Topological constraints on the relaxation of complex magnetic fields

Gunnar Hornig

Topological constraints on the relaxation of complex magnetic fields

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Newly emerging magnetic flux can show a complicated linked or interwoven topology of the magnetic field. The complexity of this linkage or knottedness of magnetic flux is related to the free energy stored in the magnetic field. Magnetic reconnection provides a process to release this energy on the time scale of the dynamics. At the same time it approximately conserves the total magnetic helicity. Therefore the conservation of total magnetic helicity is a crucial constraint for the relaxation of complex magnetic fields. However, the total magnetic helicity is only the first, most elementary, quantity of an infinite series of topological invariants of the magnetic field. All these invariants are strictly conserved in ideal magnetohydrodynamics. As an example a preliminary set of these invariants is derived. The relevance of these higher order invariants for the final state of relaxation under magnetic reconnection and their implications for the release of magnetic energy are discussed.

Original language	English
Title of host publication	Magnetic fields and solar processes, proceedings of the 9th European Meeting on Solar Physics. 12-18 September 1999, Florence, Italy
Editors	A. Wilson
Place of Publication	Noordwijk
Publisher	European Space Agency
Pages	5-8
Number of pages	4
ISBN (Print)	9290927925, 9789290927921
Publication status	Published - 1999
Event	The 9th European Meeting on Solar Physics: Magnetic Fields and Solar Processes - Florence, Italy Duration: 12 Sept 1999 → 18 Sept 1999 http://www.esa.int/esapub/bulletin/bullet101/bul101_publicat.pdf

Publication series

Name	ESA special publications
Publisher	European Space Agency
Number	448

Conference

Conference	The 9th European Meeting on Solar Physics: Magnetic Fields and Solar Processes
Country/Territory	Italy
City	Florence
Period	12/09/99 → 18/09/99
Internet address	http://www.esa.int/esapub/bulletin/bullet101/bul101_publicat.pdf

Keywords

Magnetic fields
Topological invariants
Magnetic reconnection

Access to Document

http://cdsweb.cern.ch/record/401590

1 Other

Topological constraints on the relaxation of complex magnetic fields
Hornig, G., Sept 1999.
Research output: Contribution to conference › Other

Cite this

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title = "Topological constraints on the relaxation of complex magnetic fields",

abstract = "Newly emerging magnetic flux can show a complicated linked or interwoven topology of the magnetic field. The complexity of this linkage or knottedness of magnetic flux is related to the free energy stored in the magnetic field. Magnetic reconnection provides a process to release this energy on the time scale of the dynamics. At the same time it approximately conserves the total magnetic helicity. Therefore the conservation of total magnetic helicity is a crucial constraint for the relaxation of complex magnetic fields. However, the total magnetic helicity is only the first, most elementary, quantity of an infinite series of topological invariants of the magnetic field. All these invariants are strictly conserved in ideal magnetohydrodynamics. As an example a preliminary set of these invariants is derived. The relevance of these higher order invariants for the final state of relaxation under magnetic reconnection and their implications for the release of magnetic energy are discussed.",

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author = "Gunnar Hornig",

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editor = "A. Wilson",

booktitle = "Magnetic fields and solar processes, proceedings of the 9th European Meeting on Solar Physics. 12-18 September 1999, Florence, Italy",

address = "Netherlands",

note = "The 9th European Meeting on Solar Physics: Magnetic Fields and Solar Processes ; Conference date: 12-09-1999 Through 18-09-1999",

url = "http://www.esa.int/esapub/bulletin/bullet101/bul101_publicat.pdf",

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Hornig, G 1999, Topological constraints on the relaxation of complex magnetic fields. in A Wilson (ed.), Magnetic fields and solar processes, proceedings of the 9th European Meeting on Solar Physics. 12-18 September 1999, Florence, Italy. ESA special publications, no. 448, European Space Agency, Noordwijk , pp. 5-8, The 9th European Meeting on Solar Physics: Magnetic Fields and Solar Processes, Florence, Italy, 12/09/99. <http://cdsweb.cern.ch/record/401590>

Topological constraints on the relaxation of complex magnetic fields. / Hornig, Gunnar.
Magnetic fields and solar processes, proceedings of the 9th European Meeting on Solar Physics. 12-18 September 1999, Florence, Italy. ed. / A. Wilson. Noordwijk : European Space Agency, 1999. p. 5-8 (ESA special publications; No. 448).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Topological constraints on the relaxation of complex magnetic fields

AU - Hornig, Gunnar

PY - 1999

Y1 - 1999

N2 - Newly emerging magnetic flux can show a complicated linked or interwoven topology of the magnetic field. The complexity of this linkage or knottedness of magnetic flux is related to the free energy stored in the magnetic field. Magnetic reconnection provides a process to release this energy on the time scale of the dynamics. At the same time it approximately conserves the total magnetic helicity. Therefore the conservation of total magnetic helicity is a crucial constraint for the relaxation of complex magnetic fields. However, the total magnetic helicity is only the first, most elementary, quantity of an infinite series of topological invariants of the magnetic field. All these invariants are strictly conserved in ideal magnetohydrodynamics. As an example a preliminary set of these invariants is derived. The relevance of these higher order invariants for the final state of relaxation under magnetic reconnection and their implications for the release of magnetic energy are discussed.

AB - Newly emerging magnetic flux can show a complicated linked or interwoven topology of the magnetic field. The complexity of this linkage or knottedness of magnetic flux is related to the free energy stored in the magnetic field. Magnetic reconnection provides a process to release this energy on the time scale of the dynamics. At the same time it approximately conserves the total magnetic helicity. Therefore the conservation of total magnetic helicity is a crucial constraint for the relaxation of complex magnetic fields. However, the total magnetic helicity is only the first, most elementary, quantity of an infinite series of topological invariants of the magnetic field. All these invariants are strictly conserved in ideal magnetohydrodynamics. As an example a preliminary set of these invariants is derived. The relevance of these higher order invariants for the final state of relaxation under magnetic reconnection and their implications for the release of magnetic energy are discussed.

KW - Magnetic fields

KW - Topological invariants

KW - Magnetic reconnection

M3 - Conference contribution

SN - 9290927925

SN - 9789290927921

T3 - ESA special publications

SP - 5

EP - 8

BT - Magnetic fields and solar processes, proceedings of the 9th European Meeting on Solar Physics. 12-18 September 1999, Florence, Italy

A2 - Wilson, A.

PB - European Space Agency

CY - Noordwijk

T2 - The 9th European Meeting on Solar Physics: Magnetic Fields and Solar Processes

Y2 - 12 September 1999 through 18 September 1999

ER -

Topological constraints on the relaxation of complex magnetic fields

Abstract

Publication series

Conference

Keywords

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Research output

Topological constraints on the relaxation of complex magnetic fields

Cite this