## 1 Introduction  
### Background  
In partially ionized plasma, electrons, neutral particles (molecules or atoms), and ions coexist. The collision cross sections (scattering cross sections or momentum transfer cross sections) of the interactions between the electrons and the neutral particles (the neutrals) of each gaseous species in the plasma are numbers that influence the mobility of these electrons within these neutrals. Rather than being geometric cross-sectional areas, they actually describe the chance of a collision event [1]. Higher collision cross sections result in more frequent electron-neutral collisions, which, in turn, result in a shorter mean free path of the electrons. This restriction on the continuous straight-line movement of the electrons causes a decline in the plasma electric conductivity [2]. For a single gaseous species \"s\" with a number density (\(n_{s}\)) and with a collision cross section (\(Q_{s}\)) for the particles of that species, the free path length (\(\lambda_{e}\)) of the electrons colliding with the neutral particles of that species is \[\lambda_{e}=\frac{1}{n_{s}\,Q_{s}} \tag{1}\]  
And the electron-neutral collision cyclic frequency is  
\[\
u_{e-n}(v_{e})=n_{s}\,Q_{s}(v_{e})\;v_{e} \tag{2}\]  
where (\(v_{e}\)) is the electron speed (velocity magnitude), which is amplified at higher temperatures, and which also can be induced via an applied magnetic field that the electron experiences when moving parallel to that magnetic field. The time between two successive electron-neutral collisions is the reciprocal of the electron-neutral collision cyclic frequency. Thus, the time between electron-neutral collisions is expressed as  
\[\tau_{e-n}(v_{e})=\frac{1}{n_{s}\,Q_{s}(v_{e})\;v_{e}} \tag{3}\]  
If the average time between electron-neutral collisions is denoted as \(\overline{\tau}_{e-n}\), with a corresponding average electron-neutral collision cyclic frequency of \(\overline{v}_{e-n}\), and a corresponding average collision cross section of \(\overline{Q}_{s}\), and also an average electron speed of \(\overline{v}_{e}\), then these quantities are related as follows:  
\[\overline{\tau}_{e-n}=\frac{1}{n_{s}\,\overline{Q}_{s}\,\overline{v}_{e}} \tag{4}\]  
\[\overline{v}_{e-n}=n_{s}\,\overline{Q}_{s}\,\overline{v}_{e} \tag{5}\]  
And the electron mobility can then be found as  
\[\mu_{e-n}=\frac{e\,\overline{\tau}_{e-n}}{m_{e}}=\frac{e}{m_{e}\,\overline{v} _{e-n}}=\frac{e}{m_{e}\;n_{s}\,\overline{Q}_{s}\,\overline{v}_{e}} \tag{6}\]  
And the electric conductivity of the plasma gas due to the movement of these mobile electrons is  
\[\sigma_{e-n}=n_{e}\,e\;\mu_{e-n}=\frac{n_{e}\,e^{2}\,\overline{\tau}_{e-n}}{m _{e}}=\frac{n_{e}\,e^{2}}{m_{e}\,\overline{v}_{e-n}}=\frac{n_{e}\,e^{2}}{m_{e} \,n_{s}\,\overline{Q}_{s}\,\overline{v}_{e}} \tag{7}\]  
If it is important to maximize plasma electric conductivity, such as in magnetohydrodynamic (MHD) power generation [3; 4; 5; 6], the electron collision cross sections should be minimized. The topic of the collision cross sections of electrons has received research attention in several studies over many years [7; 8; 9; 10; 11; 12; 13; 14; 15]. The collision cross section of an electron depends on the kinetic energy of the electron and thus depends on its speed [16; 17]. However, such a detailed description can be too cumbersome and time-consuming for practically estimating the electric conductivity of plasma, where finding the electron-neutral collision cross sections is just one stage of several stages of computation needed to find a single electric conductivity value for a plasma gas mixture. For example, finding the Coulomb scattering of electrons due to ions and other electrons, and finding the number densities of each neutral species, are other stages of computations that should be completed as prerequisites for estimating the electric conductivity [18; 19].