June 8, Wednesday: Transverse Motion (continued)

Transverse Motion (D. Stratakis)

Single-particle dynamics

[slides]

• The ideal trajectory and motion relative to it

• Tracing particle trajectories through a focusing system

  • Drift space

  • Thin lens quadrupole

• Hill's equation

• Intro to simple "optical" matrix representation

Courant-Snyder parametrization

[slides]

• Courant-Snyder parameters and emittance

• Hill’s equation and analytical treatment of transverse motion

• Envelope function and phase advance

• Mismatches

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