Transport Phenomena in a Nonuniform Slightly Ionized Gas

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Abstract
The authors have obtained the solution of Boltzmann's equation for electrons in a nonuniform slightly ionized gas, in the presence of the gradients of electron collision frequency and density as well as the external static and alternating electric field and the static magnetic field. Electrical and thermal currents have been obtained in the integral form as a function of collision frequency and f0, the isotropic part of distribution function of electron velocities. A linear ordinary differential equation for f0 involving collision frequency as well as external fields and gradients of electron density and collision frequency is set up. An important result obtained is the fact that high gradients of electron density and collision frequency lead to a non-Maxwellian distribution of electron velocities. This is applicable to a wide variety of problems, involving plasma sheaths. Another result, clearly brought out by the present vector treatment is the fact that the current in general has a part proportional to the magnetic vector besides those proportional to the electric fields and gradient vectors and their vector product with the magnetic vector. However, this part vanishes when the magnetic vector is perpendicular to electric field and gradient vectors. Applications and limitations of present analysis have been discussed.

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