Statistical mechanics of colliding beams (Q761103)

The observed performance of electron-positron colliding-beam storage rings is poorly understood theoretically. The problem of a storage ring's behavior is a particular instance of statistical mechanics in an external environment that varies periodically with time, in the limit of weak - and not necessarily isotropic - friction and (additive) noise. As a practical starting point for a general theory of such problems, the following ansatz is suggested: Phase space submanifolds (tori) with fixed canonical actions are manifolds of approximately equal probability density. Such an approach is especially well suited to analysis of the long-time effects of nonlinear resonance on storage ring behavior. Formal consequences of this ansatz and some associated conceptual difficulties are discussed. These issues are considered from the standpoint of ''two- time'' analysis. An example of a concrete application, closely related to Kramers' analysis of noise-induced barrier crossing, is provided. This paper is meant to be self-contained, so that it can be understood by readers outside the storage-ring community.