Geodesic plasma flows instabilities of Riemann twisted solar loops

TL;DR

This paper investigates the stability of Riemannian twisted solar loops by analyzing their geometric properties, revealing how curvature influences plasma flow stability and potential solar flare production.

Contribution

It introduces a geometric framework using Riemannian curvature to analyze plasma flow stability in twisted solar loops, a novel approach in solar physics.

Findings

Thick magnetic tubes dampen flow speed due to curvature effects.

Negative sectional curvature indicates potential flow instability.

Twist in magnetic flux tubes affects plasma velocity and stability.

Abstract

Riemann and sectional curvatures of magnetic twisted flux tubes in Riemannian manifold are computed to investigate the stability of the plasma astrophysical tubes. The geodesic equations are used to show that in the case of thick magnetic tubes, the curvature of planar (Frenet torsion-free) tubes have the effect ct of damping the flow speed along the tube. Stability of geodesic flows in the Riemannian twisted thin tubes (almost filaments), against constant radial perturbations is investigated by using the method of negative sectional curvature for unstable flows. No special form of the flow like Beltrami flows is admitted, and the proof is general for the case of thin magnetic flux tubes. In the magnetic equilibrium state, the twist of the tube is shown to display also a damping effect on the toroidal velocity of the plasma flow. It is found that for positive perturbations and angular speed of the flow, instability is achieved, since the sectional Ricci curvature of the magnetic twisted tube metric is negative. Solar flare production may appear from these geometrical instabilities of the twisted solar loops.