Axisymmetric magnetic field modes in heterogeneous domains

Inspired by the setup of the von-K\'arm\'an-Sodium (VKS) dynamo experiment numerical simulations of the kinematic induction equation have been carried out in a cylindrical domain. A localized internal distribution of large relative permeability is considered that represents soft iron material within a conducting fluid flow.

So called paramagnetic pumping at the interface between fluid and soft iron causes a selective enhancement of the axisymmetric azimuthal field component, ultimately leading to a decoupling between poloidal and toroidal magnetic field. For moderate magnetic Reynolds numbers, the poloidal component decays faster than the toroidal part or the simplest non-axisymmetric mode ($m1$). This effect only concerns the necessarily decaying axisymmetric field and does not occur in case of a larger/smaller electrical conductivity.

The phenomenon requires a particular setup e.g. a thin disk-like permeability distribution and remains restricted to the axisymmetric field modes. However, these properties indeed apply to the VKS dynamo.

The separation of poloidal and toroidal modes might be important with regard to mean field dynamo models of the VKS dynamo since the decoupling effectively disrupts the possibility for a closure of the dynamo cycle. However, the separation of the axisymmetric field modes can be prevented by an non-axisymmetric permeability distribution, which might give a hint why dynamo action is absent in experiments where the fluid flow is driven by an impeller system composed of soft iron disks and stainless steel blades.