Unified quasi-optical theory of short-wavelength radiation amplification by relativistic electron beams moving near the impedance surfaces

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.