A third-order topological invariant for three magnetic fields

Christoph Mayer, Gunnar Hornig

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The topology of divergence-free fields is important in many parts of physics, e. g. in magnetohydrodynamics, plasma physics, hydrodynamics, superfluids etc. With the focus on applications in magnetohydrodynamics, our principal aim is the characterisation of magnetic fields by the means of invariants. In this report an introduction to the problem of finding higher order invariants is given. Then a third-order link integral of three magnetic fields is presented, which can be shown to be a topological invariant and therefore an invariant in ideal magnetohydrodynamics. This integral generalises the known third-order link invariant derived from the Massey triple product, which could only be applied to isolated flux tubes. As an example three magnetic fields not confined to flux tubes are given that possess a third-order linkage.
Original languageEnglish
Title of host publicationTubes, sheets and singularities in fluid dynamics
Subtitle of host publicationproceedings of the NATO ARW, 2-7 September 2001, Zakopane, Poland
EditorsK. Bajer, H. K. Moffatt
PublisherKluwer Academic Publishers
Pages151-156
Number of pages6
ISBN (Print)9781402009808, 1402009801
DOIs
Publication statusPublished - 2002

Publication series

NameFluid mechanics and its applications
Number71(3)
ISSN (Print)0926-5112

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magnetohydrodynamics
magnetic fields
tubes
plasma physics
linkages
divergence
topology
hydrodynamics
physics
products

Cite this

Mayer, C., & Hornig, G. (2002). A third-order topological invariant for three magnetic fields. In K. Bajer, & H. K. Moffatt (Eds.), Tubes, sheets and singularities in fluid dynamics: proceedings of the NATO ARW, 2-7 September 2001, Zakopane, Poland (pp. 151-156). (Fluid mechanics and its applications; No. 71(3)). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-48420-X_22
Mayer, Christoph ; Hornig, Gunnar. / A third-order topological invariant for three magnetic fields. Tubes, sheets and singularities in fluid dynamics: proceedings of the NATO ARW, 2-7 September 2001, Zakopane, Poland. editor / K. Bajer ; H. K. Moffatt. Kluwer Academic Publishers, 2002. pp. 151-156 (Fluid mechanics and its applications; 71(3)).
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Mayer, C & Hornig, G 2002, A third-order topological invariant for three magnetic fields. in K Bajer & HK Moffatt (eds), Tubes, sheets and singularities in fluid dynamics: proceedings of the NATO ARW, 2-7 September 2001, Zakopane, Poland. Fluid mechanics and its applications, no. 71(3), Kluwer Academic Publishers, pp. 151-156. https://doi.org/10.1007/0-306-48420-X_22

A third-order topological invariant for three magnetic fields. / Mayer, Christoph; Hornig, Gunnar.

Tubes, sheets and singularities in fluid dynamics: proceedings of the NATO ARW, 2-7 September 2001, Zakopane, Poland. ed. / K. Bajer; H. K. Moffatt. Kluwer Academic Publishers, 2002. p. 151-156 (Fluid mechanics and its applications; No. 71(3)).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Mayer C, Hornig G. A third-order topological invariant for three magnetic fields. In Bajer K, Moffatt HK, editors, Tubes, sheets and singularities in fluid dynamics: proceedings of the NATO ARW, 2-7 September 2001, Zakopane, Poland. Kluwer Academic Publishers. 2002. p. 151-156. (Fluid mechanics and its applications; 71(3)). https://doi.org/10.1007/0-306-48420-X_22