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

Aims. We investigate 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 is related to the external field and the differential rotation as H ∝ B 0 i B 0 j Ω i, j. Methods. We do isothermal MHD simulations of a quasi-incompressible media 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. Obviously, differential rotation dΩ/dz only needs an external axial field B 0 to produce remarkable amounts of the helicities. Any regular time-dependency of the helicity could not be found. The resulting axial α-effect α zz 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 α-effect disappear.