Dynamo experiments in torsioned toroidal devices

TL;DR

This paper demonstrates that steady perturbations in magnetic fields within twisted Riemannian flux tubes, characterized by Frenet torsion, can support dynamo action, with implications for plasma devices and magnetic field generation.

Contribution

It introduces the role of Frenet torsion in supporting dynamo action in twisted flux tubes, expanding on previous Moebius flow models and linking torsion to magnetic field amplification.

Findings

Frenet torsion can support dynamo action in flux tubes.

A specific torsion value of approximately 7.5×Ω^θ Hz^{-1} m^{-1} is identified.

Magnetic field perturbations of about 0.03 G are sufficient for dynamo activity.

Abstract

Recently Shukurov, Stepanov and Sokoloff [\textbf{Phys. Rev. E 69 (2008)}] have suggested that Moebius flows can support dynamo action. In this report, it is shown that a steady perturbation of a magnetic field in a general twisted Riemannian flux tube may support dynamo action. Instead of the twist number used in the above reference, the focus here is on the Frenet torsion of the magnetic flux tube. A relation between the constant torsion of the screw dynamo torus, its internal radius, and the ratio between toroidal and poloidal flow. Solution of self-induction equation for the screw dynamo torsioned flow, can be solved to yield a Frenet torsion as high as ${\tau}_{0}\approx{7.5{\times}{\Omega}^{\theta}Hz^{-1}m^{-1}}$, for an applied random magnetic field of $<B^{0}>\approx{45 G}$ for an induced steady perturbation of $B_{1}\approx{0.03G}$, as in the Perm Riemannian torus experiment. The Moebius strip plays the role of the propeller divertor which imprints the angular velocity ${\Omega}^{\theta}$, around the torus axis, to the dynamo flow, here this role is played by torsion. Actually this situation is already familiar to plasma physicists, where in stellarators torsion substitutes very well the role played by external magnetic fields in tokamaks making magnetic fields twist along plasma toroidal devices. Weak torsion of the torus channel is assumed.