This study is concerned with the early evolution of magnetic fields and differential rotation of intermediate-mass stars which may evolve into Ap stars. We report on simulations of the interplay of differential rotation and magnetic fields, the stability limits and non-linear evolution of such configurations, and the prospects of dynamo action from the unstable cases. The axisymmetric problem delivers a balance between field amplification and back-reaction of the magnetic field on the differential rotation. The non-axisymmetric case involves also the Tayler instability of the amplified toroidal fields. We consider limits for field amplification and apply these to young A stars.
Apart from its application to Ap stars, the instability is scrutinized for the fundamental possibility of a dynamo. We are not looking for a dynamo as an explanation for the Ap star phenomenon. The kinetic helicity is concentrated near the tangent cylinder of the inner sphere of the computational domain and is negative in the Northern hemisphere. This appears to be a ubiquitous effect not special to the Tayler instability. The latter is actually connected with a positive current helicity in the bulk of the spherical shell giving rise to a small, but non-vanishing α-effect in non-linear evolution of the instability.