The pinch-type instability of helical magnetic fields

¹ Leibniz-Institut für Astrophysik Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany
e-mail: mschultz@aip.de; delstner@aip.de
² Helmholtz-Zentrum Dresden-Rossendorf, PO Box 510119, 01314 Dresden, Germany
e-mail: gruediger@aip.de

Received: 23 August 2010
Accepted: 20 February 2011

Abstract

The current-driven instability of toroidal magnetic fields under the influence of both axial magnetic-field components and (differential) rotation is studied. The MHD equations are solved by means of a simplified model with cylindric geometry that assumes both the axial field and the axial current as uniform and the fluid as incompressible. If azimuthal and axial field components are nearly the same size, then the instability is (slightly) supported, and modes with m > 1 dominate. If the axial field dominates, then the most unstable modes again have m > 1, but the field is strongly stabilized. The modes are suppressed by a fast rigid rotation where the m = 1 mode maximally resists. Only this mode becomes best re-animated for Ω > Ω_A (Ω_A the Alfvén frequency) if the rotation has a negative shear. The general finding of the linear theory is that the higher modes with m > 1 do not play an important role for the stability of rotating fluids. If applied to dynamo-generated galactic magnetic fields influenced by the typical rotation law with constant azimuthal velocity, the result is that galactic fields should only be marginally unstable against perturbations with m ≤ 1. Modes with higher m may not appear. The corresponding growth rates are close to the rotation period of the inner part of the galaxy.