Magnetic Flux-Current Surfaces of 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 astrophysical plasma structures. A magnetic flux-current surface is a surface, in which both magnetic field lines and current lines lie. We for the first time derive 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.

Magnetohydrostatic Modeling of the Solar Atmosphere

“…It is worth noting that, by taking divergence of equation ( 20), the two current systems are conserved separately (Low 1993). An interesting inference from the uncoupled currents is that there exists magnetic flux-current surface where the magnetic flux surface and the current surface overlap (Choe & Minhwan 2013). Low (1993) showed that all MHS equilibria of symmetric system have uncoupled electric currents with two independent coordinates.…”