Frequency dependence of the penetration of electromagnetic fields through an elliptical hole in a thin metallic wall.

Abstract

The static approximation suggests that, for a given hole area, the use of a long narrow slot in a beam pipe gives a reduced coupling impedance. But for a long slot the slot length may be comparable with the wavelength, making the static approximation a poor one. In this paper we derive expressions for the generalized polarizability and susceptibility [Cheng, Fedotov, and Gluckstern, Phys. Rev. E 52, 3127 (1995)] of an elliptical hole in a thin plane metallic screen, as a function of hole dimensions and wavelength. In particular, we construct a variational form that allows us to obtain an approximate analytic result for the resonant frequency of a cavity with such a hole. In the calculations we include the effects of finite wavelength, but still confine our attention to reduced wavelengths no smaller than the primary hole dimensions. We then use these results to estimate the coupling impedance of a long narrow elliptical slot in a beam pipe, and show that the effect of finite wavelength is important. \textcopyright{} 1996 The American Physical Society.