Radiation guiding in a free electron laser

Abstract
Analytic solutions of radially localized eigenmodes of radiation in Compton regime free electron lasers are obtained to demonstrate the radiation guiding property of the electron beam. The radial width of the radiation field Rs is found to be related to the beam radius Rb by RsRbp1/6, where p=(c/Rb)30ωp0ω20, in a cold beam approximation. Here β0c, ωp0, and ω0 are the electron quivering velocity resulting from the pump, the equilibrium beam plasma frequency on the beam axis, and the pump wave frequency, respectively, in the electron beam rest frame. Finite temperature effects, curvature effects, and transverse motional effects of the beam are also studied.

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