Resistive evolution of toroidal field configurations and their relation to magnetic clouds

Abstract

We study the resistive evolution of a localized self-organizing magnetohydrodynamic equilibrium. In this configuration the magnetic forces are balanced by a pressure force caused by a toroidal depression in the pressure. Equilibrium is attained when this low pressure region prevents further expansion into the higher-pressure external plasma. We find that, for the parameters investigated, the resistive evolution of the structures follows a universal pattern when rescaled to resistive time. The finite resistivity causes both a decrease in the magnetic field strength and a finite slip of the plasma fluid against the static equilibrium. This slip is caused by a Pfirsch-Schl\"uter type diffusion, similar to what is seen in tokamak equilibria. The net effect is that the configuration remains in Magnetostatic equilibrium whilst it slowly grows in size. The rotational transform of the structure becomes nearly constant throughout the entire structure, and decreases according to a power law. In simulations this equilibrium is observed when highly tangled field lines relax in a high-pressure (relative to the magnetic field strength) environment, a situation that occurs when the twisted field of a coronal loop is ejected into the interplanetary solar wind. In this paper we relate this localized MHD equilibrium to magnetic clouds in the solar wind.