Hydrodynamic Plasma Flow in a Strong Magnetic Field

Priest

et al. 2014

A&A

Context. Separators, which are in many ways the three-dimensional equivalent to two-dimensional nulls, are important sites for magnetic reconnection. Magnetic reconnection occurs in strong current layers which have very short length scales. Aims. The aim of this work is to explore the nature of current layers around separators. A separator is a special field line which lies along the intersection of two separatrix surfaces and forms the boundary between four topologically distinct flux domains. In particular, here the current layer about a separator that joins two 3D nulls and lies along the intersection of their separatrix surfaces is investigated. Methods. A magnetic configuration containing a single separator embedded in a uniform plasma with a uniform electric current parallel to the separator is considered. This initial magnetic setup, which is not in equilibrium, relaxes in a non-resistive manner to form an equilibrium. The relaxation is achieved using the 3D MHD code, Lare3d, with resistivity set to zero. A series of experiments with varying initial current are run to investigate the characteristics of the resulting current layers present in the final (quasi-)equilibrium states. Results. In each experiment, the separator collapses and a current layer forms along it. The dimensions and strength of the current layer increase with initial current. It is found that separator current layers formed from current parallel to the separator are twisted. Also the collapse of the separator is a process that evolves like an infinite-time singularity where the length, width and peak current in the layer grow slowly whilst the depth of the current layer decreases.

Section: Introductionmentioning

confidence: 99%

The nature of separator current layers in MHS equilibria

Stevenson

Priest

et al. 2014

A&A

“…Dungey 1953;Green 1965;Somov & Syrovatskii 1976;Vekstein & Priest 1993;Craig 1994;Bungey & Priest 1995) and numerically, including the effects of plasma pressure (e.g. Rastätter et al 1994;Craig & Litvinenko 2005;Pontin & Craig 2005;Fuentes-Fernández et al 2011).…”

Section: Introductionmentioning

confidence: 99%

Magnetohydrodynamics dynamical relaxation of coronal magnetic fields

Fuentes-Fernández

2012

A&A

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.

“…zero plasma beta), an initially perturbed X-point field relaxes to a potential equilibrium with a Y-type infinitesimally thin current sheet where the current is zero everywhere except within the magnetic tangential discontinuity, where it develops a singularity of the form j z = δ(A z −A z0 ). These potential configurations are described by Green (1965) and Somov & Syrovatskii (1976). Later, Bungey & Priest (1995) expanded these solutions for potential and force-free fields giving a general expression for these force-free current sheets.…”

Section: Introductionmentioning

confidence: 99%

“…In two dimensions, in particular, the topology of the current sheet formed after an X-type null point collapse has been well studied analytically for potential and force-free fields by several authors (e.g. Dungey 1953;Green 1965;Somov & Syrovatskii 1976;Craig 1994;Bungey & Priest 1995).…”

Section: Introductionmentioning

confidence: 99%

Magnetohydrodynamics dynamical relaxation of coronal magnetic fields

Fuentes-Fernández

Hood

2011

A&A

Context. Magnetic neutral points are potential locations for energy conversion in the solar corona. 2D X-points have been widely studied in the past, but only a few of those studies have taken finite plasma beta effects into consideration, and none of them look at the dynamical evolution of the system. At the moment there exists no description of the formation of a non-force-free equilibrium around a two-dimensional X-point. Aims. Our aim is to provide a valid magnetohydrostatic equilibrium from the collapse of a 2D X-point in the presence of a finite plasma pressure, in which the current density is not simply concentrated in an infinitesimally thin, one-dimensional current sheet, as found in force-free solutions. In particular, we wish to determine if a finite pressure current sheet will still involve a singular current, and if so, what is the nature of the singularity. Methods. We use a full MHD code, with the resistivity set to zero, so that reconnection is not allowed, to run a series of experiments in which an X-point is perturbed and then is allowed to relax towards an equilibrium, via real, viscous damping forces. Changes to the magnitude of the perturbation and the initial plasma pressure are investigated systematically. Results. The final state found in our experiments is a "quasi-static" equilibrium where the viscous relaxation has completely ended, but the peak current density at the null increases very slowly following an asymptotic regime towards an infinite time singularity. Using a high grid resolution allows us to resolve the current structures in this state both in width and length. In comparison with the well known pressureless studies, the system does not evolve towards a thin current sheet, but concentrates the current at the null and the separatrices. The growth rate of the singularity is found to be t D , with 0 < D < 1. This rate depends directly on the initial plasma pressure, and decreases as the pressure is increased. At the end of our study, we present an analytical description of the system in a quasi-static non-singular equilibrium at a given time, in which a finite thick current layer has formed at the null. The dynamical evolution of the system and the dependence of the final state on the initial plasma and magnetic quantities is discussed, as are the energetic consequences.