Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-29T15:12:35.610Z Has data issue: false hasContentIssue false
  • English
  • Français

Clebsch representations in the theory of minimum energy equilibrium solutions in magnetohydrodynamics

Published online by Cambridge University Press:  13 March 2009

Hanno Rund ,
Daniel R. Wells  and
Lawrence Carl Hawkins
Hanno Rund
Affiliation:
Department of Mathematics, University of Arizona, Tucson, Arizona 85721
Daniel R. Wells
Affiliation:
Department of Physics, University of Miami, Coral Gables, Florida 33124
Lawrence Carl Hawkins
Affiliation:
Department of Physics, University of Miami, Coral Gables, Florida 33124
Get access Rights & Permissions [Opens in a new window]

Abstract

The introduction of Clebsch representations allows one to formulate the problem of finding minimum energy solutions for a magneto-fluid as a well-posed problem in the calculus of variations of multiple integrals. When the latter is subjected to integral constraints, the Euler–Lagrange equations of the resulting isoperimetric problem imply that the fluid velocities are collinear with the magnetic field. If, in particular, one constraint is abolished, Alfvén velocities are obtained. In view of the idealized nature of the model treated here, further investigations of more sophisticated structures by means of Clebsch representations are anticipated. Preliminary results of a similar calculation utilizing a modified two fluid model are discussed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 20 , Issue 3 , December 1978 , pp. 329 - 344
Copyright
Copyright © Cambridge University Press 1978

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

Bateman, H. 1929 Proc. R. Soc. A 125, 598.Google Scholar
Bateman, H. 1930 Proc. Nat. Acad. Sci. U.S.A. 16, 816.Google Scholar
Bernstein, I. B., Frieman, E. A., Kruskal, M. D. & Kulsrud, R. M. 1958 Proc. Roy. Soc. A 244, 17.Google Scholar
Chandrasekhar, S. & Woltjer, L. 1958 Proc. Nat. Acad. Sci. U.S.A. 44, 285.Google Scholar
Eckart, C. 1960 Phys. Fluids, 3, 421.Google Scholar
Kippenhahn, R. & Möllenhoff, C. 1975 Plasmaphysik. Bibliographisches Institut, Zürich.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th ed.Cambridge University Press.Google Scholar
Rund, H. 1972 Utilitas Math. 1, 157.Google Scholar
Rund, H. 1973 The Hamilton–Jacobi Theory in the Calculus of Variations, augemented and revised reprint. Krieger Publications.Google Scholar
Rund, H. 1976 Topics in Differential Geometry (ed. Rund, H. and Forbes, W. F.). Academic.Google Scholar
Rund, H. 1977 Math. Phys. 18 84.Google Scholar
Rund, H. 1978 Arch. Rat. Mech. Anal., 67 305.Google Scholar
Seliger, R. L. & Whitham, G. B. 1968 Proc. R. Soc. A 305, 1.Google Scholar
Taylor, J. B 1974 Phys. Rev. Lett. 33, 1139.Google Scholar
Wells, D. R. 1970 J. Plasma Phys. 4 645.Google Scholar
Wells, D. R. 1976 Pulsed High Beta Plasmas (ed. Evans, D. E.). Pergamon.Google Scholar
Wells, D. R. & Norwood, J. Jr, 1968 J. Plasma Phys. 11 1582.Google Scholar
Weyl, H. 1935 Ann. Math. (2) 36, 607.Google Scholar
Woltjer, L. 1958 Proc. Nat. Acad. Sci. U.S.A. 44, 489.Google Scholar
Woltjer, L. 1960 Rev. Mod. Phys. 32 914.Google Scholar