A third-order topological invariant for three magnetic fields
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.
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- A third-order topological invariant for three magnetic fields
- Book Title
- Tubes, Sheets and Singularities in Fluid Dynamics
- Book Subtitle
- Proceedings of the NATO RAW held in Zakopane, Poland, 2–7 September 2001, Sponsored as an IUTAM Symposium by the International Union of Theoretical and Applied Mechanics
- Book Part
- pp 151-156
- Print ISBN
- Online ISBN
- Series Title
- Fluid Mechanics and Its Applications
- Series Volume
- Series ISSN
- Springer Netherlands
- Copyright Holder
- Kluwer Academic Publishers
- Additional Links
- eBook Packages
- Editor Affiliations
- 2. Institute of Geophysics, Warsaw University
- 3. Department of Applied Mathematics and Theoretical Physics, University of Cambridge
- Author Affiliations
- 4. Theoretische Physik IV, Fakultät für Physik und Astronomie, Ruhr-Universität Bochum, 44780, Bochum, Germany
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