Suppressed fluctuations..

TL;DR

This paper investigates how magnetic field fluctuations are suppressed in dynamo processes along curved and twisted filaments, deriving relations between magnetic Reynolds number, torsion, and diffusion, and confirming slow dynamo behavior in non-stretched flows.

Contribution

It provides a new analytical expression linking magnetic Reynolds number with torsion and length scale, and demonstrates slow dynamo behavior in curved, twisted filaments with astronomical data.

Findings

Suppression of magnetic fluctuations occurs in curved, twisted filaments.

Derived relation: Rm ≈ (τ₀ L)/η for non-zero torsion.

Confirmed slow dynamo behavior consistent with Vishik's argument.

Abstract

Suppression of fluctuations of normally perturbed magnetic fields in dynamo waves and slow dynamos along curved (folded), torsioned (twisted) and non-stretched, diffusive filaments are obtained. This form of fluctuations suppression has been recently obtained by Vainshtein et al [PRE 56, (1997)] in nonlinear ABC and stretch-twist-fold (STF) dynamos by using a magnetic Reynolds number of the order of $Rm\approx{10^{4}}$. Here when torsion does not vanish an expression between magnetic Reynolds number and length scale L as with constant torsion ${\tau}_{0}$ itself is obtained, such as $Rm\approx{\frac{{\tau}_{0}L}{\eta}}$ is obtained. At coronal loops $Rm\approx{10^{12}}$ and torsion of the twisted structured loop from astronomical data by Lopez-Fuentes et al [Astron. and Astrophys. (2003)] of ${\tau}\approx{9.0{\times}10^{-10}}cm^{-1}$ is used to compute a very slow magnetic diffusion of ${\eta}\approx{10^{-8}}$. The slow dynamo obtained here is in agreement with Vishik arguement that fast dynamo cannot be obtained in non-stretched dynamo flows. When torsion vanishes helical turbulence is quenched and but ${\alpha}$-dynamos cannot be maintained since exponential stretching depends on torsion. This is actually Zeldovich antidynamo theorem for torsion-free or planar filaments which has been discussed by the other also recently in another context [Astr Nach. (2008)]. The suppression of magnetic field fluctuations is actually a result of the coupling of the magnetic diffusion and Frenet torsion of helical turbulence.