Effects of toroidal forces in current loops embedded in a background plasma

A theoretical study of the effects of toroidal forces in current loops is presented. The model loop is embedded in a plasma such as the solar corona. The magnetic field and current density have toroidal and poloidal components. The footpoints of the loop are assumed to be stationary in the dense photosphere, and current conservation is assumed to be established in or below the photosphere. Starting with non-force-free model loops in MHD equilibrium, the expansion motion of the loops is investigated. Some equilibrium loops are found to be unstable to major radial expansion. The condition for instability is given in terms of a parameter, which is a measure of the ratio of fluxes above and below the photosphere associated with the current loop. The motion of an unstable loop is due to the toroidicity of the current loop and is determined by the Lorentz force, pressure gradient, and drag force due to the ambient gas. It is found that model loops can exhibit a wide range of expansion motion with a correspondingly wide range of magnetic-energy dissipation due to drag heating.