Current Singularities at Quasi-Separatrix Layers and Three-Dimensional Magnetic Nulls

TL;DR

This study investigates how singular current structures form in three-dimensional magnetic fields with nulls and QSLs, revealing that nulls attract stronger, potentially fast-reconnection currents, while QSLs produce weaker, unbounded singularities.

Contribution

It demonstrates that magnetic nulls attract dominant, fast-reconnection currents, and provides a detailed analysis of current formation at nulls and QSLs using a magneto-frictional relaxation method.

Findings

Null points attract stronger, faster-growing currents.

QSLs produce weaker, unbounded singularities.

Null-related currents scale with resolution, supporting fast reconnection models.

Abstract

The open problem of how singular current structures form in line-tied, three-dimensional magnetic fields is addressed. A Lagrangian magneto-frictional relaxation method is employed to model the field evolution towards the final near-singular state. Our starting point is an exact force-free solution of the governing magnetohydrodynamic (MHD) equations which is sufficiently general to allow for topological features like magnetic nulls to be inside or outside the computational domain, depending on a simple set of parameters. Quasi-separatrix layers (QSLs) are present in these structures and together with the magnetic nulls, they significantly influence the accumulation of current. It is shown that perturbations affecting the lateral boundaries of the configuration lead not only to collapse around the magnetic null, but also to significant QSL currents. Our results show that once a magnetic null is present, the developing currents are always attracted to that specific location and show a much stronger scaling with resolution than the currents which form along the QSL. In particular, the null point scalings can be consistent with models of "fast" reconnection. The QSL currents also appear to be unbounded but give rise to weaker singularities, independent of the perturbation amplitude.