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

Published online by Cambridge University Press:  01 October 2007

N. ARINAMINPATHY ,
J. E. ALLEN  and
J. R. OCKENDON
N. ARINAMINPATHY
Affiliation:
OCIAM, Mathematical Institute, Oxford OX1 3LB, UK ([email protected])
J. E. ALLEN
Affiliation:
OCIAM, Mathematical Institute, Oxford OX1 3LB, UK ([email protected])
J. R. OCKENDON
Affiliation:
OCIAM, Mathematical Institute, Oxford OX1 3LB, UK ([email protected])
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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.

Type
Papers
Information
Journal of Plasma Physics , Volume 73 , Issue 5 , October 2007 , pp. 793 - 810
Copyright
Copyright © Cambridge University Press 2006

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