The Appleton-Hartree formula and dispersion curves for the propagation of electromagnetic waves through an ionized medium in the presence of an external magnetic field part 1: curves for zero absorption

Abstract

This paper gives dispersion curves derived from the Appleton-Hartree formula in the case of zero absorption. The value of the magnetic field is taken as that of the earth's field at Slough. The curves are drawn to show the value of the squares of the indices of refraction and attenuation as functions of the electron density for a series of twelve frequencies, which are chosen to illustrate the various classes of curve and the boundary curves separating the classes and, in the case of frequencies above 1.321 megacycles per second, the various regions of short and ultra-short waves. The derivation and general properties of the Appleton-Hartree formula and the various possible modes of propagation are also discussed. The dispersion curves are classified according to the infinities they contain and a diagram is given to show how the classes of curve holding for any angle of inclination of the direction of propagation to the magnetic field H depend on the ratio of the longitudinal component of H to H itself. The use of the zeros and infinities of the dispersion curves in the interpretation of propagation phenomena is described and a summarizing diagram is given, showing how the possible propagation of zero, one or two basic modes for any frequency depends on the electron density. The polarization corresponding to each dispersion curve is shown graphically and the general properties of the polarizations of the basic propagation modes are discussed.