Helicity generation and alpha-effect by Vandakurov-Tayler instability with z-dependent differential rotation

TL;DR

This study uses isothermal MHD simulations to explore how z-dependent differential rotation induces helicity and alpha-effect via Vandakurov-Tayler instability, highlighting the role of external axial fields in helicity generation.

Contribution

It demonstrates that differential rotation combined with an external axial magnetic field can produce helicity and alpha-effect through Vandakurov-Tayler instability, with a specific relation between helicity and the external field.

Findings

Helicity and alpha-effect are generated by the instability.

Helicity relates to external magnetic field and differential rotation.

Helicity and alpha-effect vanish when the external field is removed.

Abstract

We investigate in isothermal MHD simulations the instability of toroidal magnetic fields resulting by the action of z-dependent differential rotation on a given axial field B^0 in a cylindrical enclosure where in particular the helicity of the resulting nonaxisymmetric flow is of interest. The idea is probed that helicity H is related to the external field and the differential rotation as H ~ B^0_i B^0_j Omega_i,j. 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. Obviously, differential rotation dOmega/dz only needs an external axial field B^0_z to produce remarkable amounts of the helicities. Any regular time-dependency of the helicity could not be found. The resulting axial alpha-effect is mainly due to the current helicity, the characteristic time scale between both the values is of order of the rotation time. If the axial field is switched off then the helicity and the alpha-effect disappear.