On self and mutual winding helicity

Simon Candelaresi, Gunnar Hornig, David MacTaggart (Lead / Corresponding author), Radostin D. Simitev

Research output: Working paper/PreprintPreprint


The topological underpinning of magnetic fields connected to a planar boundary is naturally described by field line winding. This observation leads to the definition of winding helicity, which is closely related to the more commonly calculated relative helicity. Winding helicity, however, has several advantages, and we explore some of these in this work. In particular, we show, by splitting the domain into distinct subregions, that winding helicity can be decomposed naturally into "self" and "mutual" components and that these quantities can be calculated, in practice, for magnetic fields with complex geometries and topologies. Further, winding provides a unified topological description from which known expressions for self and mutual helicity can be readily derived and generalized. We illustrate the application of calculating self and mutual winding helicities in a simulation of an evolving magnetic field with non-trivial field line topology.
Original languageEnglish
Number of pages16
Publication statusPublished - 19 Aug 2021


  • math-ph
  • math.MP
  • nlin.CD
  • physics.flu-dyn
  • physics.plasm-ph


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  • On self and mutual winding helicity

    Candelaresi, S., Hornig, G., MacTaggart, D. & Simitev, R. D., Dec 2021, In: Communications in Nonlinear Science and Numerical Simulation. 103, 11 p., 106015.

    Research output: Contribution to journalArticlepeer-review

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