Melezhyk P. Theory of eigen and forced electromagnetic oscillations in open two-dimensional structures.

The subject of the study is the electromagnetic field of open electromagnetic structures. The purpose is to study properties of eigen electromagnetic oscillations in open structures with insertions of different material nature. The research methods include the Riemann-Hilbert problem, reduction, and Trauba methods. Theoretical and practical results deal with the development of new methods of analysis of one type of open structures with insertions of different physical nature. The comprehensive analysis of the properties of spectra of eigen complex frequencies and resonance types of oscillations have been carried out for the first time in the resonance frequency range where the existing asymptotic and approximation theories cannot be applied. A strict mathematical model of the effect of inter-type coupling of eigen oscillations in open structures has been built. The relation between the oscillations having different physical nature, i.e. eigen oscillations of an open resonator and eigen azimuth surface oscillations of a plasma cylinder, has been for the first time established. The effect consisting in increase of Q-factor of the open resonator has been found when dielectric and perfectly conducting insertions have been introduced into it. The field of application is radio physics.