Simulation of Time-Dependent Energy Modulation by Wake Fields and its Impact on Gain in the VUV free Electron Laser of the TESLA Test Facility

For shorter bunches and narrower undulator gaps the interaction between the electrons in the bunch and the wake fields becomes so large that the FEL amplification is affected. For a typical vacuum chamber of an X-ray or VUV Free Electron Laser three major sources of wake fields exist: a resistance of the beam pipe, a change in the geometric aperture and the surface roughness of the beam pipe. The generated wake fields, which move along with the electrons, change the electron energy and momentum, depending on the electron longitudinal and transverse position. In particular, the accumulated energy modulation shifts the electrons away from the resonance condition. Based on an analytic model the energy loss by the wake fields has been incorporated into the time-dependent FEL simulation code GENESIS 1.3. For the parameters of the TESLA Test Facility the influence of the bunch length, beam pipe diameter and surface roughness has been studied. The results are presented in this paper.