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On waves in incompressible Hall magnetohydrodynamics

Published online by Cambridge University Press:  01 October 2007

FOUAD SAHRAOUI ,
SÉBASTIEN GALTIER  and
GÉRARD BELMONT
FOUAD SAHRAOUI
Affiliation:
Centre d'études des Environnements Terrestre et Planétaires, CETP/CNRS-UVSQ, 10–12 avenue de l'Europe, 78140 Vélizy, France (fouad.sahraoui@cetp.ipsl.fr)
SÉBASTIEN GALTIER
Affiliation:
Institut d'Astrophysique Spatiale (IAS)/CNRS-Université Paris-Sud, F-91405 Orsay, France
GÉRARD BELMONT
Affiliation:
Centre d'études des Environnements Terrestre et Planétaires, CETP/CNRS-UVSQ, 10–12 avenue de l'Europe, 78140 Vélizy, France (fouad.sahraoui@cetp.ipsl.fr)
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Abstract

Hall magnetohydrodynamics (HMHD) is a mono-fluid approximation extending the validity domain of the ordinary MHD system to spatial scales down to a fraction of the ion skin depth or frequencies comparable to the ion gyrofrequency. In the paper by Galtier (2006 J. Plasma Physics), an incompressible limit of the HMHD system is used for developing a wave turbulence theory. Nevertheless, the possibility and the consequences of such an approximation are different in HMHD and in MHD. Here, we analyse these differences by investigating the properties of the HMHD equations in the incompressible limit: the existence of linear modes, their dispersion relations and polarizations. We discuss the possibility of replacing the fluid closure equation of a complete HMHD system by an incompressibility hypothesis and determine the validity range.

Type
Papers
Information
Journal of Plasma Physics , Volume 73 , Issue 5 , October 2007 , pp. 723 - 730
Copyright
Copyright © Cambridge University Press 2006

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