Current singularities in line-tied three-dimensional magnetic fields

TL;DR

This study investigates how finite amplitude 3D disturbances in line-tied magnetic fields lead to current formation, emphasizing the role of quasi-separatrix layers and null points through ideal relaxation simulations.

Contribution

It demonstrates the dependence of current localization and scaling on QSL dimensions and boundary proximity, contrasting with null point behavior in line-tied magnetic fields.

Findings

Current structures form in QSLs influenced by line-tying.

Current location and scaling depend on QSL size relative to boundaries.

Null points attract current but are affected by boundary proximity.

Abstract

This paper considers the current distributions that derive from finite amplitude perturbations of line-tied magnetic fields comprising hyperbolic field structures. The initial equilibrium on which we principally focus is a planar magnetic X-point threaded by a uniform axial field. This field is line-tied on all surfaces but subject to three-dimensional (3D) disturbances that alter the initial topology. Results of ideal relaxation simulations are presented which illustrate how intense current structures form that can be related, through the influence of line-tying, to the quasi-separatrix layers (QSLs) of the initial configuration. It is demonstrated that the location within the QSL that attracts the current, and its scaling properties, are strongly dependent on the relative dimensions of the QSL with respect to the line-tied boundaries. These results are contrasted with the behavior of a line-tied 3D field containing an isolated null point. In this case, it is found that the dominant current always forms at the null, but that the collapse is inhibited when the null is closer to a line-tied boundary.