Slow plasma dynamo driven by electric current helicity in non-compact Riemann surfaces of negative curvature

TL;DR

This paper investigates slow plasma dynamos driven by electric current helicity on non-compact Riemann surfaces with negative curvature, exploring how curvature influences dynamo behavior and magnetic field growth.

Contribution

It introduces a study of slow plasma dynamos on non-compact negatively curved Riemann surfaces, extending previous work on dynamo mechanisms in curved geometries.

Findings

Electric current helicity is approximately 2.34 m^{-1}.

Magnetic field growth rate is about 0.022.

Dynamo action is influenced by surface curvature and helicity.

Abstract

Boozer addressed the role of magnetic helicity in dynamos [Phys Fluids \textbf{B},(1993)]. He pointed out that the magnetic helicity conservation implies that the dynamo action is more easily attainable if the electric potential varies over the surface of the dynamo. This provided us with motivation to investigate dynamos in Riemannian curved surfaces [Phys Plasmas \textbf{14}, (2007);\textbf{15} (2008)]. Thiffeault and Boozer [Phys Plasmas (2003)] discussed the onset of dissipation in kinematic dynamos. When curvature is constant and negative, a simple simple laminar dynamo solution is obtained on the flow topology of a Poincare disk, whose Gauss curvature is $K=-1$. By considering a laminar plasma dynamo [Wang et al, Phys Plasmas (2002)] the electric current helicity ${\lambda}\approx{2.34m^{-1}}$ for a Reynolds magnetic number of $Rm\approx{210}$ and a growth rate of magnetic field $|{\gamma}|\approx{0.022}$. Negative constant curvature non-compact $\textbf{H}^{2}$, has also been used in one-component electron 2D plasma by Fantoni and Tellez (Stat Phys, (2008)). Chicone et al (CMP (1997)) showed fast dynamos can be supported in compact $\textbf{H}^{2}$. PACS: 47.65.Md. Key-word: dynamo plasma.