On the errors of isotropic approximation to the geometric-optics description of ionospheric radio wave propagation

A geometric optics approach is of vital importance when considering high frequency radio wave propagation and space weather effects. Isotropic approximation, i. e. neglect the effect of the Earth’s magnetic field, is widely used to simplify the ray-optical description of ionospheric propagation of radio waves. In particular, the advantage of this approach is that for a set of ionospheric models it allows to obtain analytical solutions for the parameters of the ray path. It has been extensively discussed in the literature that the isotropic approximation works quite well for oblique ionospheric sounding being representative of the ordinary mode. Thus, it has been established that with increasing the launch angle (i. e. for more oblique paths), the isotropic approximation error decreases, in fact not being able to distinguish between isotropic and anisotropic media for paths of the order of thousand kilometers long. The efficiency of the approximation is of vital importance for applications where simplification of the software implementation and reduction of the calculation execution time is required. However, this description under certain conditions may produce a significant error. In particular, it is not applicable for vertical and near-vertical sounding in the cases where operating frequency is close to critical frequencies of E and F2 layers. Two-dimensional ray tracing scheme is applied to the initial value problem and to the boundary value problem. The refractive index of the ionosphere is given by the Appleton-Hartree formula (ignoring collisions). Thus, the purpose of the study is to examine the no-field approximation error under different conditions of radio wave propagation on the basis of ray tracing analysis.