Quasi-Optical Theory of Relativistic Cherenkov Oscillators and Amplifiers with Oversized Electrodynamic Structures

Using the quasi-optical approach, we investigate wave propagation along the periodically corrugated surfaces and their interaction with rectilinear relativistic electron beams (REBs). At the periodical structure, the field can be expanded into a series of spatial harmonics, which, in the case of shallow corrugations, represent paraxial wavebeams with mutual coupling described within the method of effective surface magnetic currents. We present the dispersion equation for the normal waves. Two limit cases can be recognized: in the first one, the frequency is far from the Bragg resonance and the wave propagation can be described within the impedance approximation with the field presented as a sum of the fundamental slow wave and its spatial harmonics. In the interaction with a rectilinear REB, this corresponds to the convective instability of particles' synchronism with the fundamental (0th) or higher spatial harmonics (TWT regime), or the absolute instability in the case of synchronism with the -1st harmonic of the backward wave (BWO regime). In the latter case, at the frequencies close to the Bragg resonance, the field is presented as two antiparallel quasioptical wavebeams, leading to the absolute instability used in the surface-wave oscillators operating in the pi-mode regime. Based on the developed theory, we determine the main characteristics of relativistic Cherenkov amplifiers and oscillators with oversized electrodynamical systems. We demonstrate the prospects for the practical implementation of relativistic surface-wave devices in submillimeter wavebands.