Ray trace calculation of ionospheric propagation at lower frequencies

The Raytrace/Ionospheric Conductivity and Electron Density–Bent-Gallagher model has been revised to make it applicable to ionospheric propagation at low radio frequencies (0.5–5.0 MHz), where the ionosphere and magnetic anisotropy drastically alter propagation paths and provide a severe test of propagation model algorithms. The necessary revisions are discussed, and the model is applied to the problem of ionospheric penetration from a source below the ionosphere to a receiver above the ionosphere. It is necessary to include the electron collision frequency in the Appleton-Hartree index of refraction in order to permit ionospheric penetration for radio frequencies below the maximum plasma frequency (e.g., whistler modes). The associated reformulation of the ray trace equations for a complex index of refraction is straightforward. Difficulties with numerical methods are cited for the lowest frequencies, and future improvements are indicated.