Quasi-optical theory of coaxial and cylindrical relativistic surface-wave oscillators

In terms of a quasi-optical approach, a nonlinear nonstationary theory of surface-wave oscillators, coaxial and cylindrical multiwave Cherenkov oscillators (MCOs) fed by large-diameter tubular electron beams, is constructed. The small curvature of the waveguide walls allows one to appreciably simplify the MCO dynamics analysis by considering a quasi-plane model. In this model, local surface fields near the corrugated cylindrical wall are close to fields of a plane corrugated with the same depth and period and the cylindrical geometry is taken into account by introducing azimuthal periodicity conditions. The results obtained in terms of the averaged approach are compared with those of direct numerical particle-in-cell (PIC) simulation and experimental data. Remarkably, PIC simulation demonstrates the existence of a single-frequency oscillation regime at long perimeters in which the self-synchronization of different azimuthal modes takes place. As a result, an azimuthally asymmetric stationary field distribution sets in, which can be assigned to dissipative structures well known in the theory of self-sustained oscillation systems.