A theory of bunch lengthening in electron storage rings with localized wake force sources

The longitudinal motion of electrons in a storage ring cannot be described correctly with the usual Fokker-Planck equation when a wake force is fully local, unless some complicated regularization is performed. Instead, a mapping formulation is proposed which is based on a complete description of the behavior of the distribution function. With some approximation, the method leads to a set of mapping equations for a few parameters. As an example, a simple soluble model is constructed which turns out to show good qualitative agreement with multiparticle tracking, but qualitative disagreement with conventional theory