Rays in magnetoionic theory

Abstract

In a homogeneous magnetoionic medium the refractive index for a radio wave is given by the Appleton-Hartree formula which assumes that the angle between the wave normal and the superimposed magnetic field is known. But a radio signal travels along a path known as the “ray” which in general has a different direction from the wave normal, and in some problems it is the ray direction which is known and the wave normal direction is at first unknown. A formula is given for finding the refractive indices when the ray direction is given. There are then six different possible waves whose characteristics are determined by the solutions of an equation of degree six. The properties of this equation are illustrated by discussing some real solutions when electron collisions are neglected, although the theory is valid also when the refractive indices and wave normal directions are complex. The six solutions give directly the saddle points of an integrand used by some authors to express the “far field” of a point source of radio waves within the medium.