Abstract
The FDTD model of electromagnetic wave propagation in the Earth-ionosphere cavity was developed under assumption of axisymmetric system, solving the reduced Maxwell’s equations in a 2D spherical coordinate system. The model was validated on different conductivity profiles for the electric and magnetic field components for various locations on Earth along the meridian. The characteristic electric and magnetic altitudes, the phase velocity and attenuation rate were calculated. We compared the results of numerical and analytical calculations and found good agreement between them. The undertaken FDTD modeling enables us to analyze the Schumann resonances and the propagation of individual lightning discharges occurring at various distances from the receiver. The developed model is particularly useful when analyzing ELF measurements.
Highlights
The finite-difference time-domain (FDTD) is a numerical analysis technique based on time-dependent differential Maxwell’s equations
FDTD modeling in 3D Cartesian coordinates system was used for verification of Wait's and Cooray-Rubinstein analytical formulas, describing lightning-radiated electric and magnetic fields for a mixed propagation path and for the fractal rough ground surface (Zhang et al, 2012a; Zhang et al, 2012b; Li et al, 2013; Li et al, 2014)
Summary and conclusions In this paper, we analyzed the solutions of Maxwell's equations obtained by the FDTD method for an axisymmetric uniform Earth-ionosphere cavity
Summary
The finite-difference time-domain (FDTD) is a numerical analysis technique based on time-dependent differential Maxwell’s equations It was originally developed for Cartesian coordinate system, but after elaboration of the code for spherical 20 coordinates, it found applications in studies of ELF and VLF radio wave propagation in the Earth-ionosphere waveguide (Holland, 1983; Hayakawa and Otsuyama, 2002; Simpson and Taflove, 2002; Otsuyama et al, 2003; Yang and Pasko, 2005; Yu et al, 2012; Samimi et al, 2015). When a small part of the Earth-ionosphere cavity needs to be analyzed, a local volume can be divided into FDTD grid in 25 2D cylindrical (Cummer, 2000; Hu and Cummer, 2006; Qin et al, 2019), or 3D Cartesian coordinate systems (Araki et al., 2018; Suzuki et al, 2016) It facilitates taking into account some complex inhomogeneities and ionospheric anisotropy in the analysis of ELF/VLF radio waves. FDTD modeling in 3D Cartesian coordinates system was used for verification of Wait's and Cooray-Rubinstein analytical formulas, describing lightning-radiated electric and magnetic fields for a mixed propagation path (vertically stratified 30 conductivity) and for the fractal rough ground surface (Zhang et al, 2012a; Zhang et al, 2012b; Li et al, 2013; Li et al, 2014)
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