  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 alpha-effect in non-linear evolution
of the instability.
