The theory of the cosmic background radio signal received within the ionosphere

Abstract
The electric and magnetic fields to be expected within the ionosphere from a background source uniformly distributed across the sky are studied. The ray theory for an isotropic, horizontally stratified loss-free slowly varying ionosphere is first given, and it is shown that the mean-square moduli of the electric field components have n times their free-space value, and the mean-square moduli of the magnetic field components have n 3 times their free-space value where n is the local refractive index. The corrections to be expected when a full-wave theory is used are discussed. The ray theory for an anisotropic, loss-free ionosphere is then given and it is shown that the energy flux in a given direction is proportional to the Gaussian curvature at the associated point on the refractive index surface. For the ordinary wave, near the level of reflexion, the electric field is predominantly parallel to the earth’s magnetic field, and the small perpendicular component is nearly 100% circularly polarized. Results for the magnetic fields and for the fields of the extraordinary wave are also given and discussed.

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