Rf stability, control and bunch lengthening in electron synchrotron storage rings

A self-consistent theory for nonlinear longitudinal particle motion and rf cavity excitation in a high energy electron storage ring is developed. Coupled first order equations for the motion of an arbitrary number of particles and for the field in several rf cavities are given in the form used in control system theory. Stochastic quantum excitation of synchrotron motion is included, as are the effects of rf control system corrections. Results of computations for double cavity bunch lengthening are given. 11 refs., 4 figs., 1 tab