Electron macrokinetics in partially ionized gases: The hydrodynamic regime

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Abstract
The concept of macrokinetic distributions is used to investigate the macroscopic dynamics of an assembly of electrons in a weakly ionized gas in the hydrodynamic regime. In this regime, the macrokinetic distribution (MKD) is shown to obey an equation that is equivalent to the Boltzmann equation in the time scale of electron-density transport. Formal, approximate solutions to this equation are obtained whose range of validity depend on the magnitude of the spatial derivatives of the density. Specific conditions on the magnitude of these derivatives have been obtained. Explicit expressions for the MKD are presented for the case of a quasi-Lorentz gas model. They have been used to evaluate the electron current density in the hydrodynamic regime and to obtain expressions for the mobility and diffusion coefficient. In the regime of large electron-density gradient, these coefficients have been found to depend on the normalized gradient. The consequences of these results are illustrated for the case of constant collision frequency.