Spectral characteristics of the integral operator of the internal problem of electrodynamics for elliptical frame structure

The article is devoted to the analysis of electrodynamic properties elliptical frame structure. Taking into account double symmetry internal problem of electrodynamics for the structure under consideration in the framework of the thin-wire approximation is reduced to four integral Fredholm equations of the first kind, written with respect to independent current functions. A study of spectral characteristics of the integral operators of the corresponding integral equations for various values of the electrical length and ellipticity of the frame. It is shown that the eigenfunctions of integral operators for close values of these parameters have a high degree of correlation, with In this case, the eigenfunctions are close in form to trigonometric functions. Features of the frequency dependence of the eigenvalues integral operators. The conclusion is made about the resonant nature of these dependences, what makes an elliptical frame structure in many respects similar to the previously considered tubular vibrator and spherical spiral particle. The results presented in the article form an in-depth understanding of the processes occurring in the structure under consideration, and also serve as a guideline in the construction of approximation models for solving the internal tasks.