Braided magnetic fields: equilibria, relaxation and heating

D. I. Pontin (Lead / Corresponding author), S. Candelaresi, A. J. B. Russell, G. Hornig

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We examine the dynamics of magnetic flux tubes containing non trivial field line braiding (or linkage), using mathematical and computational modelling, in the context of testable predictions for the laboratory and their significance for solar coronal heating. We investigate the existence of braided force-free equilibria, and demonstrate that for a field anchored at perfectly-conducting plates, these equilibria exist and contain current sheets whose thickness scales inversely with the braid complexity – as measured for example by the topological entropy. By contrast, for a periodic domain braided exact equilibria typically do not exist, while approximate equilibria contain thin current sheets. In the presence of resistivity, reconnection is triggered at the current sheets and a turbulent relaxation ensues. We finish by discussing the properties of the turbulent relaxation and the existence of constraints that may mean that the final state is not the linear force-free field predicted by Taylor’s hypothesis.
Original languageEnglish
Article number054008
Pages (from-to)1-10
Number of pages10
JournalPlasma Physics and Controlled Fusion
Issue number5
Early online date19 Apr 2016
Publication statusPublished - 1 May 2016


  • equilibria
  • magnetic fields
  • magnetic topology
  • relaxation


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