The Mathematical Institute, University of Oxford, Eprints Archive

Modelling an isolated dust grain in a plasma using matched asymptotic expansions

Ockendon, J. R. and Arinaminpathy, N. and Allen, J. (2006) Modelling an isolated dust grain in a plasma using matched asymptotic expansions. Plasma Physics . pp. 1-18. (In Press)

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Abstract

The study of dusty plasmas is of significant practical use and scientific interest. A characteristic feature of dust grains in a plasma is that they are typically smaller than the electron Debye distance, a property which we exploit using the technique of matched asymptotic expansions. We first consider the case of a spherical dust particle in a stationary plasma, employing the Allen–Boyd–Reynolds theory, which assumes cold, collisionless ions. We derive analytical expressions for the electric potential, the ion number density and ion velocity. This requires only one computation that is not specific to a single set of dust–plasma parameters, and sheds new light on the shielding distance of a dust grain. The extension of this calculation to the case of uniform ion streaming past the dust grain, a scenario of interest in many dusty plasmas, is less straightforward. For streaming below a certain threshold we again establish asymptotic solutions but above the streaming threshold there appears to be a fundamental change in the behaviour of the system.

Item Type:Article
Subjects:O - Z > Partial differential equations
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:633
Deposited By:John R. Ockendon
Deposited On:27 Jul 2007
Last Modified:20 Jul 2009 14:23

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