To the electrodynamic theory of a thin-wire structure

A thin-wire structure is one of the most important objects from the point of view of electrodynamics, as it serves as the basis for constructing various radiating structures, which include many types of single-element and multi-element vibrator, loop, and spiral antennas, as well as re-radiating structures such as diffraction grates, замедляющие структуры, microwave lenses, metamaterials, etc. The analysis of such structures involves solving the internal and external electrodynamics problems in a sequential manner. The article develops a unified methodology for solving the internal and external problems of electrodynamics for various thin-wire radiating and re-radiating structures based on integral representations of the electromagnetic field using the method of eigenfunctions, and it also formulates generalized conclusions based on the results obtained for a number of thin-wire structures. The concept of a projection integral representation of an electromagnetic field is introduced. It is shown that on the basis of the method of eigen functions for specific thin-wire structures, optimal projection integral representations of an electromagnetic field can be constructed, with the help of which it is possible to effectively solve the internal and external problem of electrodynamics, as well as to obtain a clear physical interpretation of the physical processes taking place in structures. The computational features of the proposed methods are considered. It is shown that from the point of view of the eigenfunction method, a thin-wire structure is an open resonator, the losses in which are due to the radiation of electromagnetic waves into the space surrounding the structure. A classification of resonance phenomena occurring in thin-wire structures is given.