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: proceedings 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

    Fingerprint

    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)).
    @inbook{819ceac5fee94044bbeaddd1cb02cf12,
    title = "A third-order topological invariant for three magnetic fields",
    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.",
    author = "Christoph Mayer and Gunnar Hornig",
    note = "dc.description.sponsorship: Volkswagen Foundation",
    year = "2002",
    doi = "10.1007/0-306-48420-X_22",
    language = "English",
    isbn = "9781402009808",
    series = "Fluid mechanics and its applications",
    publisher = "Kluwer Academic Publishers",
    number = "71(3)",
    pages = "151--156",
    editor = "K. Bajer and Moffatt, {H. K.}",
    booktitle = "Tubes, sheets and singularities in fluid dynamics: proceedings of the NATO ARW, 2-7 September 2001, Zakopane, Poland",
    address = "Netherlands",

    }

    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

    TY - CHAP

    T1 - A third-order topological invariant for three magnetic fields

    AU - Mayer, Christoph

    AU - Hornig, Gunnar

    N1 - dc.description.sponsorship: Volkswagen Foundation

    PY - 2002

    Y1 - 2002

    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.

    U2 - 10.1007/0-306-48420-X_22

    DO - 10.1007/0-306-48420-X_22

    M3 - Chapter

    SN - 9781402009808

    SN - 1402009801

    T3 - Fluid mechanics and its applications

    SP - 151

    EP - 156

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

    A2 - Bajer, K.

    A2 - Moffatt, H. K.

    PB - Kluwer Academic Publishers

    ER -

    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