# Non-linear tearing of 3D null point current sheets

## Abstract

The manner in which the rate of magnetic reconnection scales with the Lundquist number in realistic three-dimensional (3D) geometries is still an unsolved problem. It has been demonstrated that in 2D rapid non-linear tearing allows the reconnection rate to become almost independent of the Lundquist number (the “plasmoid instability”). Here, we present the first study of an analogous instability in a fully 3D geometry, defined by a magnetic null point. The 3D null current layer is found to be susceptible to an analogous instability but is marginally more stable than an equivalent 2D Sweet-Parker-like layer. Tearing of the sheet creates a thin boundary layer around the separatrix surface, contained within a flux envelope with a hyperbolic structure that mimics a spine-fan topology. Efficient mixing of flux between the two topological domains occurs as the flux rope structures created during the tearing process evolve within this envelope. This leads to a substantial increase in the rate of reconnection between the two domains.

- Authors:

- Division of Mathematics, University of Dundee, Dundee (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22303764

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 21; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BOUNDARY LAYERS; CURRENTS; INSTABILITY; MAGNETIC RECONNECTION; NONLINEAR PROBLEMS

### Citation Formats

```
Wyper, P. F., E-mail: peterw@maths.dundee.ac.uk, and Pontin, D. I., E-mail: dpontin@maths.dundee.ac.uk.
```*Non-linear tearing of 3D null point current sheets*. United States: N. p., 2014.
Web. doi:10.1063/1.4893149.

```
Wyper, P. F., E-mail: peterw@maths.dundee.ac.uk, & Pontin, D. I., E-mail: dpontin@maths.dundee.ac.uk.
```*Non-linear tearing of 3D null point current sheets*. United States. doi:10.1063/1.4893149.

```
Wyper, P. F., E-mail: peterw@maths.dundee.ac.uk, and Pontin, D. I., E-mail: dpontin@maths.dundee.ac.uk. Fri .
"Non-linear tearing of 3D null point current sheets". United States.
doi:10.1063/1.4893149.
```

```
@article{osti_22303764,
```

title = {Non-linear tearing of 3D null point current sheets},

author = {Wyper, P. F., E-mail: peterw@maths.dundee.ac.uk and Pontin, D. I., E-mail: dpontin@maths.dundee.ac.uk},

abstractNote = {The manner in which the rate of magnetic reconnection scales with the Lundquist number in realistic three-dimensional (3D) geometries is still an unsolved problem. It has been demonstrated that in 2D rapid non-linear tearing allows the reconnection rate to become almost independent of the Lundquist number (the “plasmoid instability”). Here, we present the first study of an analogous instability in a fully 3D geometry, defined by a magnetic null point. The 3D null current layer is found to be susceptible to an analogous instability but is marginally more stable than an equivalent 2D Sweet-Parker-like layer. Tearing of the sheet creates a thin boundary layer around the separatrix surface, contained within a flux envelope with a hyperbolic structure that mimics a spine-fan topology. Efficient mixing of flux between the two topological domains occurs as the flux rope structures created during the tearing process evolve within this envelope. This leads to a substantial increase in the rate of reconnection between the two domains.},

doi = {10.1063/1.4893149},

journal = {Physics of Plasmas},

number = 8,

volume = 21,

place = {United States},

year = {Fri Aug 15 00:00:00 EDT 2014},

month = {Fri Aug 15 00:00:00 EDT 2014}

}