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

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

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. DOI: 10.1007/0-306-48420-X_22

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. DOI: 10.1007/0-306-48420-X_22

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)). Available from, DOI: 10.1007/0-306-48420-X_22

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title = "A third-order topological invariant for three magnetic fields",

author = "Christoph Mayer and Gunnar Hornig",

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AU - Mayer,Christoph

AU - Hornig,Gunnar

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N2 - 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.

AB - 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.

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BT - Tubes, sheets and singularities in fluid dynamics: proceedings of the NATO ARW, 2-7 September 2001, Zakopane, Poland

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