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

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

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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

Titel:Confirmation of the Occurrence of the Hall Instability in the Non-linear Regime
AutorenInstitution oder E-Mail-AdresseAutoren-ORCID
Pons, Josejose.pons@ua.esNICHT SPEZIFIZIERT
Geppert, Ulrichulrich.geppert@dlr.deNICHT SPEZIFIZIERT
Datum:April 2010
Erschienen in:Astronomy & Astrophysics
Referierte Publikation:Ja
In Open Access:Nein
In ISI Web of Science:Ja
DOI :10.1051/0004-6361/201014197
Verlag:EDP Sciences
Stichwörter:magnetohydrodynamics (MHD), stars: neutron, stars: magnetic field, stars: evolution
HGF - Forschungsbereich:Verkehr und Weltraum (alt)
HGF - Programm:Weltraum (alt)
HGF - Programmthema:W - keine Zuordnung
DLR - Schwerpunkt:Weltraum
DLR - Forschungsgebiet:W - keine Zuordnung
DLR - Teilgebiet (Projekt, Vorhaben):W - keine Zuordnung (alt)
Standort: Berlin-Adlershof
Institute & Einrichtungen:Institut für Raumfahrtsysteme
Hinterlegt von: Geppert, Prof. Dr.rer.nat. habil. Ulrich
Hinterlegt am:21 Dez 2010 15:24
Letzte Änderung:06 Okt 2016 12:01

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