A Theory for Efficient Calculation of Electron Transport and Reaction Rate Coefficients in Weakly Ionized Magnetized Plasma

In the absence of a magnetic field, the electron energy distribution function (EEDF) obtained in the local field approximation of the Lorentzian gas model varies as a function of the reduced electric field E/N where E denotes the magnitude of the electric field and N denotes neutral atmospheric density. In the presence of an additional magnetic field, the EEDF becomes a function of the reduced gyrofrequency ωce/N (where ωce = qeB/me is the electron gyrofrequency for a given magnetic field B), and the angle between E and B, χ. As a result, rate constants of electron impact processes in addition to electron transport coefficients will vary as a function of (E/N, ωce/N, χ). In this work we present a theory for the substitution of (E/N, ωce/N, χ) with an effective reduced field Eeff/N. While it may be readily seen that for cases of nonmagnetized and fully magnetized electrons Eeff = E and Eeff = Ecosχ, respectively, we present a solution for calculation of Eeff for partially magnetized electrons. Preliminary comparison of electron rate and transport coefficients as a function of (E/N, ωce/N, χ) obtained via BOLSIG+ [Hagelaar and Pitchford, Plasma Sources Sci. Technol. 14, 722-733, 2005] and via the presented method are demonstrated for air, the atmosphere of Jupiter, and CO2. The new approach may be used in modeling of partially magnetized plasmas encountered in the context of transient luminous events, e.g., sprite streamers in the atmosphere of Jupiter [Giles et al., J. Geophys. Res., 125, e2020JE006659, 2020], in modeling the propagation of lightning's electromagnetic pulse in Earth's ionosphere [e.g., Nagano et al., JASTP, 65, 615-625, 2003; R. A. Marshall, Very low frequency radio signatures of transient luminous events above thunderstorms, PhD thesis, Stanford University, 2009; Marshall et al., J. Geophys. Res., 115, A00E17, 2010], and in various applications of nonthermal CO2 plasma [Starikovskiy et al., Phys. Rev. E, 103, 063201, 2021].