Magnetic neutral sheets in evolving fields. I - General theory. II - Formation of the solar corona

This paper treats the problem of hydrostatic equilibrium of a large-scale magnetic field embedded in a fluid with infinite electrical conductivity. It was shown some years ago that a necessary condition for static equilibrium is the invariance of the small-scale pattern in the field along the large-scale direction. A varying topological pattern implies that there is no fluid pressure distribution for which the field is everywhere static. Magnetic neutral sheets form, and dynamical reconnection of the field occurs. In the present paper it is shown that the invariance is also a sufficient condition for the existence of a fluid pressure distribution producing static equilibrium. However, even in the simplest cases the requirements on the fluid pressure are extreme and a priori unlikely. We conclude that almost all twisted flux tubes packed together produce dynamical nonequilibrium and dissipation of their twisting. This is the basic effect behind the long-standing conjecture that the shuffling of the footprints of the bipolar magnetic fields in the Sun is responsible for heating the active corona.