Equilibria, dynamics, and current sheet formation in magnetically confined coronae

The dynamics of magnetic fields in closed regions of solar and stellar coronae are investigated with a reduced magnetohydrodynamic (MHD) model in the framework of the Parker scenario for coronal heating. A novel analysis of reduced MHD equilibria shows that their magnetic fields have an asymmetric structure in the axial direction with variation length scale z_ℓ ∼ ℓB₀/b, where B₀ is the intensity of the strong axial guide field, b that of the orthogonal magnetic field component, and ℓ the scale of $b.$ Equilibria are then quasi-invariant along the axial direction for variation scales larger than approximatively the loop length z_ℓ ≳ L_z, and increasingly more asymmetric for smaller variation scales z_ℓ ≲ L_z. The critical length z_ℓ ∼ L_z corresponds to the magnetic field intensity threshold b ∼ ℓB₀/L_z. Magnetic fields stressed by photospheric motions cannot develop strong axial asymmetries. Therefore, fields with intensities below such a threshold evolve quasi-statically, readjusting to a nearby equilibrium, without developing nonlinear dynamics or dissipating energy. But stronger fields cannot access their corresponding asymmetric equilibria; hence, they are out of equilibrium and develop nonlinear dynamics. The subsequent formation of current sheets and energy dissipation is necessary for the magnetic field to relax to equilibrium, since dynamically accessible equilibria have variation scales larger than the loop length z_ℓ ≳ L_z, with intensities smaller than the threshold b ≲ ℓB₀/L_z. The dynamical implications for magnetic fields of interest to solar and stellar coronae are investigated numerically and the impact on coronal physics discussed.