Some perturbation effects in cavity resonators

Abstract

An investigation, partly theoretical and partly experimental, has been made of some effects which occur when the boundary of a cavity is deformed slightly. First, the theory of natural electromagnetic oscillations inside lossless cavities is summarized. Then a general theory, following along the lines of conventional first-order perturbation theory, is given. The theory has been applied to the perturbation of a right-circular cylindrical cavity. Two cases have been considered: the E010 mode, a non-degenerate case; and the H011 and E111 modes, a triply degenerate case. These two cases have also been investigated experimentally. Theory and experiment are in reasonable agreement, even for quite large deformations, when the deformation is applied gradually over a large area of the cavity wall. For sharp abrupt changes in the geometry of the cavity wall, however, it appears that the first-order perturbation theory can be applied only for very small distortions. The general results, theoretical and experimental, which have been obtained, show that if the frequency of the operating mode is well separated from the frequencies of other modes, a deformation of the boundary changes only the frequency of the operating mode and not its electromagnetic field configuration. If the frequency of the operating mode is near to the frequencies of other modes, a slight deformation of the cavity boundary, as well as changing the frequency of the operating mode, may also change its electromagnetic field configuration. “Lossy” material or resistance wires, introduced into a cavity with a view to damping out unwanted modes, may also affect the desired resonance if certain types of deformation are present.