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Confirmation of the Occurrence of the Hall Instability in the Non-linear Regime

Pons, Jose and Geppert, Ulrich (2010) Confirmation of the Occurrence of the Hall Instability in the Non-linear Regime. Astronomy & Astrophysics, 513 (L12), L12-L16. EDP Sciences. DOI: 10.1051/0004-6361/201014197. ISSN 0004-6361.

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Abstract

Context. The non-linear Hall term present in the induction equation in the electron-magneto-hydrodynamics limit is responsible for the Hall drift of the magnetic field and, in some cases, for the so-called Hall instability. Aims: We investigate whether or not the growth rates and eigenfunctions found in the linear analysis are consistent with the results of non-linear numerical simulations. Methods: Following the linear analysis of Rheinhardt & Geppert, we study the same cases for which the Hall instability was predicted by solving the non-linear Hall induction equation using a two-dimensional conservative and divergence-free finite difference scheme that overcomes intrinsic difficulties of pseudo-spectral methods and can describe situations with arbitrarily high magnetic Reynolds numbers. Results: We show that unstable modes can grow to the level of the background field without being overwhelmed by the Hall cascade, and cause a complete rearrangement of the field geometry. We confirm both the growth rates and eigenfunctions found in the linearized analysis and hence the instability. In the non-linear regime, after the unstable modes grow to the background level, the naturally selected modes become stable and oscillatory. Later on, the evolution tends to select the modes with the longest possible wavelengths, but this process occurs on the magnetic diffusion timescale. Conclusions: We confirm the existence of the Hall instability. We argue against using the misleading terminology that associates the non-linear Hall term with a turbulent Hall cascade, since small-scale structures are not created everywhere. The field evolves instead in a Burgers-like manner, forms local structures with strong gradients which become shocks in the zero resistivity limit, and Hall waves are launched and propagated through the entire dom

Document Type:Article
Title:Confirmation of the Occurrence of the Hall Instability in the Non-linear Regime
Authors:
AuthorsInstitution or Email of Authors
Pons, Josejose.pons@ua.es
Geppert, Ulrichulrich.geppert@dlr.de
Date:April 2010
Journal or Publication Title:Astronomy & Astrophysics
Refereed publication:Yes
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:513
DOI:10.1051/0004-6361/201014197
Page Range:L12-L16
Publisher:EDP Sciences
ISSN:0004-6361
Status:Published
Keywords:magnetohydrodynamics (MHD), stars: neutron, stars: magnetic field, stars: evolution
HGF - Research field:Aeronautics, Space and Transport (old)
HGF - Program:Space (old)
HGF - Program Themes:W - no assignement
DLR - Research area:Space
DLR - Program:W - no assignement
DLR - Research theme (Project):W -- no assignement (old)
Location: Berlin-Adlershof
Institutes and Institutions:Institute of Space Systems
Deposited By: Prof. Dr.rer.nat. habil. Ulrich Geppert
Deposited On:21 Dec 2010 15:24
Last Modified:12 Dec 2013 21:09

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