Stretch-Twist-Fold and slow filamentary dynamos in liquid sodium Madison Dynamo Experiments

TL;DR

This paper presents an analytical model of filamentary dynamos driven by magnetic filament curvature energy, exploring conditions for fast and slow dynamo action relevant to liquid sodium experiments like MDE.

Contribution

It introduces a simplified analytical approach to filamentary dynamo modeling based on curvature energy, extending previous numerical and theoretical work, and relates findings to experimental setups.

Findings

Absence of stretching prevents fast dynamo action.

Zero torsion in filaments inhibits dynamo support.

Unstretched filaments exhibit Vishik anti-fast dynamo behavior.

Abstract

Recently Ricca and Maggione [MHD (2008)] have presented a very simple and interesting model of stretch-twist-fold dynamo in diffusive media based on numerical simulations of Riemannian flux tubes. In this paper we present a yet simpler way of analytically obtaining fast and slow dynamo, generated by by the curvature energy of magnetic filaments in diffusive media. geometrical model for the galactic or accretion disk dynamo in shear flows is presented. In the fast dynamo case it is shown that the absence of stretching leads to the absence of fast dynamos and when torsion of filaments vanishes the dynamo action cannot be support as well. This is the Cowling-Zeldovich theorem for planar flows. Isotropy of the magnetic fields hypothesis is used to compute the fast nature of dynamo. A similar result using non-holonomic Frenet frame has been recently obtained for filamentary dynamos [Garcia de Andrade, AN (2008)]. The stretch-twist-fold (STF) filamented models discussed here may serve to formulate future experiments in the Madison Dynamo Experiment (MDE) facility [Nornberg et al, Phys Plasmas (2008)]. Though their running experiments deal with magnetic fields that are orthogonal to the flow, other topologies are also used here, with an eye in future experiments. Unstretched filaments in MDE shows Vishik anti-fast dynamo action applies [Garcia de Andrade[Phys Plasmas (2008)].