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Title: 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 » 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.« less

Authors:
 [1]
  1. 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}
}