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The nonlinear evolution of a helical wiggler, free‐electron laser is investigated within the framework of a macroclump model for the trapped electrons. The model describes the nonlinear evolution of a right‐circularly polarized electromagnetic wave with frequency ωs and wave number ks, and slowly varying amplitude as(z,t) and phase δs(z,t) (eikonal approximation). The model further assumes that the trapped electrons can be treated as tightly bunched macroclumps that interact coherently with the radiation field. The analysis is carried out in the ponderomotive frame, which leads to a substantial simplification in both the analytical and numerical studies. As a first application, the nonlinear evolution of the primary signal is examined when ∂/∂l’=0 (no spatial variation of the wave amplitude and phase). The evolution equations are reduced to quadrature, and the maximum excursion of the wave amplitude as,max is calculated analytically. Subsequently, the nonlinear evolution of the sideband instability is i...

Macroclump model of the nonlinear evolution of the sideband instability in a helical wiggler free-electron laser