Transient analysis of a bunched beam free electron laser

The problem of the bunched beam operation of a free electron laser was studied. Assuming the electron beam to be initially monoenergetic, the Maxwell-Vlasov equations describing the system reduce to a third order partial differential equation for the envelope of the emitted light. The Green's function corresponding to an arbitrary shape of the electron bunch, which describes the transient behavior of the system, is obtained. The Green's function was used to discuss the start up problem as well as the power output and the power spectrum of a self-amplified spontaneous emission.