The ‘Waveguide mode’ theory of radio wave propagation when the ionosphere is not sharply bounded

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Abstract
The propagation of radio waves to great distances can be treated by considering the space between the earth and the ionosphere as a wave guide and discussing the properties of the various waveguide modes. Previous authors have generally assumed that the upper boundary of the waveguide is a sharply bounded homogeneous ionosphere. The paper describes a method of calculating the mode characteristics for any horizontally stratified ionosphere in which the electron density and collision frequency vary with height in some arbitrary prescribed manner. The theory is given in full for a flat, perfectly conducting earth with no magnetic field, and its extension is outlined in an appendix. The paper presents the results of some calculations carried out on EDSAC 2, the automatic digital computer at the University Mathematical Laboratory, Cambridge. The effect on the waveguide modes of changing from a sharp to a gradual boundary on an otherwise homogeneous ionosphere is investigated by considering a variation of electron density (N) with height (z) according to the law N = N0 (1+tanhβ(z-h)) using a range of values of β, and mode characteristics are also calculated for an ionosphere in. which the electron density increases exponentially with increasing height. The effect on the waveguide modes of changes in the parameters of the exponential model, and the difference between the modes for vertical and horizontal polarization are described.

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