Surface Roughness Study for the TESLA-FEL

This report summarizes the surface roughness wake eld study for the TESLA FEL transfer line and the undulator. At present di erent models have been developed by K.Bane [1], G.Stupakov [2], A.Novokhatski, M.Timm,T.Weiland [3] to study the e ect of a random surface roughness in a beam pipe, and by K.Bane, A.Novokhatski [4], G.Stupakov [5], M.Dohlus [6] to calculate the wake in beam pipes with periodic surface structure. The e ects of surface structures with small and large transverse dimensions are estimated separately by two periodic models. The rms amplitudes and wavelenghts of the corrugations are computed from a real measured surface function [7] after lowand high-pass ltering respectively. The longitudinal wake potentials of rectangular and sinusoidal periodical surfaces and the longitudinal resistive wall wake are calculated numerically and analytically respectively.