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On the most probable states of two-dimensional plasmas

Published online by Cambridge University Press:  13 March 2009

C. E. Seyler
C. E. Seyler
Affiliation:
School of Electrical Engineering, Cornell University, Ithaca, New York 14853-3801, USA
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Abstract

The Charney-Hasegawa-Mima equation and two-dimensional magnetohydrodynamics (MHD) have ideal Lagrangian invariants that are used as the basis for most probable state analysis. An information-theoretic entropy defined in terms of the Lagrangian invariants leads to predictions for relationships between the field quantities. These relationships are tested through numerical solution of the equations through the turbulent relaxation of random initial conditions to coherent states. It is found that the predictions for the most probable state for the Charney—Hasegawa—Mima equation are essentially correct, whereas for two-dimensional MHD they are not. Questions and issues are raised pertaining to why a most probable state analysis based upon Lagrangian invariants seems to work in the case of the Charney—Hasegawa—Mima equation but not for two-dimensional MHIJ. A qualitatively correct entropy is proposed for two-dimensional MHD based upon field variables that are not local invariants.

Type
Research Article
Information
Journal of Plasma Physics , Volume 56 , Issue 3: Special Issue: Honour of David Montgomery , December 1996 , pp. 553 - 567
Copyright
Copyright © Cambridge University Press 1996

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