Review of Surface Roughness Effect on Beam Quality

In recent years a strong attention arose around the problem of the e.m. interaction of an ultra-relativistic beam with the residual roughness inside a beam tube, in particular in the framework of future 4th generation coherent light sources. The main concern was the effect of the wake-fields on the relative energy spread of the beam which has to be of the order of 10^-4, as for example in the LCLS and TESLA case. Although the real roughness has a stochastic feature, most studies dealt with periodic structure, or dielectric-equivalent layer which are considered to be conservative with respect the stochastic case. In this paper we will review the main theoretical models, and the most significant measurements trying to provide to the reader a complete picture of the present status of understanding.