A 3-D FDTD Methodology for Modeling the Propagation of VLF Whistler Mode PLHR Waves Through the Ionosphere

Abstract

The finite-difference time-domain (FDTD) method was previously applied to high-frequency electromagnetic wave propagation through 250 km of the F region of the ionosphere. That modeling approach was limited to electromagnetic wave propagation above the critical frequency of the ionospheric plasma, and it did not include the lower ionosphere layers or the top of the F-region. This paper extends the previous modeling methodology to frequencies below the critical frequency of the plasma and to altitudes encompassing the ionosphere. The following changes to the previous work were required to generate this model: (a) the D, E and top of the F regions of the ionosphere were added; and (b) the perfectly matched layer absorbing boundary on the top side of the grid was replaced with a collisional plasma to prevent reflections. We apply this model to the study of extremely low frequency (ELF) and very low frequency (VLF) electric power line harmonic radiation (PLHR) through the ionosphere. The model is compared against analytical predictions and applied to PLHR propagation in polar, mid-latitude and equatorial regions. Also, to further demonstrate the advantages of the grid-based FDTD method, PLHR propagation through a polar cap patch with inhomogeneities is studied. The presented modeling methodology may be applied to additional scenarios in a straightforward manner and can serve as a useful tool for better tracking and studying electromagnetic wave propagation through the ionosphere at any latitude and in the presence of irregularities of any size and shape.