Longitudinal wakefield for synchrotron radiation

It is of interest to determine how short a bunch can be maintained in a storage ring. Some aspects of this problem depend on specific details of the storage ring design. Instability thresholds depend on the strength of the wakefields. In this paper we determine the longitudinal wakefield due to curvature of the electron orbit, both in free space and between parallel plates with infinite conductivity. Our study leads to the conclusion that as long as the vertical aperture of the vacuum chamber is not too small, the wakefield due to image charges does not significantly vary along a short bunch. Therefore, we suggest that in the determination of the equilibrium bunch length of very short bunches, the effect of the conducting plates can be neglected. The starting point for bunch lengthening calculations should be the free space wakefield