June 16, Thursday: Stability and Beam Manipulations

Transfer Maps, Beam Stability, Periodic Motion (P. Snopok)

Transfer Maps, Glass Optics

[slides]

  • Transfer maps

  • Glass optics

  • Point-to-point, parallel-to-point, and point-to-parallel systems and their properties

Periodic Motion, Transverse Stability

[slides]

  • Periodic motion

  • Weak and strong focusing

  • Combined function magnets

  • Transverse stability criterion

  • Normal form coordinates (linear)

Longitudinal Stability (review)

[slides]

  • Longitudinal stability

  • Phase stability principle

  • Stable bucket (and its size)

  • Longitudinal emittance

See also:

Lecture notes by Linda Spentzouris:

  • Longitudinal dynamics: longitudinal beam structure, difference and differential equations, energy error to travel time error, phase space trajectories, synchrotron frequency

  • Transverse dynamics: magnetic fields, equations for transverse motion, machine tune and the Twiss parameters, transfer maps