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Abstract The finite‐difference time‐domain (FDTD) method was previously applied to high‐frequency electromagnetic wave propagation through 250 km of theFregion 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 theF‐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) theD,Eand top of theFregions 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.
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This content will become publicly available on February 4, 2026
An open source code for modeling radio wave propagation in earth’s ionosphere
We present FARR (Finite-difference time-domain ARRay), an open source, high-performance, finite-difference time-domain (FDTD) code. FARR is specifically designed for modeling radio wave propagation in collisional, magnetized plasmas like those found in the Earth’s ionosphere. The FDTD method directly solves Maxwell’s equations and captures all features of electromagnetic propagation, including the effects of polarization and finite-bandwidth wave packets. By solving for all vector field quantities, the code can work in regimes where geometric optics is not applicable. FARR is able to model the complex interaction of electromagnetic waves with multi-scale ionospheric irregularities, capturing the effects of scintillation caused by both refractive and diffractive processes. In this paper, we provide a thorough description of the design and features of FARR. We also highlight specific use cases for future work, including coupling to external models for ionospheric densities, quantifying HF/VHF scintillation, and simulating radar backscatter. The code is validated by comparing the simulated wave amplitudes in a slowly changing, magnetized plasma to the predicted amplitudes using the WKB approximation. This test shows good agreement between FARR and the cold plasma dispersion relations for O, X, R, and L modes, while also highlighting key differences from working in the time-domain. Finally, we conclude by comparing the propagation path of an HF pulse reflecting from the bottomside ionosphere. This path compares well to ray tracing simulations, and demonstrates the code’s ability to address realistic ionospheric propagation problems.
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- Award ID(s):
- 2301644
- PAR ID:
- 10584935
- Publisher / Repository:
- Frontiers
- Date Published:
- Journal Name:
- Frontiers in Astronomy and Space Sciences
- Volume:
- 12
- ISSN:
- 2296-987X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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