VLF electromagnetic radiation in a magnetoionic medium

We examine VLF electromagnetic radiation through an ionized gas in a permanent magnetic field (magnetoionic medium). Such a medium can be taken as a model of the ionosphere. We work from the Fourier transform of the dyadic Green's function which relates the current density and the electric field. Asymptotic expansions of the function are obtained for both small and large separation. The expansions for small separation can be used to discuss the power radiated by a current distribution (antenna). Special attention is given to the power radiated by a Hertzian dipole, and a conflict in the literature (Staras, 1964; Lee and Papas, 1965) is resolved. The expansion for large separation can be used to discuss the far field. The radiated far field is shown to propagate most strongly along the field lines of the permanent magnetic field. The far field radiated by a Hertzian dipole is considered.