Nonlinear stability in anisotropic magnetohydrodynamics

  • John M. Finn
  • Guo-Zheng Sun
A. Classical Nonlinear Dynamics and Chaos
Part of the Lecture Notes in Physics book series (LNP, volume 278)


Formal stability, i.e., positive energy linear stability, and nonlinear stability are defined. The generic way in which a system with infinite degrees of freedom may be nonlinearly unstable in spite of formal stability is illustrated. The “energy-Casimir” method of proof of nonlinear stability is applied to “relaxed states” of anisotropic magnetohydrodynamics (MHD). Such states are consistent with ergodic magnetic field lines and are formally stable under mild restrictions. Specifically, there is no free energy to drive interchange modes. Nonlinear stability is guaranteed under somewhat more restrictive conditions than is formal stability.


Poisson Bracket General Entropy Formal Stability Nonlinear Stability Magnetic Helicity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. Holm, J. Marsden, T. Ratiu, and A. Weinstein, Phys. Rep. 123, 1 (1985).ADSCrossRefGoogle Scholar
  2. 2.
    V. I. Arnold, Am. Math. Soc. Trans. 19, 267 (1969).Google Scholar
  3. 3.
    See, for example, R. Littlejohn, All-Conference Proceedings No. 88, 47 (1981).ADSGoogle Scholar
  4. 4.
    J. Finn and T. Antonsen, Jr., Phys. Fluids 26, 3540 (1983).ADSCrossRefGoogle Scholar
  5. 5.
    P. Morrison and J. Greene, Phys. Rev. Lett. 45, 790 (1980).ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    G. Sun and J. Finn, to be submitted to Phys. Fluids.Google Scholar
  7. 7.
    C. Grebogi, E. Ott, J. Yorke, these proceedings, Fig. Ia.Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • John M. Finn
    • 1
  • Guo-Zheng Sun
    • 1
  1. 1.University of MarylandCollege Park

Personalised recommendations