EQUILIBRIUM OF SOLAR CORONAL ARCADES

Properties of two-dimensional straight (symmetric in z) magnetic arcade equilibria in the solar corona are studied within the framework of magnetohydrodynamics (MHD). Sequences of MHD equilibria are obtained by solving the Grad-Shafranov equation with the footpoint displacement or the entropy prescribed. It is shown that no multiple solutions, or bifurcations, result. This is to be contrasted with the approach of prescribing the axial magnetic field Bz(ψ) or pressure p(ψ), in which bifurcations do occur. The physical conditions for which the footpoint displacement or entropy, as opposed to Bz or p, must be specified are discussed. It is argued that these conditions are more likely to occur in the corona than those under which Bz and p may be prescribed. The lack of bifurcations indicates that equilibrium will not be lost as the footpoint displacement or entropy is increased. The limiting configurations for infinite footpoint displacement and infinite entropy are also discussed. It is shown that although the current density does become somewhat peaked, the total current in the peak region decreases as the system is sheared (or heated). In fact, the current in this peak region contains a rapidly decreasing fraction of the total current, so that the limiting configuration is not one in which the current is concentrated into a current sheet.