Dynamos driven by poloidal flows in untwisted, curved and flat Riemannian diffusive flux tubes

TL;DR

This paper investigates the conditions under which poloidal flows in untwisted, curved, and flat Riemannian diffusive flux tubes can support dynamo action, challenging classical anti-dynamo theorems and highlighting the role of curvature and diffusion.

Contribution

It demonstrates that diffusion enables dynamo action driven by poloidal flows in certain Riemannian flux tubes, providing new insights into magnetic field generation in plasma and geophysical contexts.

Findings

Diffusion in thin flux tubes can lead to slow dynamo action.

Negative Frenet curvature is associated with dynamo activity.

In absence of diffusion, magnetic energy does not grow, but poloidal fields generate toroidal fields.

Abstract

Recently Vishik anti-fast dynamo theorem, has been tested against non-stretching flux tubes [Phys Plasmas 15 (2008)]. In this paper, another anti-dynamo theorem, called Cowling's theorem, which states that axisymmetric magnetic fields cannot support dynamo action, is carefully tested against thick tubular and curved Riemannian untwisted flows, as well as thin flux tubes in diffusive and diffusionless media. In the non-diffusive media the Cowling's theorem is not violated in thin Riemann-flat untwisted flux tubes, where the Frenet curvature is negative. Nevertheless the diffusion action in the thin flux tube leads to a a dynamo action driven by poloidal flows as shown by Love and Gubbins (Geophysical Res.) in the context of geodynamos. Actually it is shown that a slow dynamo action is obtained. In this case the Frenet and Riemann curvature still vanishes. In the case of magnetic filaments in diffusive media dynamo action is obtained when the Frenet scalar curvature is negative. Since the Riemann curvature tensor can be expressed in terms of the Frenet curvature of the magnetic flux tube axis, this result can be analogous to a recent result obtained by Chicone, Latushkin and Smith, which states that geodesic curvature in compact Riemannian manifolds can drive dynamo action in the manifold. It is also shown that in absence of diffusion, magnetic energy does not grow but magnetic toroidal magnetic field can be generated by the poloidal field, what is called a plasma dynamo.