Generation of axisymmetric modes in cylindrical kinematic mean-field dynamos of VKS type

In an attempt to understand why the dominating magnetic field observed in the von-Kármán-Sodium (VKS) dynamo experiment is axisymmetric, we investigate in the present paper the ability of mean field models to generate axisymmetric eigenmodes in cylindrical geometries. An $α$-effect is added to the induction equation and we identify reasonable and necessary properties of the $α$ distribution so that axisymmetric eigenmodes are generated. The parametric study is done with two different simulation codes. We find that simple distributions of $α$-effect, either concentrated in the disk neighbourhood or occupying the bulk of the flow, require unrealistically large values of the parameter $α$ to explain the VKS observations.