On self and mutual winding helicity

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

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
38 Downloads (Pure)


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
Article number106015
Number of pages11
JournalCommunications in Nonlinear Science and Numerical Simulation
Early online date29 Aug 2021
Publication statusPublished - Dec 2021


  • Helicity
  • Magnetic topology
  • Magnetohydrodynamics

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics


Dive into the research topics of 'On self and mutual winding helicity'. Together they form a unique fingerprint.

Cite this