Euler potentials for the MHD Kamchatnov-Hopf soliton solution

Details Euler potentials for the MHD Kamchatnov-Hopf soliton solution Euler potentials for the MHD Kamchatnov-Hopf soliton solution

2001-11-30

arxiv.org/abs/physics/0111212v1

Physics

Plasma Physics

15 pages, 12 figures

Scientific paper

In the MHD description of plasma phenomena the concept of magnetic helicity turns out to be very useful. We present here an example of introducing Euler potentials into a topological MHD soliton which has non-trivial helicity. The MHD soliton solution (Kamchatnov, 1982) is based on the Hopf invariant of the mapping of a 3D sphere into a 2D sphere; it can have arbitrary helicity depending on control parameters. It is shown how to define Euler potentials globally. The singular curve of the Euler potential plays the key role in computing helicity. With the introduction of Euler potentials, the helicity can be calculated as an integral over the surface bounded by this singular curve. A special programme for visualization is worked out. Helicity coordinates are introduced which can be useful for numerical simulations where helicity control is needed.

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