Nonlinear traveling waves in a helical wiggler free-electron laser.

Abstract

Nonlinear electromagnetic wave propagation is investigated in a system consisting of a relativistic, cold-electron beam propagating through a helical wiggler magnetic field. By transforming to wiggler coordinates and introducing the traveling-wave ansatz, a set of three, coupled, nonlinear ordinary differential equations is derived which describes nonlinear wave propagation in the system. In the Compton-regime 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 (\ensuremath{\beta}=u/c) that are less than the dimensionless beam speed (${\ensuremath{\beta}}_{b}$=${V}_{0}$/c).