EDP Sciences
Free Access
Volume 479, Number 2, February IV 2008
Page(s) L33 - L36
Section Letters
DOI https://doi.org/10.1051/0004-6361:20077781

A&A 479, L33-L36 (2008)
DOI: 10.1051/0004-6361:20077781


Helicity generation and ${\alpha}$-effect by Tayler instability with z-dependent differential rotation

M. Gellert, G. Rüdiger, and D. Elstner

Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany
    e-mail: [mgellert;gruediger;delstner]@aip.de

(Received 3 May 2007 / Accepted 22 December 2007)

Aims.We investigate the instability of toroidal magnetic fields resulting from the action of z-dependent differential rotation on a given axial field $\vec B^0$ in a cylindrical enclosure where, in particular, the helicity of the resulting nonaxisymmetric flow is of interest. We probe the idea that helicity is related to the external field and the differential rotation as ${\cal H} \propto B^0_i\, B^0_j\, {\Omega}_{i,j}$.
Methods.We conduct isothermal magnetohydrodynamic simulations of a quasi-incompressible medium with finite viscosity and conductivity in a perfectly conducting container, and analyze both the kinematic and current helicity of the resulting field by regarding the nonaxisymmetric parts of the field as fluctuations.
Results.The observed instability leads to a nonaxisymmetric solution with dominating mode m=1. With the onset of instability, both kinematic and current helicity are produced which fulfill the suggested relation ${\cal H} \propto B^0_i\, B^0_j\, {\Omega}_{i,j}$. Obviously, differential rotation $\mathrm{d}{\Omega}/\mathrm{d}z$ only needs an axial field B0z to produce significant helicity. Any regular time-dependency of the helicity could not be found. The resulting axial ${\alpha}$-effect $\alpha_{zz}$ is mainly due to the current helicity, the characteristic time scale between both the values is of the order of the rotation time. If the axial field is switched off, then the helicity and the ${\alpha}$-effect disappear, and a dynamo is not observed.

Key words: magnetohydrodynamics (MHD)

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