THEORETICAL ANALYSIS OF A LASER UNDULATOR-BASED HIGH GAIN FEL

The use of laser (or RF) undulators is nowadays con-sidered attractive for FEL applications, particularly those that aim to utilize relatively low-energy electron beams. In the context of the standard theoretical analysis, the counter-propagating laser pulse is usually treated in the plane-wave approximation, neglecting amplitude and phase variation. In this paper, we develop a three-dimensional, analytical theory of a high-gain FEL based on a laser or RF undulator, taking into account the longitudinal variation of the undula-tor field amplitude, the laser Gouy phase and the effects of emittance and energy spread in the electron beam. Working in the framework of the Vlasov-Maxwell formalism, we de-rive a self-consistent equation for the radiation amplitude in the linear regime, which is then solved to good approxima-tion by means of an orthogonal expansion technique. Nu-merical results obtained from our analysis are used in the study of an example of a compact, laser undulator-based, X-ray FEL