Low energy aspects of circular accelerators

Performance in circular accelerators can be limited by some of the same sorts of phenomena described by Miller and Wangler in their lectures on low energy behavior in linear accelerators. In general the strength of the perturbation required to degrade performance is reduced in circular accelerators due to the repetitive nature of the orbits. For example, we shall see that space-charge can severely limit performance in circular accelerators even when operating far from the ''space-charge dominated regime'' as defined in linear accelerators. We will be discussing two particular aspects of low energy operation in circular accelerators -- space-charge and transition. ''Low energy'' is defined within the context of these phenomena. We shall see that the phenomena are really only relevant in hadron accelerators