Turbulent ${\alpha}$-effect in twisted magnetic flux tubes dynamos in Riemannian space

TL;DR

This paper analytically explores the first-order torsion $ ext{α}$-effect in twisted magnetic flux tubes within Riemannian space, revealing how the dynamo's growth rate depends on the tube's curvature and torsion, and demonstrating conditions for dynamo action.

Contribution

It provides an analytical solution for the $ ext{α}$-effect dynamo in twisted flux tubes in Riemannian space, highlighting the role of torsion and curvature in dynamo behavior.

Findings

Magnetic field components decay as r^{-1} and grow exponentially in time.

Dynamo speed depends on the Frenet curvature of the flux tube.

Dynamo action requires simultaneous sign changes in torsion and curvature.

Abstract

Analytical solution of first order torsion ${\alpha}$-effect in twisted magnetic flux tubes representing a flux tube dynamo in Riemannian space is presented. Toroidal and poloidal component of the magnetic field decays as $r^{-1}$, while grow exponentially in time. The rate of speed of the helical dynamo depends upon the value of Frenet curvature of the tube. The $\alpha$ factor possesses a fundamental contribution from constant torsion tube approximation. It is also assumed that the curvature of the magnetic axis of the tube is constant. Though ${\alpha}$-effect dynamo equations are rather more complex in Riemann flux tube coordinates, a simple solution assuming force-free magnetic fields is shown to be possible. Dynamo solutions are possible if the dynamo action is able to change the signs of torsion and curvature of the dynamo flux tube simultaneously.