Instabilities and beam intensity limitations in circular accelerators

The main aim of these lectures will be to give an insight into the physics of the mechanisms of instabilities and beam intensity limitations in circular accelerators. Three different techniques will be used to evaluate the various instabilities. The first will be using few-particle models, the second will use matrix techniques involving eigenvalues, and the third technique will use Sacherers modal analysis technique. For each instability the threshold or the growth rate will be evaluated with particular attention to the parameter dependence.