Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T14:38:07.040Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ([email protected])
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 ([email protected])
Get access Rights & Permissions [Opens in a new window]

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

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

Balbus, S. A. and Terquem, C. 2001 Linear analysis of the Hall effect in protostellar disks Astrophys. J. 552, 235–247.CrossRefGoogle Scholar
Bhattacharjee, A. 2004 Impulsive magnetic reconnection in the Earth's magnetotail and the solar corona Annu. Rev. Astron. Astrophys. 42, 365–384.CrossRefGoogle Scholar
Birn, J., Galsgaard, K., Hesse, M., Hoshino, M., Huba, J., Pritchett, P. L., Shindler, K., Yin, L., Buchner, J., Neukirch, T. and Priest, E. R. 2005 Forced magnetic reconnection. Geophys. Res. Lett. 32, doi: 10.1029/2004GL022058.CrossRefGoogle Scholar
Cumming, A., Arras, P. and Zweibel, E. 2004 Magnetic field evolution in neutron star crusts due to the Hall effect and ohmic decay Astrophys. J. 609, 999–1017.CrossRefGoogle Scholar
Fitzpatrick, R. 2004 Scaling of forced magnetic reconnection in the Hall-magnetohy-drodynamic problem. Phys. Plasmas 11, 937–946.CrossRefGoogle Scholar
Galtier, S. 2006 Wave turbulence in incompressible Hall MHD. J. Plasma Physics 72 (5), 721–769.CrossRefGoogle Scholar
Galtier, S. and Bhattacharjee, A. 2003 Anisotropic weak whistler wave turbulence in electron magnetohydrodynamics. Phys. Plasmas 10, 3065–3076.CrossRefGoogle Scholar
Galtier, S., Nazarenko, S., Newell, A. C. and Pouquet, A. 2000 A weak turbulence theory for incompressible magnetohydrodynamics. J. Plasma Physics 63, 447–488.CrossRefGoogle Scholar
Ghosh, S. and Goldstein, M. L. 1997 Anisotropy in Hall MHD turbulence due to a mean magnetic field. J. Plasma Physics 57, 129–154.CrossRefGoogle Scholar
Huba, J. D. 1995 Hall magnetohydrodynamics in space and laboratory plasmas. Phys. Plasmas 2 (6), 2504–2513.CrossRefGoogle Scholar
Krishan, V. and Mahajan, S. M. 2005 Modeling of short scale turbulence in the solar wind Nonlin. Proc. Geophys. 359, L27–L29.Google Scholar
Mininni, P. D., Gómez, D. O. and Mahajan, S. M. 2003 Dynamo action in magnetohydro-dynamics and Hall-magnetohydrodynamics. Astrophys. J. 587, 472–481.CrossRefGoogle Scholar
Ohsaki, S. and Mahajan, S. M. 2004 Hall current and Alfvén wave. Phys. Plasma 11, 898.CrossRefGoogle Scholar
Sahraoui, F., Belmont, G., Pinçcon, J. L., Rezeau, L., Balogh, A., Robert, P. and Cornilleau-Wehrlin, N. 2004 Magnetic turbulent spectra in the magnetosheath: new insights. Ann. Geophys. 22, 2283–2288.CrossRefGoogle Scholar
Sahraoui, F., Belmont, G. and Rezeau, L. 2003 Hamiltonian canonical formulation of Hall MHD: toward an application to weak turbulence. Phys. Plasmas 10, 1325–1337.CrossRefGoogle Scholar
Vaivads, A., Khotyaintsev, Y., André, M., Horbury, T., Retinò, A., Buchert, S. C., Rogers, B. N., Décréau, P., Paschmann, G. and Phan, T. D. 2004 Structure of magnetic diffusion region from four-spacecraft observations. Phys. Rev. Lett. 93, 105001.CrossRefGoogle ScholarPubMed