Coherent Radiation Effects in the Lcls Undulator∗

For X-ray Free-Electron Lasers such as LCLS and TESLA FEL, a change in the electron energy while amplifying the FEL radiation can shift the resonance condition out of the bandwidth of the FEL. The largest sources of energy loss is the emission of incoherent undulator radiation. Because the loss per electron depends only on the undulator parameters and the beam energy, which are fixed for a given resonant wavelength, the average energy loss can be compensated for by a fixed taper of the undulator. Coherent radiation has a strong enhancement proportional to the number of electrons in the bunch for frequencies comparable to or longer than the bunch dimension. If the emitted coherent energy becomes comparable to that of the incoherent emission, it has to be included in the taper as well. However, the coherent loss depends on the bunch charge and the applied compression scheme and a change of these parameters would require a change of the taper. This imposes a limitation on the practical operation of Free-Electron Lasers, where the taper can only be adjusted manually. In this presentation we analyze the coherent emission of undulator radiation and transition undulator radiation for LCLS, and estimate whether the resulting energy losses are significant for the operation of LCLS.