Role of soft-iron impellers on the mode selection in the VKS dynamo experiment

A crucial point for the understanding of the von-K\'arm\'an-Sodium (VKS) dynamo experiment is the influence of soft-iron impellers. We present numerical simulations of a VKS-like dynamo with a localized permeability distribution that resembles the shape of the flow driving impellers. It is shown that the presence of soft-iron material essentially determines the dynamo process in the VKS experiment. % An axisymmetric magnetic field mode can be explained by the combined action of the soft-iron disk and a rather small $\alpha$-effect parametrizing the induction effects of unresolved small scale flow fluctuations

Fractional divergence-measure fields, Leibniz rule and Gauss–Green formula

Given a E (0, 1] and p E [1, +co], we define the space DMa,p(R-n) of L-p vector fields whose a-divergence is a finite Radon measure, extending the theory of divergence-measure vector fields to the distributional fractional setting. Our main results concern the absolute continuity properties of the a-divergence-measure with respect to the Hausdorff measure and fractional analogues of the Leibniz rule and the Gauss-Green formula. The sharpness of our results is discussed via some explicit examples

The integral equation approach to kinematic dynamo theory and its application to dynamo experiments in cylindrical geometry

The conventional magnetic induction equation that governs hydromagnetic dynamo action is transformed into an equivalent integral equation system. An advantage of this approach is that the computational domain is restricted to the region occupied by the electrically conducting fluid and to its boundary. This integral equation approach is first employed to simulate kinematic dynamos excited by Beltrami-like flows in a finite cylinder. The impact of externally added layers around the cylinder on the onset of dynamo actions is investigated. Then it is applied to simulate dynamo experiments within cylindrical geometry including the von Karman sodium (VKS) experiment and the Riga dynamo experiment. A modified version of this approach is utilized to investigate magnetic induction effects under the influence of externally applied magnetic fields which is also important to measure the proximity of a given dynamo facility to the self-excitation threshold.Comment: 22 pages, 14 figure