Joint Universities Accelerator School
Transverse beam dynamics

1- The Ideal Storage Ring: Lorentz force and particle momentum - define the magnetic guide field, focusing elements and the equation of motion, single particle trajectories, matrix description of lattice elements.


2- Particle Trajectographies in a Circular Accelerator: Beam orbit, transverse particle oscillation and tune, defining the beam size, general solution of the equation of motion: the amplitude betatron function, phase space area of a particle ensemble: the beam emittance, stability criterion in periodic structures.


3- Lattice Design in Particle Accelerators: calculation of the optical parameters, FoDo cells: design and optimisation, interaction regions: the low beta insertion.


4- Changing the Particle Momentum: beam acceleration and adiabatic shrinking of the emittance, dispersion trajectories, orbit lengthening and the momentum compaction factor.


5- Errors in Field and Gradient: Quadrupole errors and tune shift, chromaticity and its correction, sextupole magnets and the dynamic aperture.