The Existence Condition for Magnetic Flux-Current Surfaces in Magnetohydrostatic Equilibria

Abstract:

Magnetohydrostatic equilibria, in which the Lorentz force, the plasma pressure force and the gravitational force balance out to zero, are widely adopted as the zeroth order states of many space plasma systems. A magnetic flux-current surface is a surface, whose tangent plane is locally spanned by the magnetic field vector and the current density vector at each point in it; in other words, it is a surface, in which both magnetic field lines and current lines lie. We have derived the necessary and sufficient condition for existence of magnetic flux-current surfaces in magnetohydrostatic equilibria. It is also shown that the existence of flux-current surfaces is a necessary (but not sufficient) condition for the ratio of gravity-aligned components of current density and magnetic field to be constant along each field line. However, its necessary and sufficient condition is found to be very restrictive. This finding gives a significant constraint in modeling solar coronal magnetic fields as force-free fields using photospheric magnetic field observations.