Langevin Equation and the ac Conductivity of Non-Maxwellian Plasmas

The use of the Langevin equation $\{\frac{d\mathrm{v}}{\mathrm{dt}}+g\mathrm{v}=(\frac{q}{m}\left)\right[{\mathrm{E}}_0{e}^{i\omega t}+\left(\frac{\mathrm{v}}{c}\right)\times \mathrm{H}\left]\right\}$ to describe the electrical conductivity of a non-Maxwellian plasma (a weakly ionized gas in which the average electron collision frequency is temperature dependent) may be in error unless it is understood that the dissipative term, $g$, is complex. In the limiting cases of either high or low pressures the imaginary part of $g$ is negligible. The real and imaginary parts of $g$ are evaluated for these limiting cases, for four different gases; air, helium, Maxwellian gas, and water. The real part of $g$ is shown to be the average collision frequency multiplied by a numerical factor, the size of which depends on the nature of the gas and the pressure limit.