Kononenko O. Mathematical model of the coaxial gyrotrons with the corrugated inserts for the numerical analysis of the eigen modes

Eigen modes of the corrugated gyrotron resonators are the object of the study. Purpose of the study is a development of the mathematical models for the corrugated resonators for the analysis of the eigen electromagnetic oscillations and discrete mathematical models for the numerical experiments concerning the gyrotron electromagnetic properties computations. Methods from the following disciplines are used in the dissertation: mathematical physics, theory of the integral and differential equations, linear algebra, numerical computations (method of the discrete singularities), object-oriented programming. For the first time mathematical model of the corrugated gyrotron resonator is developed for the eigen TM modes. Novel discrete model of the hypersingular integral equation of the 1-st kind is built and could be used for the study of the TM modes. For the first time mathematical model is developed for the standing waves and arbitrary dielectrics in the working area and corrugations. Cutoff wavenumbers,eigen frequencies, eigen fields, Ohmic losses are computed and visualized. Obtained results could be used for the construction and optimization of the effective gyrotron resonator systems.