Abstract
Abstract. 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.
Highlights
The results of the analytical and numerical study of very low-frequency (VLF) electromagnetic (EM) wave/beam propagation in the lithosphere–atmosphere–ionosphere– magnetosphere system (LAIM), in particular in the Earth– ionosphere waveguide (WGEI), are presented
The differences of the proposed model for the simulation of VLF waves in the WGEI from others can be summarized in three main points. (i) In distinction to the impedance invariant imbedding model (Shalashov and Gospodchikov, 2011; Kim and Kim, 2016), our model provides an optimal balance between the analytical and numerical approaches
It combines analytical and numerical approaches based on the matrix sweep method (Samarskii, 2001). This model allows for analytically obtaining the tensor impedance and, at the same time, provides high effectiveness and stability for modeling. (ii) In distinction to the full-wave finitedifference time domain models (Chevalier and Inan, 2006; Marshall and Wallace, 2017; Yu et al, 2012; Azadifar et al, 2017), our method provides the physically clear lower and upper boundary conditions, in particular physically justified upper boundary conditions corresponding to the radiation of the waves propagation in the WGEI to the upper ionosphere and magnetosphere
Summary
The results of the analytical and numerical study of very low-frequency (VLF) electromagnetic (EM) wave/beam propagation in the lithosphere–atmosphere–ionosphere– magnetosphere system (LAIM), in particular in the Earth– ionosphere waveguide (WGEI), are presented. (ii) In distinction to the full-wave finitedifference time domain models (Chevalier and Inan, 2006; Marshall and Wallace, 2017; Yu et al, 2012; Azadifar et al, 2017), our method provides the physically clear lower and upper boundary conditions, in particular physically justified upper boundary conditions corresponding to the radiation of the waves propagation in the WGEI to the upper ionosphere and magnetosphere This allows for the determination of the leakage modes and the interpretation of ground-based and satellite measurements of the VLF beam characteristics.
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