Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-07-03T06:12:06.188Z Has data issue: false hasContentIssue false
  • English
  • Français

An inhomogeneous plasma equilibrium: asymptotic self-similar solutions

Published online by Cambridge University Press:  13 March 2009

E. Saiz ,
J. Gutierrez  and
Y. Cerrato
E. Saiz
Affiliation:
Departamento de Fisica, Universidad de Alcalá de Henares, Madrid, Spain
J. Gutierrez
Affiliation:
Departamento de Fisica, Universidad de Alcalá de Henares, Madrid, Spain
Y. Cerrato
Affiliation:
Departamento de Fisica, Universidad de Alcalá de Henares, Madrid, Spain
Get access Rights & Permissions [Opens in a new window]

Abstract

A perfectly conducting hot plasma in thermodynamic equilibrium is studied without taking account of the effects of collisions and viscosity. The medium is inhomogeneous, unbounded, axisymmetric and subject to a magnetic field B0 parallel to the axis of symmetry of the cylinder. Plasma equilibrium is investigated using a magnetohydrodynamic model, and the system of equations is closed with an equation of state corresponding to the adiabatic law for an ideal gas. Transformation groups are applied to generate asymptotic selfsimilar solutions for the density, pressure and magnetic field magnitudes on the equilibrium, and thus to obtain the spatial dependence of the invariant solutions since the temporal variable is eliminated. From consideration of the nature of these solutions, necessary conditions for equilibria in finite inhomogeneous media are obtained. Results are given for inhomogeneous media with finite conductivity. The degrees of inhomogeneity for pressure and density and their relations with dimensionless constants, arising from the group parameters, provide information on certain drastic changes in equilibrium temperature profiles.

Type
Research Article
Information
Journal of Plasma Physics , Volume 47 , Issue 3 , June 1992 , pp. 491 - 503
Copyright
Copyright © Cambridge University Press 1992

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

Bluman, G. W. 1974 Q. Appl. Maths 31, 403.CrossRefGoogle Scholar
Bluman, G. W. & Cole, J. D. 1974 Similarity Methods for Differential Equations. Springer.CrossRefGoogle Scholar
Bluman, G. W. & Kumei, S. 1980 J. Math. Phys. 21, 1019.CrossRefGoogle Scholar
Burgan, J. R., Feix, M. R., Fijalkov, E., Gutierrez, J. & Munier, A. 1978 a Applied Inverse Problems (ed. Sabatier, P. C.), p. 248 (Lecture Notes in Physics, vol. 85). Springer.CrossRefGoogle Scholar
Burgan, J. R., Gutierrez, J., Fijalkov, E., Navet, M. & Feix, M. R. 1978 b J. Plasma Phys. 19, 135.CrossRefGoogle Scholar
Cerrato, Y., Gutierrez, J. & Ramos, M. 1989 J. Phys. A 22, 419.Google Scholar
Chen, F. F. 1974 Introduction to Plasma Physics, p. 179. Plenum.Google Scholar
Dresner, L. 1988 Math. Comput. Modelling 11, 531.CrossRefGoogle Scholar
Feix, M. R., Bouquet, S. & Lewis, H. R. 1987 Physica 28 D, 80.Google Scholar
Fuchs, J. C. & Richter, E. W. 1987 J. Phys. A 20, 3135.Google Scholar
Gutierrez, J., Munier, A., Burgan, J. R., Feix, M. R., Fijalkov, E. 1979 Nonlinear Problems in Theoretical Physics: Proceedings of the IX GIFT International Seminar on Theoretical Physics, Jaca, Huesca, Spain, June 1978 (ed. Ranada, A.), p. 151 (Lecture Notes in Physics, vol. 98). Springer.CrossRefGoogle Scholar
Melrose, D. B. 1986 Instabilities in Space and Laboratory Plasmas, p. 127. Cambridge University Press.CrossRefGoogle Scholar
Moraux, M., Fijalkov, E. & Feix, M. R. 1981 J. Phys. A 14, 1611.Google Scholar
Olver, P. 1986 Applications of Lie Groups to Differential Equations. Springer.CrossRefGoogle Scholar
Ovsjannikov, L. V. 1962 Group Properties of Differential Equations. California Institute of Technology.Google Scholar
Thompson, W. B. 1962 An Introduction to Plasma Physics, p. 43. Addison-Wesley.CrossRefGoogle Scholar
Velikovich, A. L. & Liberman, M. A. 1985 Soviet Phys. JETP 62, 694.Google Scholar