Abstract
In the free electron laser (FEL) the resonant interaction between the radiation field and electron beam can result in optical guiding and steering of the radiation beam. These and other phenomena in a realistic modeling of the FEL can be numerically studied using the Source Dependent Expansion (SDE) method which is a novel source dependent Laguerre-Gaussian modal representation of the fully three-dimensional radiation field. Unlike the vacuum Laguerre-Gaussian modal expansion, the longitudinal spatial dependence of the radiation waist and curvature are determined and characterized by the source term in the wave equation. Among the advantages of this general SDE approach is that few modes are needed to accurately describe the radiation. Hence, fast and accurate numerical solutions of the fully three-dimensional FEL problem can be obtained over distances of many Rayleigh lengths.
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