Magnetohydrodynamics dynamical relaxation of coronal magnetic fields

III. 3D spiral nulls

School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, UK
e-mail: jorge@mcs.st-and.ac.uk

Received: 8 March 2012
Accepted: 14 June 2012

Abstract

Context. The majority of studies on stressed 3D magnetic null points consider magnetic reconnection driven by an external perturbation, but the formation of a genuine current sheet equilibrium remains poorly understood. This problem has been considered more extensively in two dimensions, but lacks a generalization into 3D fields.

Aims. 3D magnetic nulls are more complex than 2D nulls and the field can take a greater range of magnetic geometries local to the null. Here, we focus on one type and consider the dynamical non-resistive relaxation of 3D spiral nulls with initial spine-aligned current. We aim to provide a valid magnetohydrostatic equilibrium, and describe the electric current accumulations in various cases, involving a finite plasma pressure.

Methods. A full MHD code was used, with the resistivity set to zero so that reconnection is not allowed, to run a series of experiments in which a perturbed spiral 3D null point was allowed to relax towards an equilibrium via real, viscous damping forces. Changes to the initial plasma pressure and other magnetic parameters were systematically investigated.

Results. For the axisymmetric case, the evolution of the field and the plasma is such that it concentrates the current density into two cone-shaped regions along the spine, thus concentrating the twist of the magnetic field around the spine, leaving a radial configuration in the fan plane. The plasma pressure redistributes to maintain the current density accumulations. However, it is found that changes in the initial plasma pressure do not significantly modify the final state. In the cases where the initial magnetic field is not axisymmetric, an infinite-time singularity of current perpendicular to the fan is found at the location of the null.