Nonlinear evolutionary processes in a free-electron laser generator of diffracted radiation

Nonlinear evolutionary processes with two control parameters, one of which is related to the electrodynamic structure (positive feedback) and the other is related to the constant electric field applied to the electron flux, are studied in a free-electron laser, which is a diffracted-radiation oscillator. To this end, first, the linear spectral problem for an open-cavity resonator is investigated and the dispersion relation near the Morse critical point is established. Then the nonlinear evolutionary equation with two control parameters is constructed. Analysis of the latter makes it possible to determine the properties of the parametric dependence of the bifurcation and structural stability, which are determined by small variations of the control parameter (tuning of the cavity). This explains the operating efficiency of a diffracted-radiation oscillator in the millimeter and submillimeter wavelength ranges.