Magnetohydrodynamics dynamical relaxation of coronal magnetic fields

IV. 3D tilted 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: 6 September 2012
Accepted: 12 April 2013

Abstract

Context. There are various types of reconnection that may take place at 3D magnetic null points. Each different reconnection scenario must be associated with a particular type of current layer.

Aims. A range of current layers may form because the topology of 3D nulls permits currents to form by either twisting the field about the spine of the null or by folding the fan and spine into each other. Additionally, the initial geometry of the field can lead to variations in the currents that are accumulated. Here, we study current accumulations in so-called 3D “tilted” nulls formed by a folding of the spine and fan. A non-zero component of current parallel to the fan is required such that the null’s fan plane and spine are not perpendicular. Our aims are to provide valid magnetohydrostatic equilibria and to describe the current accumulations in various cases involving finite plasma pressure.

Methods. To create our equilibrium current structures we use a full, non-resistive, magnetohydrodynamic (MHD) code so that no reconnection is allowed. A series of experiments are performed in which a perturbed 3D tilted null relaxes towards an equilibrium via real, viscous damping forces. Changes to the initial plasma pressure and to magnetic parameters are investigated systematically.

Results. An initially tilted fan is associated with a non-zero Lorentz force that drives the fan and spine to collapse towards each other, in a similar manner to the collapse of a 2D X-point. In the final equilibrium state for an initially radial null with only the current perpendicular to the spine, the current concentrates along the tilt axis of the fan and in a layer about the null point with a sharp peak at the null itself. The continued growth of this peak indicates that the system is in an asymptotic regime involving an infinite time singularity at the null. When the initial tilt disturbance (current perpendicular to the spine) is combined with a spiral-type disturbance (current parallel to the spine), the final current density concentrates in three regions: one on the fan along its tilt axis and two around the spine, above and below the fan. The increased area of current accumulation leads to a weakening of the singularity formed at the null. The 3D spine-fan collapse with generic current studied here provides the ideal setup for non-steady reconnection studies.