Model of the propagation of very low-frequency beams in the Earth–ionosphere waveguide: principles of the tensor impedance method in multi-layered gyrotropic waveguides

The modeling of very low-frequency (VLF) electromagnetic (EM) beam propagation in the Earth–ionosphere waveguide (WGEI) is considered. A new tensor impedance method for modeling the propagation of electromagnetic beams in a multi-layered and inhomogeneous waveguide is presented. The waveguide is assumed to possess the gyrotropy and inhomogeneity with a thick cover layer placed above the waveguide. The influence of geomagnetic field inclination and carrier beam frequency on the characteristics of the polarization transformation in the Earth–ionosphere waveguide is determined. The new method for modeling the propagation of electromagnetic beams allows us to study the (i) propagation of the very low-frequency modes in the Earth–ionosphere waveguide and, in perspective, their excitation by the typical Earth–ionosphere waveguide sources, such as radio wave transmitters and lightning discharges, and (ii) leakage of Earth–ionosphere waveguide waves into the upper ionosphere and magnetosphere. The proposed approach can be applied to the variety of problems related to the analysis of the propagation of electromagnetic waves in layered gyrotropic and anisotropic active media in a wide frequency range, e.g., from the Earth–ionosphere waveguide to the optical waveband, for artificial signal propagation such as metamaterial microwave or optical waveguides.

Model of Propagation of VLF Beams in the Waveguide Earth-Ionosphere. Principles of Tensor Impedance Method in Multilayered Gyrotropic Waveguides

Modeling propagation of VLF electromagnetic beams in the waveguide earth-ionosphere (WGEI) is of a great importance because variation in the characteristics of these waves is an effective instrument for diagnostics the influences on the ionosphere from above (Sun-Solar Wind-Magnetosphere-Ionosphere), from below (the most powerful meteorological, seismogenic and other sources in the lower atmosphere and lithosphere/Earth, such as hurricanes, earthquakes, tsunamis etc.), from inside the ionosphere (strong thunderstorms and lightning discharges) and even from the far space (such as gamma-flashes, cosmic rays etc.). Thus, VLF became one of the most universal instrument for monitoringthe Space Weather in the direct sense of this term, i.e. the state of the Sun-Earth space and the ionosphere as it is particularly determined by all possible relatively powerful sources, wherever they are placed. This paper is devoted mostly to modelling VLF electromagnetic beam propagation in the WGEI. We present a new tensor impedance method for modelling propagation of electromagnetic beams (TIMEB) in a multi-layered/inhomogeneous waveguide. Suppose that such a waveguide, i.e. WGEI, possesses the gyrotropy and inhomogeneity with a thick cover layer placed above the waveguide. Note a very useful and attractive feature of the proposed TIMEB method: in spite of a large thickness of the waveguide cover layer, the proposed effective impedance approach reflects an impact of such a cover on the electromagnetic (EM) waves, which propagate in the waveguide. This impedance approach can be applied for EM waves/beams in layered gyrotropic/anisotropic active media in very wide frequency range, from VLF to optics. Moreover, this approach can be applied to calculations of EM waves/beams propagation in the media of an artificial origin such as metamaterial microwave or optical waveguides. The results of the modelling the propagation of VLF beams in the WGEI are included. The qualitative comparison between the theory and experimental observation of increasing losses of VLF waves in the WGEI is discussed. The new proposed method and its further development allows the comparison with the results of the future rocket experiment. This method allows to model (i) excitation of the VLF modes in the WGEI and their excitation by the typical VLF sources, such as radio wave transmitters and lightning discharges and (ii) leakage of VLF waves/beams into the upper ionosphere/magnetosphere.