Abstract
The theory of the stability of high intensity particle beams in circular accelerators and storage rings is developed. A simple one dimensional oscillator system is used to introduce the discussion of the stability problem and of the effect of a frequency distribution. These results are then extended to the case of a system of particles executing synchrotron and betatron oscillations in a circular accelerator. In the absence of a general solution of the stability problems, it is convenient to introduce a classification of the instabilities, using the characteristic times and lengths of the particle system. This allows us to identify a set of parameters of the particle beam for which one can establish the stability conditions.
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