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

Abstract

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.

Quasi-Optical Theory of Relativistic Cherenkov Oscillators and Amplifiers with Oversized Electrodynamic Structures

“…The differences between planar and cylindrical models are specifically emphasized. It should be noted that most of the theoretical results presented here were verified by direct 3D PIC simulations [36][37][38][39][40][41], although we opt to leave the comparisons out of the current presentation.…”

“…As shown in [36][37][38][39][40][41][42], such a corrugated plate can be substituted by a regular surface y = 0 with an effective surface magnetic current…”

“…Further, we refer to this approximation as an impedance approximation [41], as Equation ( 16) yields an impedance-type relation between the electric and magnetic field amplitudes on the surface:…”

“…According to Section 2.1, under such conditions the impedance approximation is valid. Neglecting the Ohmic losses for simplicity, assuming that all the processes are monochromatic at the same carrier frequency ω, and using Equations ( 16) and ( 63), we describe the wave amplification in the fundamental-harmonic TWT by equations [38,41]…”

“…Under such conditions, it is natural to use the quasi-optical approach for the description of radiation propagation [36][37][38][39][40][41]. The main simplified assumption, proposed in [36] and further developed in [37] and used in the presented analysis, is the approximation of relatively shallow corrugation depth in the scale of its period and wavelength.…”