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We study theoretically an electron frequency self-multiplier in which a surface mode of a periodic system is self-excited at a low frequency for a comparatively low current. The electron bunches, which appear as a result of this, excite the volume mode of an open resonator at the doubled frequency (coherent Smith-Purcell radiation). The open-resonator scheme allows one to obtain the higher power and coherence degree of radiation compared with the presently popular frequency multiplication scheme with an open periodic system (diffraction grating). The weakly relativistic and relativistic variants of the multipliers with a two-mirror open resonator designed for obtaining a high-power coherent radiation in the short-wavelength part of the millimeter and submillimeter ranges are studied numerically. The developed approach can also be used for designing high-power frequency multipliers on the basis of an array of nonlinear solid-state elements.

An orotronlike feedback can provide a significant increase in the selectivity and power of frequency-multiplied Smith–Purcell radiation of the electron bunches formed in the course of self-excitation of a grating surface eigenmode. This method looks promising for efficient terahertz generation from both weakly and mildly relativistic electron beams.

A non-stationary two-dimensional theory of interaction of a surface wave and a wide sheet electron beam is developed. This theory is used for studying the problem of mode competition and non-coherent transverse distribution of the microwave field in the surface-wave generation process. According to numerical simulations based on a quasi-optical equation, transverse diffraction of surface wave provides stable stationary generation in a wide range of beam widths and currents. The developed theory can be applied both to surface-wave oscillator and to a Smith-Purcell free-electron laser, where surface pi-type eigenmode excitation provides the beam bunching and enhances the power of the Smith-Purcell radiation at the frequency harmonics of the surface wave.

We combine impedance approximation with a quasi-optical approach to describe the amplification of short-wavelength radiation by rectilinear relativistic electron beams (REBs) moving near the impedance surfaces. We consider a number of physical systems in which wave propagation and amplification by REBs under certain conditions can be described within the developed unified approach. These include metal surfaces with shallow periodical corrugations, the surface of the isotropic plasma, and metals with finite conductivity. In the latter case, resistive instability arises. For the specified class of systems, universal (differing only in the definition of impedance) linear and nonlinear equations are obtained, which allow for finding the instability increments, the spatial profiles of excited fields, and the efficiency of energy extraction.