Mitina I. Numerical modeling of electromagnetic fields in open and closed resonators

The object of research is free oscillations of closed and opened electromagnetic cavities, as well as a resonance in opened systems. The aim of research is to construct mathematical models to solve the membrane problem for a coaxial gyrotron cavity with a corrugated inner conductor, as well as to solve problems for resonant and free electromagnetic oscillations of the simplified gyrotron cavity. The thesis uses the methods of mathematical physics, linear algebra, mathematical analysis, the theory of integral equations, numerical methods. Mathematical models for finding the transverse wave numbers, damping coefficients and the corresponding membrane functions of TE modes of the coaxial gyrotron cavity with an arbitrary corrugated inner conductor have been developed at first time. Results of numerical experiments which indicate that ohmic losses can be reduced substantially by choosing the appropriate form of corrugations have been obtained for the first time. Mathematical models to study the resonant and free electromagnetic oscillations of the three-dimensional simplified gyrotron cavity have been developed at first time. Based on developed models it has been created the software for performing numerical analysis of the membrane problem and the simplified gyrotron cavity. The developed technique is planned to be used in design and for optimization of the modern coaxial gyrotron cavities.