Spectral Characteristics of the Integral Operator of the Internal Problem of Electrodynamics for Cylindrical Spiral Structure

The article is dedicated to the analysis of electrodynamic properties of the cylindrical spiral structure. Internal problem for the considered structure in the framework of the thin-wire approximation is reduced to a pair of independent integral Fredholm equations of the first kind, written with respect to even and odd components of the unknown current function. A study of spectral characteristics of the integral operator of the integral equation for various electrical lengths and ratios cylinder radius to its height for a fixed number of turns. Using corresponding systems of projection functions in the framework of the method of moments two independent systems of linear algebraic equations are formed with respect to the unknown expansion coefficients of the even and odd components current function. Certain features of the behavior of eigenfunctions in depending on the wave dimensions and geometrical parameters of the spiral. Features of the frequency dependence of the eigenvalues integral operator were revealed. The conclusion is made about the resonant nature of these dependencies, what makes a cylindrical spiral structure in many respects similar to the previously considered tubular vibrator, a spherical spiral particle and an elliptical frame structure. A hypothesis is put forward about the relationship between the quality factor of resonances of eigenvalues and the emergence of a traveling wave mode in the spiral. Presented results contribute to the formation of an in-depth understanding of emerging in the structure internal processes and serve as a guideline in the construction of approximation models for solving an internal problem.