CXVIII. The propagation of a radio atmospheric—II

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Abstract
In a previous paper (Budden 1951 a, referred to as Paper I), it was shown that the propagation of an atmospheric could be treated either in terms of the successive reflection of rays at the earth and the ionosphere, or by considering the space between the earth and the ionosphere as a wave-guide, and discussing the properties of the various wave-guide modes. An outline of the theory was given for the case when the top surface of the wave-guide was the boundary of a homogeneous ionized medium, and the earth's magnetic field was neglected. The present paper gives the full mathematical theory , and shows how the characteristics of the wave-guide modes may be determined in the most general case, provided that the reflecting properties of the earth and the ionosphere are known as functions of the angle of incidence which is, in general, complex. It is found that the wave-guide modes are of two types, which are described as ‘quasi-transverse magnetic’ and ‘quasi-transverse electric’. Allowance can be made for the curvature of the earth. A particular case is then discussed, in which the surface of the earth is assumed to be perfectly conducting, and the ionosphere is assumed to be a homogeneous ionized medium, with the steady magnetic field of the earth superimposed. The results of numerical calculations are given, for a few special cases, in the form of curves. These show (i) the attenuation in the various modes as a function of frequency, (ii) the polarization characteristics of the wave in typical modes, and (iii) the amplitudes of the waves which are excited in typical modes by a vertical electric dipole source.

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