Quasioptical Theory of Relativistic Čerenkov Generators and Amplifiers

Abstract

We study propagation of electromagnetic waves above periodically corrugated surfaces and excitation of such waves by rectilinear relativistic electron flows within the framework of the quasioptical approach. Near a periodic structure, the electromagnetic field can be expanded into a sum of spatial harmonics, which in the case of a low corrugation depth are paraxial wave beams whose relationship is described within the framework of the method of equivalent surface magnetic currents. Under these assumptions, we obtain a dispersion relation for normal waves, and two extreme cases are singled out on its basis. In the first case, the radiation frequency is far from the Bragg resonance frequency, and wave propagation can be described within the framework of the impedance approximation, where the field is represented in the form of a fundamental slow wave and its spatial harmonics. In the case of interaction with the electron flow, this case corresponds to a convective instability, where the particles are synchronous with the fundamental (zeroth) or higher spatial harmonics (the traveling-wave tube regime), and an absolute instability, where the particles are synchronous with the spatial harmonic of the backward waves (the backward-wave oscillator regime). In the second extreme case, which is realized at frequencies close to the Bragg resonance, the field is represented as two counter-propagating quasioptical wave beams. This determines the absolute character of the instability, which is used in generators of the surface wave at the π-type modes. Basing on the developed theory, we determined the main characteristics of the amplifier and generator schemes including growth rates, energy exchange efficiency, and the formation of a spatial self-consistent structure of the radiated field. Good prospects for application of relativistic amplifiers and generators of surface waves in the submillimeter-wave band is demonstrated.