Quantum theory of a free electron laser for strong fields

A quantum mechanical derivation of the gain of the free electron laser is presented which starts from the exact solutions of the Klein-Gordon equation in the presence of the magnetic wiggler field and the stimulating plane wave field. The gain is obtained from the transition amplitude of the electron, which is expressed in terms of the Green's function. For comparatively weak fields the usual small signal gain results, whereas for strong fields saturation behaviour is found.Supported by Deutsche Forschungsgemeinschaft