Topological constraints on the relaxation of complex magnetic fields

    Research output: Chapter in Book/Report/Conference proceedingConference contribution


    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 languageEnglish
    Title of host publicationMagnetic fields and solar processes, proceedings of the 9th European Meeting on Solar Physics. 12-18 September 1999, Florence, Italy
    EditorsA. Wilson
    Place of PublicationNoordwijk
    PublisherEuropean Space Agency
    Number of pages4
    ISBN (Print)9290927925, 9789290927921
    Publication statusPublished - 1999
    EventThe 9th European Meeting on Solar Physics: Magnetic Fields and Solar Processes - Florence, Italy
    Duration: 12 Sept 199918 Sept 1999

    Publication series

    NameESA special publications
    PublisherEuropean Space Agency


    ConferenceThe 9th European Meeting on Solar Physics: Magnetic Fields and Solar Processes
    Internet address


    • Magnetic fields
    • Topological invariants
    • Magnetic reconnection


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