Three-dimensional magnetic field reconstruction in the vks experiment through galerkin transforms

We present a method for three-dimensional (3D) magnetic field reconstruction based on Galerkin transforms. We test it over synthetic fields and real solenoidal (velocity) fields, measured in a water experiment. Our study shows that reliable reconstructions are possible provided that the probes are sufficiently sampled and located in shifted configurations. A preliminary application of our method is performed on results obtained in the VKS dynamo experiment (Bourgoin et al 2002 Phys. Fluids 14 3046). We show that the stationary dynamos obtained with counter-rotating impellers are mainly axisymmetric, with a non-axisymmetric part that decreases with increasing Reynolds numbers. Most of the azimuthal energy is localized near the (iron) impellers, confirming their importance in the dynamo process.