Evolution of Field Line Helicity in Magnetic Relaxation

TL;DR

This study investigates how individual magnetic field line helicities evolve during plasma relaxation, revealing that they are redistributed rather than annihilated, and can predict the formation of relaxed states with specific structures.

Contribution

It provides new insights into magnetic relaxation by analyzing line helicity evolution, showing their redistribution, and predicting relaxed states in non-Taylor configurations.

Findings

Line helicity is predominantly redistributed, not annihilated.

Initial line helicity distribution predicts flux tube formation.

Final relaxed states exhibit uniform line helicity within flux tubes.

Abstract

Plasma relaxation in the presence of an initially braided magnetic field can lead to self-organization into relaxed states that retain non-trivial magnetic structure. These relaxed states may be in conflict with the linear force-free fields predicted by the classical Taylor theory, and remain to be fully understood. Here, we study how the individual field line helicities evolve during such a relaxation, and show that they provide new insights into the relaxation process. The line helicities are computed for numerical resistive-magnetohydrodynamic simulations of a relaxing braided magnetic field with line-tied boundary conditions, where the relaxed state is known to be non-Taylor. Firstly, our computations confirm recent analytical predictions that line helicity will be predominantly redistributed within the domain, rather than annihilated. Secondly, we show that self-organization into a relaxed state with two discrete flux tubes may be predicted from the initial line helicity distribution. Thirdly, for this set of line-tied simulations we observe that the sub-structure within each of the final tubes is a state of uniform line helicity. This uniformization of line helicity is consistent with Taylor theory applied to each tube individually. However, it is striking that the line helicity becomes significantly more uniform than the force-free parameter.