Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T13:38:31.520Z Has data issue: false hasContentIssue false
  • English
  • Français

The drift-wave dispersion equation revisited

Published online by Cambridge University Press:  13 March 2009

R. Balescu ,
E. Vanden Eijnden  and
B. Weyssow
R. Balescu
Affiliation:
Association EURATOM-Etat Belge, Service de Physique Statisque, Plasma et Optique Non-Linéaire C.P. 231, Université Libre de Bruxelles, Campus Plaine, B-1050 Bruxelies, Belgium
E. Vanden Eijnden
Affiliation:
Association EURATOM-Etat Belge, Service de Physique Statisque, Plasma et Optique Non-Linéaire C.P. 231, Université Libre de Bruxelles, Campus Plaine, B-1050 Bruxelies, Belgium
B. Weyssow
Affiliation:
Association EURATOM-Etat Belge, Service de Physique Statisque, Plasma et Optique Non-Linéaire C.P. 231, Université Libre de Bruxelles, Campus Plaine, B-1050 Bruxelies, Belgium
Get access Rights & Permissions [Opens in a new window]

Abstract

In view of some difficulties that appeared in previous work, the drift-wave dispersion equation has been studied in great detail by stressing some features that are not discussed in the usual textbook presentations. It is shown that any analytical approximation of a plasma dispersion equation leads to a singular perturbation problem for the roots of an algebraic equation. This property is associated with a number of parasitic roots, which can be identified and eliminated from the start. The behaviour of the remaining physical roots is discussed in detail by defining characteristic regions in the parameter space spanned by the gradients of density, electron and ion temperatures. Whereas in a large domain the usual behaviour predicted by elementary drift-wave theory is recovered, it is shown that there exists a region (whose existence is not predicted by elementary theory), where the conditions of existence of a drift wave are violated, thus causing the appearance of the (spurious) singularity previously found by Balescu. The explanation of this paradoxical situation is discussed in detail. The smooth connection of these results with the limit of a spatially homogeneous plasma is considered in an appendix.

Type
Research Article
Information
Journal of Plasma Physics , Volume 50 , Issue 3 , December 1993 , pp. 425 - 444
Copyright
Copyright © Cambridge University Press 1993

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

Balescu, R. 1992 Phys. Fluids B 4, 91.CrossRefGoogle Scholar
Fried, B. D. & Conte, S. B. 1961 The Plasma Dispersion Function. Academic.Google Scholar
Fried, B. B. & Gould, R. W. 1961 Phys. Fluids 4, 139.CrossRefGoogle Scholar
Galeev, S., Oraevskii, V. N. & Sagdeev, R. Z. 1963 Soviet Phys. JETP 17, 615.Google Scholar
Gary, S. P. & Sanderson, J. J. 1978 Phys. Fluids 21, 1181.CrossRefGoogle Scholar
Gary, S. P. & Sanderson, J. J. 1979 Phys. Fluids 22, 1500.CrossRefGoogle Scholar
Gary, S. P. & Abraham-Shrauner, B. 1981 J. Plasma Phys. 25, 145.CrossRefGoogle Scholar
Ichimaru, S. 1973 Basic Principles of Plasma Physics: A Statistical Approach. Benjamin.Google Scholar
Kadomtsev, B. B. 1965 Plasma Turbulence. Academic.Google Scholar
Krall, N. A. & Trivelpiece, A. W. 1973 Principles of Plasma Physics. McGraw-Hill. (Reprinted 1986, San Francisco Press.)CrossRefGoogle Scholar
Rutherford, P. H. & Frieman, E. A. 1968 Phys. Fluids 11, 569.CrossRefGoogle Scholar
Taylor, J. B. & Hastie, R. J. 1968 Plasma Phys. 10, 479.CrossRefGoogle Scholar