Helicity, Topology, and Force-Free Magnetic Fields

Phys. Rev. E Vol. 47, p. 3607 (1993) (PDF)

Concepts from topology are increasingly finding utility in magnetohydrodynamics. This paper gives an example of how the connectivity of the domain and the gauge freedom of the vector potential can play an important role in computing the helicity of twisted magnetic fields used in several areas of astrophysics, particularly solar physics. By computing the relative helicity of a simple magnetic field configuration used to model solar prominences, it is shown that helicity can have a non-local character. This necessitates a reexamination of its conventional physical interpretation. The magnetic energy is also discussed.