Current Sheets Formation and Relaxation of Coronal Magnetic Fields

We investigate the relaxation of magnetic fields in closed regions of solar and stellar coronae, extending to further topologies our previous work (Rappazzo, A.F. & Parker, E.N., ApJL, 773, L2 (2013)). The dynamical evolution is integrated with the equations of reduced magnetohydrodynamics (RMHD) apt to model a plasma embedded in a strong guide field B0 extended along the axial direction, where the dynamical field is the orthogonal component b. Dissipative and ideal simulations are carried out in Cartesian geometry: magnetic field lines thread the system along the axial direction that spans the length L and are line-tied at the top and bottom plates in a motionless photosphere. The magnetic field b initially has only large scales, and is not in equilibrium. We show that the magnetic relaxation leads to the formation of current sheets when the intensity of the magnetic field b is beyond a critical value b_c. For values of b below this threshold (b < b_c), line-tying and field-line tension inhibit the formation of current sheets, while above the threshold (b > b_c) they form quickly on fast ideal timescales. In the ideal case, above the magnetic threshold, we show that current sheets thickness decreases in time until it becomes smaller than the grid resolution, with the analyticity strip width δ decreasing at least exponentially, after which the simulations become under-resolved.