Hostname: page-component-7479d7b7d-t6hkb Total loading time: 0 Render date: 2024-07-13T19:12:14.775Z Has data issue: false hasContentIssue false
  • English
  • Français

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 (nim.pathy@zoo.ox.ac.uk)
J. E. ALLEN
Affiliation:
OCIAM, Mathematical Institute, Oxford OX1 3LB, UK (nim.pathy@zoo.ox.ac.uk)
J. R. OCKENDON
Affiliation:
OCIAM, Mathematical Institute, Oxford OX1 3LB, UK (nim.pathy@zoo.ox.ac.uk)
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Selwyn, G. S., Haller, K. L. and Heidenreich, J. E. 1991 Rastered laser light scattering studies during plasma processing: particle contamination trapping phenomena. J. Vac. Sci. Technol. A 9, 2824.CrossRefGoogle Scholar
[2]Selwyn, G. S., Singh, J. and Bennett, R. S. 1989 In situ laser diagnostic studies of plasma generated particle contamination. J. Vac. Sci. Technol. A 7, 2758.CrossRefGoogle Scholar
[3]Roca, i Cabarrocas J. 2000 Plasma enhanced chemical vapor deposition of amorphous, polymorphous and microcrystalline silicon films. J. Non-Cryst. Solids 266, 31.CrossRefGoogle Scholar
[4]Boufendi, L. and Bouchoule, A. 2002 Industrial developments of scientific insights in dusty plasmas. Plasma Sources Sci. Technol. 11, A211.CrossRefGoogle Scholar
[5]Goertz, C. K. 1989 Dusty plasmas in the solar system. Rev. Geophys. 27, 271.CrossRefGoogle Scholar
[6]Hartquist, T. W., Havnes, O. and Morfill, G. E. 2003 The effects of charged dust on Saturn's rings. Astron. Geophys. 44 (5), 5.26.CrossRefGoogle Scholar
[7]Fortov, V. E., Ivlev, A. V., Khrapak, S. A., Khrapak, A. G. and Morfill, G. E. 2005 Complex (dusty) plasmas: current status, open issues, perspectives. Phys. Rep. 421, 1.CrossRefGoogle Scholar
[8]Konopka, U., Morfill, G. E. and Ratke, L. 2000 Measurement of the interaction potential of microspheres in the sheath of a RF discharge. Phys. Rev. Lett. 84, 891.CrossRefGoogle ScholarPubMed
[9]Konopka, U., Ratke, L. and Thomas, H. M. 1997 Central collisions of charged dust particles in a plasma. Phys. Rev. Lett. 79, 1269.CrossRefGoogle Scholar
[10]Lapenta, G. 2002 Nature of the force field in plasma wakes. Phys. Rev. E 66, 026409-1.Google ScholarPubMed
[11]Hutchinson, I. 2005 Ion collection by a sphere in a flowing plasma: 3. Floating potential and drag force. Plasma Phys. Control. Fusion 47, 71.CrossRefGoogle Scholar
[12]Kennedy, R. V. and Allen, J. E. 2002 The floating potential of spherical probes and dust grains. Part 1. Radial motion theory. J. Plasma Phys. 57, 243.CrossRefGoogle Scholar
[13]Kennedy, R. V. and Allen, J. E. 2003 The floating potential of spherical probes and dust grains II: Orbital motion theory. J. Plasma Phys. 69, 485.CrossRefGoogle Scholar
[14]Van, Dyke M. D. 1975 Perturbation Methods in Fluid Mechanics. Stanford, CA: Parabolic Press.Google Scholar
[15]Annaratone, B. M., Allen, M. W. and Allen, J. E. 1992 Ion currents to cylindrical Langmuir probes in RF plasmas. J. Phys. D: Appl. Phys. 25, 417.CrossRefGoogle Scholar
[16]Swift, J. D. and Schwar, M. J. R. 1970 Electrical Probes for Plasma Diagnostics. London: Iliffe.Google Scholar
[17]Allen, J. E., Boyd, R. L. F. and Reynolds, P. 1957 The collection of positive ions by a probe immersed in a plasma. Proc. Phys. Soc. London B 70, 297.Google Scholar
[18]Arinaminpathy, N., Allen, J. E. and Ockendon, J. R. 2005 On the effect of isolated dust grains in a plasma. DPhil, Oxford.Google Scholar
[19]Chapman, S. and Cowling, T. G. 1970 The Mathematical Theory of Non-uniform Gases. Cambridge: Cambridge University Press.Google Scholar
[20]Edwards, C., Howison, S., Ockendon, J. R. and Ockendon, H. 2005 Hypercritical shallow water flows. DPhil, Oxford.Google Scholar
[21]Hinch, E. J. 1991 Perturbation Methods (Cambridge Texts in Applied Mathematics). Cambridge: Cambridge University Press.Google Scholar