajectory and motion relative to it
- Comments on time scales, adiabatic changes and separation of motion
- Tracing particle trajectories through a focusing system
- Drift space
- Thin lens quadrupole
- Hill's equation
- Intro to simple "optical" matrix representation
Whiteboard time
Whiteboard time
Phase Space Distributions and Ellipses (T. Mohayai)
Phase Space Distributions and Ellipses (T. Mohayai)
- Particle distributions and transverse phase space
- Phase space area – emittance
- phase space distributions and second moments
- general equation/properties of phase space ellipse
- invariance of the emittance in linear system
- Courant-Snyder parameters and emittance
- Matrix formalism of ellipses and of particle motion
- Propagation of ellipse parameters through elements
- The development of a “beam envelope”
Courant-Snyder Parameterization
Courant-Snyder Parameterization
- Hill’s equation and analytical treatment of transverse motion
- Envelope function and phase advance
- Single-particle vs. “beam” emittance
- Correspondence between analytical, matrix forms
- Adiabatic damping and normalized emittance
See also:
See also:
Lecture notes by Linda Spentzouris:
- Transverse dynamics: magnetic fields, equations for transverse motion, machine tune and the Twiss parameters, transfer maps
- Emittance: particle distributions, phase space, high energy beams, transverse emittance from Hill's equation, normalized emittance