Chapter 3 Wed: Longitudinal Motion

3.1 Accelerating Structures


  • Time varying fields and accelerating gap
  • Transit Time Factor
  • The pillbox cavity – essential properties
  • Resonant Structures – quarter-wave, half-wave, etc.
  • Standing wave vs. traveling wave and multi-cell structures

3.2 Longitudinal Focusing


  • Ideal synchronous particle and ideal timing
  • Time of Flight and Slip Factor
  • Longitudinal focusing
  • Beam bunchers, rebunchers, debunchers

3.3 Transverse Effects of Longitudinal Motion


  • Adiabatic damping of betatron oscillations due to acceleration
  • Momentum dispersion
    • equation of motion of off-momentum particle
    • use of 3-D matrices
    • momentum compaction
  • RF (transverse) defocusing through an accelerating gap