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Title: Unique topological characterization of braided magnetic fields

Abstract

We introduce a topological flux function to quantify the topology of magnetic braids: non-zero, line-tied magnetic fields whose field lines all connect between two boundaries. This scalar function is an ideal invariant defined on a cross-section of the magnetic field, and measures the average poloidal magnetic flux around any given field line, or the average pairwise crossing number between a given field line and all others. Moreover, its integral over the cross-section yields the relative magnetic helicity. Using the fact that the flux function is also an action in the Hamiltonian formulation of the field line equations, we prove that it uniquely characterizes the field line mapping and hence the magnetic topology.

Authors:
 [1];  [2]
  1. Department of Mathematical Sciences, Durham University, Durham DH1 3LE (United Kingdom)
  2. Division of Mathematics, University of Dundee, Dundee DD1 4HN (United Kingdom)
Publication Date:
OSTI Identifier:
22113314
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 20; Journal Issue: 1; Other Information: (c) 2013 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CROSS SECTIONS; EQUATIONS; HAMILTONIANS; HELICITY; MAGNETIC FIELDS; MAGNETIC FLUX; MAGNETOHYDRODYNAMICS; PLASMA; SIMULATION; TOPOLOGY

Citation Formats

Yeates, A. R., and Hornig, G. Unique topological characterization of braided magnetic fields. United States: N. p., 2013. Web. doi:10.1063/1.4773903.
Yeates, A. R., & Hornig, G. Unique topological characterization of braided magnetic fields. United States. doi:10.1063/1.4773903.
Yeates, A. R., and Hornig, G. Tue . "Unique topological characterization of braided magnetic fields". United States. doi:10.1063/1.4773903.
@article{osti_22113314,
title = {Unique topological characterization of braided magnetic fields},
author = {Yeates, A. R. and Hornig, G.},
abstractNote = {We introduce a topological flux function to quantify the topology of magnetic braids: non-zero, line-tied magnetic fields whose field lines all connect between two boundaries. This scalar function is an ideal invariant defined on a cross-section of the magnetic field, and measures the average poloidal magnetic flux around any given field line, or the average pairwise crossing number between a given field line and all others. Moreover, its integral over the cross-section yields the relative magnetic helicity. Using the fact that the flux function is also an action in the Hamiltonian formulation of the field line equations, we prove that it uniquely characterizes the field line mapping and hence the magnetic topology.},
doi = {10.1063/1.4773903},
journal = {Physics of Plasmas},
number = 1,
volume = 20,
place = {United States},
year = {Tue Jan 15 00:00:00 EST 2013},
month = {Tue Jan 15 00:00:00 EST 2013}
}
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