Surface impedance of electromagnetic field excited by a grounded horizontal antenna in the Earth–ionosphere waveguide

Analytical formulas for the tangential components of extremely-low-frequency (ELF) electromagnetic field in the Earth–ionosphere plane waveguide excited by a grounded linear horizontal antenna are obtained. The behavior of surface impedance is studied as a function of electrodynamic characteristics of the waveguide and the distance from the source. It is shown that surface impedance coincides with the plane wave impedance on the Earth’s surface at distances from the source larger than the skin depth provided that the skin layer is thinner than double the waveguide’s height. The influence of the ionosphere on the amplitude of the ELF and lower-frequency magnetic field and, thus, on the impedance at the distances shorter than two ionospheric heights is theoretically substantiated. This type of effect was observed in the experiments conducted on the Kola Peninsula where the low conductivity of the Earth allowed the detection of the effect of the ionosphere on the amplitude of the magnetic field in the low-frequency band.