Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-06T08:16:53.499Z Has data issue: false hasContentIssue false
  • English
  • Français

Stabilizing and destabilizing influence of the Hall effect in a Z pinch with a step-like volume current profile

Published online by Cambridge University Press:  13 March 2009

Ulrich Schaper
Ulrich Schaper
Affiliation:
Institut für Theoretische Physik, Universität Düsseldorf, West Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

A dispersion relation is derived for axisymmetric perturbations of an infinitely extended circular incompressible Z pinch with a step-like volume current profile. This profile is characterized by constant but different volume currents in different regions of the plasma and at the step surface there is a sheet current. The stability boundaries are shifted compared with stability limits in ideal MHD theory. For equilibria with no current reversal there is a new stable range whereas for equilibria with current reversal there is a new unstable range. The number of solutions of the dispersion relation depends on the equilibrium. The behaviour of the eigenvalues near the stability boundaries is treated in accordance with bifurcation theory.

Type
Research Article
Information
Journal of Plasma Physics , Volume 30 , Issue 1 , August 1983 , pp. 169 - 178
Copyright
Copyright © Cambridge University Press 1983

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

REFERENCES

Abbamowitz, M. & Stegun, I. A. 1970 Handbook of Mathematical Functions. Dover.Google Scholar
Roos, B. W. 1969 Analytic Functions and Distributions in Physics and Engineering. Wiley.Google Scholar
Schaper, U. 1983 J. Plasma Phys. 29, 1.CrossRefGoogle Scholar
Schram, P. P. J. M. & Tasso, H. 1967 Nucl. Fusion, 7, 91.CrossRefGoogle Scholar
Tasso, H. & Schram, P. P. J. M. 1966 Nucl. Fusion, 6, 284.CrossRefGoogle Scholar
Van Kampen, N. G. 1955 Physica, 21, 949.CrossRefGoogle Scholar
Wainberg, M. M. & Trenogin, W. A. 1973 Theorie der Lösungsverzweigung bei nichtlinearen Gleichungen. Akademie-Verlag.Google Scholar