The influence of the earth’s magnetic field on radio propagation by wave-guide modes

Abstract

A general theory of radio propagation by wave-guide modes is given, which simultaneously makes allowance for the gradualness of the lowest part of the ionosphere, the earth’s curvature and the earth’s magnetic field. The method involves solving differential equations satisfied by the matrix admittance or matrix reflexion coefficient variables. The mode condition, excitation factor, and polarization of the waves in a mode are derived by evaluating the residues of a series of poles of a contour integral. The earth’s curvature is allowed for by the method of the ‘modified refractive index’, thus avoiding the use of cumbersome spherical wave functions. This also permits the replacement of a point source by a line source with consequent further simplification of the mathematics. Formulae are given which have been used for computations described elsewhere (Budden & Martin 1962; Martin 1961).