Evanescent waves propagation along a periodically corrugated surface and their amplification by relativistic electron beam (quasi-optical theory)

Abstract

By using a quasi-optical approach, we study propagation of evanescent waves along a periodically corrugated surface and their excitation by relativistic electron beams. Under assumption of a shallow (in the scale of period) corrugation, the dispersion equation for normal waves is derived and two particular cases are studied. In the first case, the wave frequency is far from the Bragg resonance; therefore, the evanescent wave propagation can be described by using the impedance approximation with deceleration of the zeroth spatial harmonic. The second case takes place at the frequencies close to the Bragg resonance. There, the field can be represented as two counter-propagating quasi-optical wave beams, which are coupled on the corrugated surface and form an evanescent normal wave. With regard to the interaction with an electron beam, the first case corresponds to the convective instability that can be used for amplification of radiation, while the second case corresponds to the absolute instability used in surface-wave oscillators. This paper is focused on studying main features of amplifier schemes, such as the increments, electron efficiency, and formation of a self-consistent spatial structure of the radiated field. For practical applications, the feasibility of realization of relativistic surface-wave amplifiers in the submillimeter wavelength range is estimated.