Tubes of Magnetic Flux and Electric Current in Space Physics

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 three-space and allows for a definition of cosmic field flux tubes and flux ropes as cores (in the sense of the physics of defects) of helical singularities. When applied to force-free flux ropes, and assuming current conservation, an interesting feature is the quantization of the radii, pitches, and helicities. One expects similar quantization effects in the general case. 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. Magnetic merging is also briefly discussed in the same framework.