Study of the longitudinal microwave instability including the synchrotron radiation effect

This paper presents a Fokker-Planck equation to describe the distribution of the particles in bunch, which includes synchrotron radiation damping effect. The subject of longitudinal microwave instability of a single bunched beam in a circular accelerator is studied with perturbation approach based on the Fokker-Planck equation, the potential well distortion effect and the synchrotron radiation damping effect being also included. The result shows that the threshold in the case of radiation damping included is a little higher than that in the case of no damping included.