A theory for modeling partially magnetized electrons under influence of external electric field in geophysical applications using fluid coefficients corresponding to non-magnetized plasma

In the presence of an external electric field and magnetic field, electron transport and rate coefficients vary as a function of the reduced electric field, reduced electron gyrofrequency, and the angle between electric field and magnetic field vectors [Starikovskiy et al., Phys. Rev. E, 103, 063201, 2021; Janalizadeh and Pasko, J. Geophys. Res.: Space Phys., 128, e2022JA031009, 2023]. We present a theory based on solution of the Boltzmann equation in non-magnetized plasma to obtain electron transport and rate coefficients in magnetized plasma by using an effective electric field [Janalizadeh et al., submitted to Plasma Sources Sci. Technol., ID:PSST-105715, 2023]. This reduces the original problem with the three input parameters mentioned above to an equivalent problem with single input parameter, the effective reduced electric field. Comparisons between exact coefficients obtained via BOLSIG+ [Hagelaar and Pitchford, Plasma Sources Sci. Technol., 14, 722-733, 2005] and approximate coefficients of the proposed method are presented for pure carbon dioxide, air, and a mixture of molecular hydrogen and atomic helium representing the giant gas planets of the solar system [Janalizadeh et al., 2023]. A study of the convergence criteria of the fixed-point iteration method, which we use to solve for the effective electric field, shows that the method always converges to a unique solution, provided a judicious choice of the initial value of the electric field for fixed-point iterations. In particular, a simple choice that ensures convergence is the initial value equal to the applied field. The modeling framework that we report in this work is applicable to a broad range of natural phenomena and gas mixtures including electrical gas discharges in the atmospheres of the Earth and Jupiter (i.e., sprites and elves).