Abstract
In the free electron laser (FEL) the resonant interaction between the radiation field and electron beam can result in radiation focusing. If the centroid of the electron beam is transversely displaced off-axis, the radiation field, under certain conditions, will follow and be guided by the electron beam. The effect of a spatial modulation on the electron beam envelope can also modify the propagation characteristics of the radiation. These and other phenomena are analytically and numerically evaluated using a novel modal representation of the fully three dimensional radiation field. In this representation the transverse modal dependence consists of the usual Laguerre-Gaussian functions whereas the longitudinal dependence is determined and characterized by the source term in the wave equation. Among the advantages of this general source dependent expansion approach is that far fewer 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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