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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. 

This paper develops a unified linear theory of cross field plasma instabilities, including the Farley–Buneman, electron thermal, and ion thermal instabilities, in spatially uniform collisional plasmas with partially unmagnetized multi-species ions. Collisional plasma instabilities in weakly ionized, highly dissipative, weakly magnetized plasmas play an important role in the lower Earth's ionosphere and may be of importance in other planetary ionospheres, stellar atmospheres, cometary tails, molecular clouds, accretion disks, etc. In the Earth's ionosphere, these collisional plasma instabilities cause intense electron heating. In the solar chromosphere, they can do the same—an effect originally suggested from spectroscopic observations and modeling. Based on a simplified 5-moment multi-fluid model, the theoretical analysis presented in this paper produces the linear dispersion relation for the combined Thermal Farley–Buneman Instability with an important long-wavelength limit analyzed in detail. This limit provides an easy interpretation of different instability drivers and wave dissipation. This analysis of instability, combined with simulations, will enable us to better understand plasma waves and turbulence in these commonly occurring collisional space plasmas.