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The energy and helicity of knotted magnetic flux tubes. (English) Zbl 0876.76086

(From the authors’ summary.) We consider magnetic relaxation of a magnetic field embedded in a perfectly conducting incompressible fluid to minimum energy magnetostatic equilibrium states. It is supposed that the magnetic field is confined to a single flux tube which may be knotted. A local non-orthogonal coordinate system, zero-framed with respect to the knot, is introduced, and the field is decomposed into toroidal and poloidal ingredients with respect to this system. The helicity of the field is then determined; this vanishes for a field that is either purely toroidal or purely poloidal. The magnetic energy functional is calculated under the simplifying assumptions that the tube is axially uniform and of circular cross-section. The case of a tube with helical axis is first considered, and new results concerning kink mode instability and associated bifurcations are obtained. Finally, we consider the case of flux tubes in the form of torus knots.
Reviewer: P.Smith (Keele)

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
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