Mean-field model of the von Kármán sodium dynamo experiment using soft iron impellers

It has been observed that dynamo action occurs in the von-Kármán-Sodium (VKS) experiment only when the rotating disks and the blades are made of soft iron. The purpose of this paper is to numerically investigate the role of soft iron in the VKS dynamo scenario. This is done by using a mean-field model based on an axisymmetric mean flow, a localized permeability distribution, and a localized α effect modeling the action of the small velocity scales between the blades. The action of the rotating blades is modeled by an axisymmetric effective permeability field. Key properties of the flow giving to the numerical magnetic field a geometric structure similar to that observed experimentally are identified. Depending on the permeability of the disks and the effective permeability of the blades, the dynamo that is obtained is either oscillatory or stationary. Our numerical results confirm the leading role played by the ferromagnetic impellers. A scenario for the VKS dynamo is proposed.