Nonlinear kinetic theory of the free electron laser

Abstract

A kinetic analysis of the nonlinear evolution of the free-electron-laser (FEL) instability is presented. The governing equations are the coupled Vlasov-Maxwell equations, which are investigated for a system consisting of a relativistic electron beam propagating through a helical wiggler magnetic field. Assuming that a single cavity mode of the electromagnetic field takes part in the lasing, a general nonlinear solution of the Vlasov equation is obtained in the resolvent formalism. Use of this solution in the wave equation provides a nonlinear description of the FEL. The saturation properties of the FEL are discussed by numerical and analytical solutions of this equation.