Chapter 4 Thu: Motion through Periodic Systems

4.1 General Comments


  • Periodic, repetitive systems and time scales
  • Matrix analysis of linear motion
  • The stability criterion

4.2 Transverse Stability


  • Application to the Weak-Focusing Betatron/Synchrotron
  • Periodic Courant-Snyder parameters
  • FODO cell parameters
  • Application to the Strong-Focusing Synchrotron
  • The betatron tune
  • Periodic dispersion

4.3 Longitudinal Stability



  • The linac and the synchrotron
  • The harmonic number h = L/(beta*lambda)
  • Difference equations and matrix solution for stable motion
  • Longitudinal (synchrotron) oscillations; synchrotron tune
  • Longitudinal emittance and adiabatic damping of phase oscillations
  • Transition energy and transition crossing
  • The inherent nonlinearity of longitudinal motion
  • Buckets, bunches, batches and trains