Towards an understanding of the Von-Karman-Sodium dynamo experiment

Numerical simulations of kinematic dynamo action have been carried out in a setup that resembles the configuration of the Von-Karman-Sodium (VKS) dynamo experiment. The results show that the high permeability domains introduced by soft iron impellers essentially determine the field generation process and are also responsible for the selection of the dominating azimuthal dynamo mode.

The material heterogeneity within the fluid give rise to three distinct effects that may influence the dynamo process. In addition to the local decrease of the magnetic diffusivity eta=(mu_0\mu_r\sigma)^(-1) so called paramagnetic pumping occurs which is proportional to the gradient of the permeability and describes the suction of magnetic field into domains with high permeability. Beside the modifications of the induction equation itself, jump conditions of the magnetic field (respectively the electric field) are enforced on the material interfaces between fluid and impellers. These jump conditions and the pumping term are responsible for the distinct behavior of high conducting(i.g. copper) and soft iron impellers.

At reasonable values for the magnetic Reynolds number (i.e around Rm=30) and rather moderate permeability (around values of 60 as suggested from recent measurements) the simulated magnetic field is dominated by an axisymmetric component. However, to obtain a growing axisymmetric eigenmode still an alpha-effect is necessary that parametrizes the induction effects of helical small scale motions. In contrast to preliminary mean field models for the VKS dynamo that have been based solely on an alpha-omega mechanism, the necessary magnitude for the alpha effect remains reasonable small if soft iron impellers are utilized.