Mean-field helicity in random ${\alpha}^{2}$-dynamo twisted flows

TL;DR

This paper analytically investigates the mean-field helicity in twisted ${ m oldsymbol{ extalpha}}^{2}$-dynamo flows within thin flux tubes, revealing conditions for magnetic field amplification related to Riemann curvature and electric current helicity.

Contribution

It provides an analytical approach to understanding dynamo action in twisted flux tubes, highlighting the role of Riemann curvature and helicity in magnetic field amplification.

Findings

Magnetic field amplification occurs when electric current helicity and Riemann curvature are negative.

Both positive and negative Riemannian curvatures support dynamo action in twisted flows.

New features emerge in ${ m oldsymbol{ extalpha}}^{2}$-dynamo flows using thin flux tube approximation.

Abstract

Here, an analytical version of numerical results is obtained in case of considering the laminar non-turbulent limit, of a twisted Riemannian thin flux tube. It is shown that the magnetic field is amplified, when electric current helicity and Riemann curvature are both negative. Thus spaces of positive and negative Riemannian curvatures seems to support dynamo action inside the torus, and not only negative Riemannian curvature surfaces as happens in 2D dynamos. New features appear in ${\alpha}^{2}$-dynamo twisted flow, using the approximation of thin tubes flux tubes. These solutions are obtained in the resonant profile of the toroidal and poloidal frequencies modes of the dynamo force-free flow.