# Separation of magnetic field lines

## Abstract

The field lines of magnetic fields that depend on three spatial coordinates are shown to have a fundamentally different behavior from those that depend on two coordinates. Unlike two-coordinate cases, a flux tube in a magnetic field that depends on all three spatial coordinates that has a circular cross section at one location along the tube characteristically has a highly distorted cross section at other locations. In an ideal evolution of a magnetic field, the current densities typically increase. Crudely stated, if the current densities increase by a factor {sigma}, the ratio of the long to the short distance across a cross section of a flux tube characteristically increases by e{sup 2{sigma}}, and the ratio of the longer distance to the initial radius increases as e{sup {sigma}}. Electron inertia prevents a plasma from isolating two magnetic field structures on a distance scale shorter than c/{omega}{sub pe}, which is about 10 cm in the solar corona, and reconnection must be triggered if {sigma} becomes sufficiently large. The radius of the sun, R{sub Circled-Dot-Operator }=7 Multiplication-Sign 10{sup 10}cm is about e{sup 23} times larger, so when {sigma} Greater-Than-Or-Equivalent-To 23, two lines separated by c/{omega}{sub pe} at one location can be separated bymore »

- Authors:

- Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027 (United States)

- Publication Date:

- OSTI Identifier:
- 22068901

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 19; Journal Issue: 11; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; CURRENT DENSITY; DISTANCE; ELECTRONS; MAGNETIC FIELDS; MAGNETIC FLUX COORDINATES; PLASMA; SOLAR CORONA; SUN

### Citation Formats

```
Boozer, Allen H.
```*Separation of magnetic field lines*. United States: N. p., 2012.
Web. doi:10.1063/1.4765352.

```
Boozer, Allen H.
```*Separation of magnetic field lines*. United States. doi:10.1063/1.4765352.

```
Boozer, Allen H. Thu .
"Separation of magnetic field lines". United States. doi:10.1063/1.4765352.
```

```
@article{osti_22068901,
```

title = {Separation of magnetic field lines},

author = {Boozer, Allen H.},

abstractNote = {The field lines of magnetic fields that depend on three spatial coordinates are shown to have a fundamentally different behavior from those that depend on two coordinates. Unlike two-coordinate cases, a flux tube in a magnetic field that depends on all three spatial coordinates that has a circular cross section at one location along the tube characteristically has a highly distorted cross section at other locations. In an ideal evolution of a magnetic field, the current densities typically increase. Crudely stated, if the current densities increase by a factor {sigma}, the ratio of the long to the short distance across a cross section of a flux tube characteristically increases by e{sup 2{sigma}}, and the ratio of the longer distance to the initial radius increases as e{sup {sigma}}. Electron inertia prevents a plasma from isolating two magnetic field structures on a distance scale shorter than c/{omega}{sub pe}, which is about 10 cm in the solar corona, and reconnection must be triggered if {sigma} becomes sufficiently large. The radius of the sun, R{sub Circled-Dot-Operator }=7 Multiplication-Sign 10{sup 10}cm is about e{sup 23} times larger, so when {sigma} Greater-Than-Or-Equivalent-To 23, two lines separated by c/{omega}{sub pe} at one location can be separated by the full scale of any magnetic structures in the corona at another. The conditions for achieving a large exponentiation, {sigma}, are derived, and the importance of exponentiation is discussed.},

doi = {10.1063/1.4765352},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 11,

volume = 19,

place = {United States},

year = {2012},

month = {11}

}