Some results for the lateral divergence of ray tubes

Physics – Optics

Scientific paper

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Field Strength, Ionospheric Propagation, Radio Transmission, Ray Tracing, Atmospheric Optics, Error Analysis, Perturbation Theory

Scientific paper

Since power is conserved within a ray tube in the absence of losses, the divergence of neighboring rays from the principal ray is important in determining the field strength of ionospherically propagated radio wave. In the analysis presented the earth's magnetic field and the loss of energy due to collisions are neglected. If the ionospheric geometry is such that the principal ray lies in a vertical plane, the equations for the ray variations lead to simple results for the divergence between neighboring rays, in particular for the lateral divergence. It is shown that the principal ray may lie in a vertical plane without the laterally diverging ray being confined to a vertical plane. The error involved in overlooking this fact is considered, and the relation of the results to a reciprocity theorem dealing with diverging rays is discussed. The difference between the elevation angles at the two ends of the principal ray is a good indicator of the error involved in neglecting the departure from a vertical plane of the laterally diverging ray.

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