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