Transverse and Longitudinal Beam Dynamics


The aim is to carefully introduce the basic ideas and concepts and transverse and longitudinal beam dynamics, for students working in all areas of accelerator physics.


Electromagnetism, mechanics, relativity at undergraduate level.


  1. Introduction
    Let’s look at a synchrotron
    Periodicity and stability
    Hierarchy of beam descriptions
    SHM and the pendulum
    Newton and Hamilton
  2. Hill’s equations
    Beams and magnets
    Derivation of Hill’s equations
    The transfer matrix approach
    Matrix properness
  3. Lattice functions
    Lattice functions
    The Courant-Synder formalism
    How to transform the lattice functions
  4. Optics and lattice design
    The FODO cell
    Lattice design
    Mini beta insertions
    Principles of lattice design
    Optical structures
  5. Errors in our lattice
    Field errors
    Closed orbit distortion
    Tune shifts
  6. Real particles
    Momentum compaction Chromaticity
  7. Longitudinal dynamics
    The principle of phase stability
    The pill-box cavity and real cavities
    Longitudinal dynamics
    Buckets and bunches
  8. Radiation effects
    Synchrotron radiation
    Damping effects (directed reading)

Lecture Notes

Part 1, Part 2