Quasi-optical theory of relativistic Cherenkov surface-wave oscillators with oversized cylindrical waveguides

Within the quasi-optical approach, we investigate the propagation of azimuthally symmetric TM waves in periodically corrugated cylindrical waveguides and their excitation by relativistic electron beams. Presenting the field as two, forward and backward, quasi-optical wavebeams coupled at the shallow corrugation, we obtain a dispersion equation for normal waves and thus a criterion of existence of the surface wave. For a finite-length corrugation section, the spectrum of axial evanescent eigenmodes is estimated; the spatial structure and the quality factor of the fundamental mode are found at an eigenfrequency close to the Bragg frequency. A self-consistent system of equations describing the interaction of electromagnetic waves with a rectilinear electron beam injected into the system is derived. Based on this model, we recognize two oscillation regimes, namely, the π-mode excitation regime and the regime of backward surface wave oscillator. We demonstrate the viability of practical implementation of relativistic surface wave oscillators with a power level of up to 140 MW in the sub-millimeter wavelength band.