Comparison of Monte Carlo and Boltzmann calculation of electron diffusion to absorbing electrodes

Abstract

Calculations have been made of the effect of absorbing electrodes on a continuous stream of electrons travelling in a gas in a uniform electric field. The effective electron drift and diffusion coefficients become a complex function of position, so that the electron density distribution is no longer given by the solution of the electron continuity equation using the usual equilibrium drift velocity and either the transverse or the longitudinal diffusion coefficients appropriate to the applied electric field and gas pressure. Calculations for a momentum transfer cross-section proportional to electron speed indicate an increase of the average electron energy of about a factor of two at the anode. Predictions using Monte Carlo methods and solutions of the Boltzmann transport equation are in good agreement. Monte Carlo calculations are also applied to predict the influence of absorbing boundaries on the Townsend-Huxley experiment (1974). Predicted current ratios compared with ratios obtained from a solution of the continuity equation lie between ratios obtained using both isotropic and conventional transverse and longitudinal diffusion coefficients.

Boundary Effects in Solution of Boltzmann's Equation for Electron Swarms

“…The reason is that the mean energy has a length scale characterizing its spatial variation comparable with that of the density. (This is also clear from inspection of the results of Lowke et al 1977;Braglia and Lowke 1979. ) In all the usual derivations of transport coefficients (Huxley and Crompton 1974;Lin et al 1979;Kumar et al 1980), the assumption (either explicit or implicit) is that variations in e are negligible in comparison with variations in n, leading to equations like (81), linearized in the gradient of n.…”

“…This is suggestive of a singularity in the distribution function. Braglia and Lowke (1979) have compared the above method against a Monte Carlo calculation for the model v oc c 2 , with good agreement. This might suggest that the boundary conditions employed by Lowke et ale (1977) are substantially correct or that, for this particular model, the solution is insensitive to the boundary conditions imposed.…”

“…This study, like the previous one by Lowke et al (1977), was performed with a simple geometry. For geometries more appropriate to experiment, the task of solving Boltzmann's equation seems formidable, and here the Monte Carlo simulation technique, already used by Braglia and Lowke (1979), would seem to offer the best prospect for a more thorough understanding of experiment. Still, solutions of Boltzmann's equations are important in their own right and the half-range equations developed in Section 2 should provide a more satisfying means of dealing with boundary effects.…”

The Effect of Diffusion on the Analysis of Pulsed Radiolysis Drift Tube Experiments

“…Elford 1972). It therefore seems unlikely that a more detailed analysis based on a more exact treatment of the role of the boundaries (Braglia and Lowke 1979) would affect the conclusions of this paper.…”

Boundary conditions for the electron kinetic equation using expansion techniques

“…the simplifying assumption that the electric field action and the inhomogeneity of the plasma occur in the same direction [2]. On the other hand, simulation techniques like Monte-Carlo methods [6][7][8][9][10][11] For instance, relations of the form [12][13][14][15] f 0 (r, U ) ∼ f r (r, U ) (1) have been adapted for the analysis of the radial inhomogeneous column plasma of glow discharges, in order to describe absorption and reflection of electrons at the wall of the discharge tube within the framework of the two-term approximation of the expansion of the EMDF in spherical harmonics. Here, f 0 and f r are the isotropic part and the radial contribution to the distribution anisotropy, which depend on the radial position r and the kinetic energy U of the electrons.…”