General method for analyzing three-dimensional effects in free-electron laser amplifiers

Abstract

Free-electron laser (FEL) configurations in which the parameters of the electron beam vary along the undulator become relevant when considering new aspects of existing FELs or when exploring novel concepts. This paper describes a fully three-dimensional, analytical method suitable for studying such systems. As an example, we consider a seeded FEL driven by a beam with varying transverse sizes. In the context of the Vlasov-Maxwell formalism, a self-consistent equation governing the evolution of the radiation field amplitude is derived. An approximate solution to this equation is then obtained by employing an orthogonal expansion technique. This approach yields accurate estimates for both the amplified power and the radiation beam size. Specific numerical results are presented for two different sets of x-ray FEL parameters.