Physical role of topological constraints in localized magnetic relaxation

A. R. Yeates (Lead / Corresponding author), A. J. B. Russell, G. Hornig

    Research output: Contribution to journalArticlepeer-review

    16 Citations (Scopus)
    34 Downloads (Pure)


    Predicting the final state of turbulent plasma relaxation is an important challenge, both in astro-physical plasmas such as the Sun's corona and in controlled thermonuclear fusion. Recent numerical simulations of plasma relaxation with braided magnetic fields identified the possibility of a novel constraint, arising from the topological degree of the magnetic field-line mapping. This constraint implies that the final relaxed state is drastically different for an initial configuration with topological degree 1 (which allows a Taylor relaxation) and one with degree 2 (which does not reach a Taylor state). Here, we test this transition in numerical resistive-magnetohydrodynamic simulations, by embedding a braided magnetic field in a linear force-free background. Varying the background force-free field parameter generates a sequence of initial conditions with a transition between topological degree 1 and 2. For degree 1, the relaxation produces a single twisted flux tube, whereas for degree 2 we obtain two flux tubes. For predicting the exact point of transition, it is not the topological degree of the whole domain that is relevant, but only that of the turbulent region.
    Original languageEnglish
    Article number20150012
    Number of pages12
    JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    Issue number2178
    Early online date8 Jun 2015
    Publication statusPublished - 8 Jun 2015


    • Coronal heating
    • Magnetic topology
    • Magnetohydrodynamics
    • Plasma relaxation

    ASJC Scopus subject areas

    • Mathematics(all)
    • Engineering(all)
    • Physics and Astronomy(all)


    Dive into the research topics of 'Physical role of topological constraints in localized magnetic relaxation'. Together they form a unique fingerprint.

    Cite this