A method of numerical analysis of linear and nonlinear nonstationary processes in relativistic Cerenkov generators based on periodic superdimensional waveguides is proposed. The main idea lies in considering a nonregular waveguide as a sequence of wave transformers and using a cross-section method. Configurations of eigenwave fields of periodic waveguides with a high-current relativistic electron beam are considered. The processes of generation development in a section of a relativistic multiwave generator are studied. We show that the system frequency is proved to be determined by the longitudinal resonances of surface waves and internal feedback.

Starting conditions for generation and features of oscillation establishment in a relativistic diffraction generator for different beam current values are numerically studied using the matrix multimode method. The efficiency boost and generation frequency stabilization are found to arise at overlap of two electron mechanisms—excitation of the fundamental oscillation of the system in the region of the 2 π -type frequencies with a resonance near the cutoff frequency of the bulk mode nearest to the 2 π type in a smooth waveguide.

The relativistic diffraction generators (RDG) are classified among the most promising sources for generation of long-pulsed high power coherent microwave radiation in the centimeter and millimeter wavelengths range. The operation of this type of microwave generators is based on Smith-Purcell radiation phenomenon. The numerical studies of the multiwave mechanisms of interaction between tubular electron beam and fields of super-dimensional axisymmetric periodical slow-wave structures (SWS) of corrugated waveguide in relativistic diffraction generator in the frequency range of 2π-type oscillations are presented in this report.