The Green's function for a linear energy chirped seeded free electron laser

Abstract

In a free electron laser (FEL), the electron beam at the undulator entrance can have a correlated energy spread. In this paper, we derive an expression of the seeded FEL Green's function for the case of an electron beam having a linear energy chirp, within the one-dimensional Vlasov–Maxwell model. This Green's function allows to evaluate the FEL electromagnetic radiation in both the lethargy and the exponential growth regime, without the asymptotic approximation introduced in previous works. We show a comparison between the proposed expression for the Green's function and the one obtained with a saddle point approximation, for both cases of short and long undulators.