Theory of short pulse FEL oscillators

A simple model for the nonlinear low gain evolution of a short pulse Compton free electron laser (FEL) oscillator is derived. An analysis of the small signal regime allows the calculation of the shape of the produced optical pulse. For small excess over threshold, a Landau-Ginzburg equation is obtained, which allows us to show that a strong superradiant efficiency enhancement occurs at small detuning. Furthermore, the knowledge of the eigenfrequencies in the small signal regime allows one to infer a scale law for the period of limit cycles occurring at larger excess over threshold. Theoretical results are compared to experimental results from FELIX.