The impedance of an electric dipole in a magneto-ionic medium

Abstract

This paper evaluates the impedance of a finite electric dipole immersed in a homogeneous, anisotropic, magneto-ionic medium with parameters appropriate to whistler frequencies in the ionosphere, i.e., X > Y^{2} \gg 1 . Although the basic formulation is also valid when collision frequency is taken into account, the computations presented here were made under the assumption that the collision frequency is zero. Under this assumption, all the matrices involved are Hermitian and the computations are simplified considerably. It is pointed out that in the ionosphere the VLF point dipole will have an infinite resistance as well as reactance even when neglecting losses in the medium. This infinity catastrophe cannot be removed by assuming small losses in the medium. It can be removed only by considering the finite dimensions of the antenna. A physical explanation of this phenomenon is presented, and some results for both resistance and reactance are given as a function of antenna dimensions, orientation and ionospheric parameters. A discussion of the far-field antenna pattern is also presented.