FEL Gain Enhancement in an Optical Klystron

Abstract

A system comprising two identical helical or planar undulators separated by a gap -- viz., an optical klystron (OK) -- is investigated. A formula for the frequency distribution of spontaneous radiation at zero angle is derived. It is shown that the spontaneous radiation line shape gradually narrows with increasing distance (up to an optimal value) between the undulators due to the constructive interference of the radiation fields formed in each of them, while the number of radiated photons decreases. The free-electron laser (FEL) gain coefficient also gradually increases, since it is proportional to the derivative of the spontaneous radiation line shape. Using the undulator parameters of the SASE XFEL and the bunch parameters of the LCLS, the total gain coefficient in the X-ray range is on the order of 2.5 and, for a different electron energy, reaches approximately 90 in the water window frequency range.