Kinetic and thermodynamic treatment for the exact solution of the unsteady Rayleigh flow problem of a rarefied homogeneous charged gas

Abstract

This article presents an exact and enhanced solution of the study in the previous paper [Can. J. Phys., 88 (2010), 501–511]. For this purpose, I use the traveling wave solution method instead of the small parameter method, which enables us to have the full exact solution without any cut-off from the value of variables. In addition, I use the accurate formula of the electron–electron collision frequency. I persist in avoiding the discontinuity in the solution caused by the Laplace transformation results, which is included in the previous study. In the present work, the kinetic and the irreversible thermodynamic properties of the charged gas are presented from the molecular viewpoint. Our study is based on the solution of the BGK (Bhatnager–Gross–Krook) model of the Boltzmann kinetic equation, with the precision value of the electron–electron collision frequency. The BGK model equation coupled with Maxwell's equations for electrons near a moving rigid plane are solved. The distinction and comparisons between the perturbed and the equilibrium velocity distribution functions are illustrated. The ratios between the different contributions of the internal energy changes are predicted via the extended Gibbs equation for both diamagnetic and paramagnetic plasmas. The results are applied to a typical model of laboratory argon plasma.