Diagnostics of hypersonic plasma by method of intrinsic electromagnetic oscillations of open resonator with non-uniform inclusions

Abstract

For various areas of radiophysics, plasma physics, studies of spectral and diffraction characteristics of open resonators containing various inhomogeneous inclusions within themselves are of great interest, the material parameters of which depend on spatial coordinates or on frequency parameters of the structure. Approximate models of optical resonators are based on integral equations, the nuclei of which are answered by non-self-conjugated completely continuous operators in some functional spaces (Hilbert or Banach spaces). The rationale for these equations does not seem mathematically correct enough. These equations are derived from the scalar formulation of the mathematically inconsistent Kirchhoff diffraction theory. Therefore, the relationship of these equations with the strict electrodynamic setting of the spectral problem is unclear and, therefore, the applicability of the corresponding models of optical resonators is unclear. The task set forth in the article is to build a strict mathematically justified and effective solution of edge problems about free and forced electromagnetic oscillations for one class of two-dimensional optical resonators with dielectric inclusions. The mirrors of this optical resonator are modeled by a final system of perfectly conductive open circular cylindrical surfaces, and the inclusions by a final system of circular cylindrical regions filled with dielectric medium. The wavelength, geometric parameters of the mirrors of the optical resonators, their mutual location, as well as the dimensions of the inclusions of a priori restrictions are not imposed. The main results obtained are also true for the case of an empty optical resonator that does not contain dielectric inclusions.