Force-Free Equilibria of a Magnetized Plasma Arcade

Magnetized plasma arcades and flux ropes appear in space and astrophysical contexts and have been the subject of many laboratory, observational, and computational studies. We develop analytical and numerical solutions to the force-free arcade problem and compare with experimental measurements from the Wheaton Impulsive Reconnection eXperiment (WIRX). A 2D cylindrical model for a thin magnetized arcade is extended to a thick arcade with constant J/B between two coaxial cylindrical boundaries. The obtained solutions are then used as initial conditions for numerical simulations with the open-source AMRVAC code. The MHD simulations permit a magnetic field that does not have strict cylindrical symmetry and is more experimentally relevant. The simulations show that the plasma arcade thickens in the middle and has a slightly different current profile relative to the analytical solution. A key characteristic of the arcade equilibrium is the profile of the angle of the magnetic field lines. Higher currents and lower magnetic fields produce large shear angles and taller, thicker arcades. In experiment, at large enough I/B, the character of the shear angle profile changes significantly, perhaps indicating a lack of equilibrium or large-scale instability. Work is ongoing to see if the 2D MHD simulations can describe similar behavior.