Variational analysis of topological stationary barotropic MHD in the case of single-valued magnetic surfaces

Tangled Magnetic Fields in Astro- and Plasma Physics; Quantised Flux in Tightly Knotted and Linked Systems

Yahalom, A.^1,2

Ariel University, Ariel

40700, Israel^1

Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge

CB3 0EH, United Kingdom^2

关键词: Aharonov-Bohm phase;    Independent functions;    Magnetic field line;    Magnetic helicity;    Magnetic surfaces;    Topological conservation;    Variational analysis;    Variational principles;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/544/1/012009/pdf
DOI  :  10.1088/1742-6596/544/1/012009

来源: IOP

【 摘 要 】

Variational principles for magnetohydrodynamics have been introduced by previous authors both in Lagrangian and Eulerian form. Yahalom & Lynden-Bell (2008) have previously introduced simpler Eulerian variational principles from which all the relevant equations of barotropic magnetohydrodynamics can be derived. These variational principles were given in terms of six independent functions for non-stationary barotropic flows with given topologies and three independent functions for stationary barotropic flows. This is less then the seven variables which appear in the standard equations of barotropic magnetohydrodynamics which are the magnetic field the velocity field and the density ρ. Later, Yahalom (2010) introduced a simpler variational principle in terms of four functions for non-stationary barotropic magnetohydrodynamics. It was shown that the above variational principles are also relevant for flows of non-trivial topologies and in fact using those variational variables one arrives at additional topological conservation laws in terms of cuts of variables which have close resemblance to the Aharonov- Bohm phase (Yahalom (2013)). In previous examples (Yahalom & Lynden-Bell (2008); Yahalom (2013)) the magnetic field lines with non-trivial topology were at the intersection of two surface one of which was always multivalued; in this paper an example is introduced in which the magnetic helicity is not zero yet both surfaces are single-valued.