Lectures in accelerator theory

Three phenomena of accelerator theory, which studies the behaviour of particle beams--the theory of single particle motion in nonlinear field, the theory of high intensity coherent motion, and the theory of coherent accumulation--are described. First, the behaviour of particles in a nonlinear field arising from the electromagnetic interaction of colliding beams, where counterrotating proton beams cross each other at a non-zero angle is studied. Beam-beam geometry, beam-beam interaction for ISABELLE, and the resonance theory of beam-beam interaction in ISABELLE are included. Second, the development of travelling waves on particle beams is studied in a situation where a uniform beam current in a circular accelerator and the excitation for the coherent motion is induced by the resistivity of the vacuum chamber wall. Electromagnetic fields are reviewed, the dispersion relation is specified, and an example of coherent stability for a point beam is given. Finally, the current accumulation process used at the proton storage rings at CERN (the ISR) is given, with focus on the incompressible fluid model