Electromagnetic Waves in Elliptic Hollow Pipes of Metal

Abstract

A theoretical study of the transmission of electromagnetic waves in hollow conducting pipes of elliptic cross section, including field configurations, critical frequencies, velocities of propagation, and attenuations for the six lowest order waves. The pipe of circular cross section is treated as a special case, and the stability of waves in it for small deformation of the cross section is discussed.

Modes of elliptical waveguides: a correction

“…This would have interchanged the nature of the extrema at 17 = 0 and n/2 and reversed the relative field directions on either side of the foci, consistent with the field plots in Ref. 1.…”

“…1 (Method 2) for two different ellipses: The first is an ellipse of semi-axes 10 and 6.614 cm, corresponding to an e of 0.75; this is the case for which the field plots are presented in Ref. 1. The second is an ellipse of semi-axes of 6 and 2 cm , corresponding to an e of .94281; this is the geometry of the waveguide (actually an accelerator beam tube) we were working on when this problem originally arose.…”

“…Chu's [1] method of arriving at the value of qmr was somewhat similar. However, rather than numerically integrating the radial equation, Chu used Fourier-Bessel expansions of the Cem and Se m , based on (at that time) unpublished M.LT.…”

“…of constant cross-section), the z-dependence of the electric and magnetic fields is simply given by e-jkzz. Hence (1) where v~ represents the two-dimensional (i.e. in the transverse plane) Laplacian, and k is the wave number (m/c) in unbounded space.…”

“…The analytic solutions for the lowest modes of an elliptical waveguide were first published some fifty years ago in a classic paper by L-J Chu [1]; references published as recently as 1986 [2] make use of Chu's original expressions and figures. In the course of checking the accuracy of a numerical field solver by using it to determine the cutoff frequencies of an elliptical waveguide, we observed that while the field solver yielded a cutoff frequency for the TMOI mode which was quite close to that shown in Refs.…”