Physical role of topological constraints in localised magnetic relaxation

TL;DR

This paper investigates how topological constraints influence magnetic relaxation in turbulent plasmas, revealing that the topological degree of the turbulent region determines the final relaxed state, with numerical simulations confirming the transition between different configurations.

Contribution

The study demonstrates the critical role of the topological degree of the turbulent region in magnetic relaxation, highlighting a transition that depends on initial conditions and topological constraints.

Findings

Degree 1 leads to a single twisted flux tube.

Degree 2 results in two flux tubes.

Transition depends on the topological degree of the turbulent region.

Abstract

Predicting the final state of turbulent plasma relaxation is an important challenge, both in astrophysical plasmas such as the Sun's corona and in controlled thermonuclear fusion. Recent numerical simulations of plasma relaxation with braided magnetic fields identified the possibility of a novel constraint, arising from the topological degree of the magnetic field-line mapping. This constraint implies that the final relaxed state is drastically different for an initial configuration with topological degree 1 (which allows a Taylor relaxation) and one with degree 2 (which does not reach a Taylor state). Here we test this transition in numerical resistive-magnetohydrodynamic simulations, by embedding a braided magnetic field in a linear force-free background. Varying the background force-free field parameter generates a sequence of initial conditions with a transition between topological degree 1 and 2. For degree 1, the relaxation produces a single twisted flux tube, while for degree 2 we obtain two flux tubes. For predicting the exact point of transition, it is not the topological degree of the whole domain that is relevant, but only that of the turbulent region.