An investigation of the propagation of electromagnetic waves in some circular cylindrical waveguides using a finite difference formulation.

This thesis is concerned with the propagation of electromagnetic waves through circular cylindrical waveguide having perfectly conducting walls. A finite difference approximation method is used to evaluate the propagation constant of the waves. The method is one of great generality. It may be used for any coaxial configuration of media inside the waveguide. In particular, the effects on propagating electromagnetic waves of a transversely magnetised ferrite tube adjacent to the waveguide wall are studied. Ferrite material is taken to have a permeability tensor of the form [image] when it is subjected to a static magnetic field along its third coordinate axis. The ferrite tube is subject to a static magnetic field formed by four magnetic poles at the corners of a square centred on the axis of the guide, like poles being at opposite corners. In the ferrite, this field leads to a permeability tensor which is dependent upon the angle in cylindrical polar coordinates when the z-axis is taken along the guide and Maxwell's equations reduce to two simultaneous second order partial differential equations with non-constant coefficients in the EZ and HZ components of the propagating electromagnetic wave. The finite difference approximation method reduces the problem to one of solving the condition for consistency of a large number of difference equations. Values of the propagation constant which satisfy this condition are found by a trial method which involves evaluating a determinant of very high order. This evaluation is carried out by computer and use is made of the banded nature of the determinant to prevent the amount of computer store required becoming prohibitive. The validity of the method is tested by applying it to several special cases with known results and its limitations and accuracy are discussed. A hypothesis is suggested to explain the numerical results.