Hostname: page-component-77c89778f8-swr86 Total loading time: 0 Render date: 2024-07-23T11:28:47.019Z Has data issue: false hasContentIssue false
  • English
  • Français

The gravitational interchange instability for perpendicular density gradients

Published online by Cambridge University Press:  13 March 2009

R. B. Paris
R. B. Paris
Affiliation:
Department of Mathemetical and Computer Sciences, Dundee Insitute of Technology, Dundee DD1 1HG, U.K.
Get access Rights & Permissions [Opens in a new window]

Abstract

The analouge of the Reyleigh–Taylor instability (the gravitational interchange mode) for an infinitely conducting, approximately one-dimensional plane plasma slab is examined when the gravitational acceleration g is taken to be perpendicular to the equalibrium density gradient δp0. In contrast with the ‘classical’ situation (where g is aligned with δp0), it is found for a current layer with Magnetic shear that there is no instability threshold equivalent to the ‘classical’ situation (where g is aligned with δp0), it is found for a current layer with magnetic shear that there is no instability threshold equivalent to the Suydam criterion: the mode is unstable for all values of |δp0|. In the weak shear limit the growth rate of the instability is shown to exhibit the familiar (g|δp0|/p0)img; scaling characteristic of the gravitational interchange mode.

Type
Research Article
Information
Journal of Plasma Physics , Volume 49 , Issue 1 , February 1993 , pp. 85 - 100
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

Abramowitz, M. 1949 J. Math. & Phys. 28, 195.CrossRefGoogle Scholar
Bernstein, I. B., Frieman, E. A., Kruskal, M. D. & Kulsrud, R. M. 1958 Proc. B. Soc. Lond. A 244, 17.Google Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Furth, H. P., Killeen, J. & Rosenbluth, M. N. 1963 Phys. Fluids. 6, 459.CrossRefGoogle Scholar
Galindo-Trejo, J. & Schindler, K. 1984 Astrophys. J.. 277, 422.CrossRefGoogle Scholar
Heading, J. 1962 An Introduction to Phase Integral Methods. Methuen.Google Scholar
Heading, J. 1973 J. Phys.. A 6, 958.Google Scholar
Kippenhahn, R. & Schlüter, A. 1957 Z. Astrophys.. 43, 36.Google Scholar
Migliuolo, S. 1982 J. Geophys. Res. 87, 8057.CrossRefGoogle Scholar
Morse, P. & Feshbach, H. 1953 Methods of Theoretical Physics. McGraw-Hill.Google Scholar
Olver, F. W. J. 1975 Phil. Trans. R. Soc. Lond. A 278, 137.Google Scholar
Paris, R. B. 1987 a Phys. Fluids. 30, 102.CrossRefGoogle Scholar
Paris, R. B. 1987 b Euratom–CEA Report EUR-CEA FC 1314.Google Scholar
Paris, R. B., Auby, N. & Dagazian, R. Y. 1986 J. Math. Phys. 27, 2188.CrossRefGoogle Scholar
Schiff, L. I. 1968 Quantum Mechanics. McGraw-Hill.Google Scholar
Tayler, R. J. 1973 Mon. Not. R. Astron. Soc. 161, 365.CrossRefGoogle Scholar
Yoshikawa, S. & White, R. B. 1980 Phys. Fluids. 23, 791.CrossRefGoogle Scholar
Zweibel, E. G. 1982 Astrophys. J. Lett. 258, L53.CrossRefGoogle Scholar