On the Theory of Anisotropic Diffusion of Electrons in Gases

Abstract

It is now recognized that when electrons move in a steady state of motion in a gas in an electric field the process of diffusion is in general anisotropic with a coefficient of diffusion DL along or against the electric force eE that is not the same as the coefficient D for directions normal to eE. A theoretical discussion of this phenomenon based upon the Maxwell-Boltzmann equation is given which also entails consideration of related matters such as the distribution functionfri(c) for an isolated travelling group, the distribution of number density n, the equation of continuity and current density, and the relation of the theory of the travelling group to that of the steady stream.

On the Validity of the Two-term Approximation in the Solution of Boltzmann's Equation for Electron Motion

“…Stochastic simulations of the drift velocity and diffusion coefficients were made for the case of a helium-like gas (M= 4a.m.u., qm = 7·oA2) at EIN= 3·036Td. The simulated transport coefficients were in good agreement with the analytic values but it was concluded that the initial spread of the swarm was not accurately described by Huxley's (1972) theory. This conclusion was later justified analytically by Skullerud (1974).…”

“…In the case of constant cross section, for example, the Jones (1975,1976) value of DL/DT (0·58) does not agree either with the result (0,69) obtained by Lucas (1970) or with the result (0·495) obtained independently by Skullerud(1969), Parker and Lowke (1969) and Huxley (1972). In each of these analytic treatments the validity of the two-term approximation was asssumed.…”

A critique of Boltzmann solution methods for calculating the longitudinal diffusion coefficient of electrons in gases

“…There have been controversies regarding previous theoretical work on the quasi-Lorentz gas model, in which only elastic collisions are considered. The equivalent DGE theories of Parker and Lowke (1969), Skullerud (1969Skullerud ( ,1974, Huxley (1972) and Huxley and Crompton (1974) give results which disagree with the Boltzmann solutions of Lucas (1970) and Francey and Jones (1976), and the Monte Carlo results of Lucas and Saelee (1975). The Monte Carlo simulation by Braglia (1977) has helped to clarify the situation by confirming the DGE theories and ascribing the discrepancy observed by Lucas and Saelee (1975) to statistical fluctuations.…”

Electron Transport Coefficients in Carbon Monoxide and Deuterium

“…It can be shown that for most of the experimental conditions used in these experiments (determined by apparatus geometry and stream divergence), the ratio R of the current received by the central circular area of the anode of radius b to the total current is given with sufficient accuracy by (Lowke 1971;Huxley 1972; see also Huxley and Crompton 1974) (3) where h is the cathode-anode separation, d 2 = b 2 + h 2 , and .\ = vdrl2DT. (Note that the dimensions of the two apparatuses and the experimental conditions were chosen so that the electron number density fell to a negligible value well inside the inner diameter of the cylindrical guard structure, obviating the necessity of specifying a radial boundary condition.…”