Nonlinear traveling waves in a free electron laser

Abstract

We investigate nonlinear electromagnetic waves in a system which consists of an intense, cold-fluid relativistic electron beam propagating in a helical magnetic field. By transforming to wiggler coordinates and introducing the traveling wave ansatz, we have obtained a set of three coupled nonlinear ordinary differential equations plus an exact invariant to describe wave motions in the system. In the Compton-approximation limit, the number of differential equations reduces to two. These equations are particularly useful for studying nonlinear saturated states of the free electron laser instability, corresponding to values of the dimensionless phase speed ( β=u/c ) that are less than the dimensionless beam speed (β_b=V_o/c ) or less than unity. This restriction on β may permit the existence of solitons for discrete values of β.