ELECTROMAGNETIC FIELD OF A BARREL-SHAPED HOLLOW RESONATOR

Abstract

In the article is investigates the electromagnetic field of a barrel-shaped hollow resonator. It is significant that in the articles of K.M. Tsibizov developed an approach for determining the fields of waveguide resonator devices with a variable cross section. In this article, this approach is extended to a barrel-shaped hollow resonator. The solution of the Airy equation, which was used by K.M. Tsibizov are approximate solutions obtained through solving an equation that reduces to one of the forms of the hypergeometric equation or the Weber equation. The radial and azimuthal components of the field of a barrel-shaped hollow resonator are the corresponding components of the field of a hollow cylindrical resonator, and the longitudinal component is described by a degenerate hypergeometric function. In this article presents the design of a barrel-shaped waveguide resonator with metal ends and writes expressions for the resonant wavelengths of a barrel-shaped resonator with metal ends for H- and E-oscillations. The resonant wavelengths and resonant frequencies for two barrel-shaped resonators with metal ends are given in accordance with a cylindrical resonator with an equal end radius of the barrel-shaped resonator and equal longitudinal dimensions. The article also presents a waveguide resonator with an open left end and writes down the first five roots of the Airy functions. The consideration of such a resonator aims at demonstrating the generality of the considered approach.The design of a barrel-shaped resonator with open ends, the sections of which are critical, is presented.It is indicated that finding solutions to the equations of functions that describe the longitudinal distribution of the field is a demonstration of the generalization of the approach developed by K.M. Tsibizov, and as examples of the study of resonators of variable cross section: a barrel-shaped waveguide resonator with metal ends, a waveguide resonator with an open left end, and a barrel-shaped resonator with open ends, which are shown in the figures.