Nonlinear theory of coaxial free-electron masers with 2D distributed feedback (quasi-optical approximation)

The nonlinear dynamics of coaxial free-electron masers with 2D distributed feedback, which is realizable in 2D Bragg structures, is analyzed in terms of a quasi-optical approximation. It is shown that feedback with the spatial synchronization of radiations from tubular electron beams with a perimeter exceeding 1000 wavelengths can be provided under such conditions. The objects of investigation are the one-section design of a free-electron maser with 2D distributed feedback and a design with a combined two-mirror resonator. In the latter, an entrance 2D Bragg mirror provides the spatial synchronization of radiation and weak reflections from a conventional exit Bragg mirror are sufficient for the self-excitation of the oscillator. The advantage of the two-mirror design is a decrease in ohmic losses. The adequacy of the geometric optics approximation used earlier to describe the dynamics of such self-excited oscillators is demonstrated under various boundary conditions for transverse (azimuthal) energy fluxes at the edges of a Bragg structure.