Maurice Kleman, Jonathan M. Robbins
The singularities of an irrotational magnetic field are lines of electric current. This property derives from the relationship between vector fields and the topology of the underlying 3-space. When applied to cosmic fields, it allows for a definition of flux tubes and flux ropes as cores (in the sense of the physics of defects) of helical singularities. An interesting feature is the quantization of the radii, pitches and helicities of force-free flux ropes. In the special case when the total electric current vanishes, a force-free rope embedded in a medium devoid of magnetic field is nonetheless topologically stable, because it is the core of a singularity of the vector potential. This is reminiscent of vortex lines in superconductors. Magnetic reconnexion is also briefly discussed in the same framework. As a general rule the concepts of the theory of defects developed in condensed matter physics prove useful in raising new questions about the physical characteristics of flux ropes and electric currents in the cosmos.
View original:
http://arxiv.org/abs/1303.2677
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