The theory of the limiting polarization of radio waves reflected from the ionosphere

In the theory of the propagation of radio waves through a homogeneous ionized medium it is well known that 'characteristic' waves, sometimes called the 'ordinary' and 'extraordinary' waves, are propagated independently. The refractive index and polarization for each characteristic wave are given by the magneto-ionic theory (Appleton 1932). If the medium is slowly varying, Booker (1936) has shown that in many cases this theory may still be applied. But there are important cases where the characteristic waves are not independent, and there is then said to be 'coupling' between them. This paper discusses the coupling which occurs in the lower part of the ionosphere. Here there is a 'limiting' region where a downcoming characteristic wave acquires the limiting polarization observed at the ground. Booker (1936) gave an approximate specification for the level of the limiting region. This paper gives a more precise specification and develops a method for calculating the limiting polarization of a downcoming characteristic wave. The theory is based on Forsterling's (1942) coupled wave equations, which apply only to vertical incidence. They contain a coupling parameter, $\psi $, which depends on the gradients of electron density and collision frequency. The level of the limiting region is specified in terms of $\psi $ and the refractive indices of the characteristic waves. The properties of a specific model of the ionosphere are discussed, and it is shown that for frequencies greater than about 1 Mc/s the limiting polarization is that given by the magneto-ionic theory for a certain 'limiting point' which occurs at a definite value of the height. This value may in general be complex, but in practical cases is almost purely real and occurs where the electron density and collision frequency are small, so that at high frequencies the limiting polarization is determined only by the magnitude and direction of the earth's magnetic field in the ionosphere.