Comparative study of Gaussian- and uniform-profile models of the equilibrium electron beam in a free-electron laser

Based on the conservation of particle number, analytical expressions of the Gaussian-profile density and self-fields of the equilibrium electron beam in a free-electron laser are deduced in terms of the macroscopic design parameters. Compared to the Gaussian-profile model, both the particle distribution and self-fields effect of the equilibrium electrons are overestimated by the uniform-profile model. It is demonstrated by experimental observation that the Gaussian-profile model is more coincident with the actual fact of the equilibrium electron beam than the uniform-profile model.