Effect of soft-iron impellers on the von Kármán–sodium dynamo

Abstract

The explanation for the observed axisymmetric magnetic field in the von Kármán-sodium (VKS) dynamo experiment is still an unresolved question. In this paper, the integral equation approach is extended to investigate the VKS dynamo action by taking into account the discontinuity of the magnetic permeability and electrical conductivity in the conducting region. When the relative magnetic permeability of the soft-iron impellers is set to 65, a steady toroidal field that is apparently axisymmetric is excited at the critical magnetic Reynolds number, Rmc≈27.23, which is close to the experimental result, Rmc≈30. Our results show that the critical magnetic Reynolds number declines as the relative magnetic permeability of the impellers increases. Furthermore, when the relative magnetic permeability is not greater than 37, an equatorial magnetic field with an azimuthal wave number m=1 is the dominant mode, otherwise a steady toroidal field with an azimuthal wave number m=0 predominates the magnetic field generated by the VKS dynamo action.