A third-order topological invariant for three magnetic fields

  • Christoph Mayer
  • Gunnar Hornig
Conference paper
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 71)


The topology of divergence-free fields is important in many parts of physics, e. g. in magnetohydrodynamics, plasma physics, hydrodynamics, superfluids etc. With the focus on applications in magnetohydrodynamics, our principal aim is the characterisation of magnetic fields by the means of invariants.

In this report an introduction to the problem of finding higher order invariants is given. Then a third-order link integral of three magnetic fields is presented, which can be shown to be a topological invariant and therefore an invariant in ideal magnetohydrodynamics. This integral generalises the known third-order link invariant derived from the Massey triple product, which could only be applied to isolated flux tubes. As an example three magnetic fields not confined to flux tubes are given that possess a third-order linkage.


Magnetic Field Field Line Flux Tube Magnetic Helicity Magnetic Flux Tube 
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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Christoph Mayer
    • 1
  • Gunnar Hornig
    • 1
  1. 1.Theoretische Physik IV, Fakultät für Physik und AstronomieRuhr-Universität BochumBochumGermany

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