The Potential-Well Distortion Effect and Coherent Instabilities of Electron Bunches in Storage Rings

The effect of electromagnetic interaction between electron bunches and the vacuum chamber of a storage ring on the longitudinal motion of bunches is studied. Specifically, the potential-well distortion effect and the so-called coherent instabilities of coupled bunches are considered. An approximate analytical solution for the frequencies of incoherent oscillations of bunches distributed arbitrarily within the ring is obtained for a distorted potential well. A new approach to determining frequencies of coherent oscillations and an approximate analytical relation for estimating the stability of a system of bunches as a function of their distribution in the accelerator orbit are presented.