MHD equilibrium and stability properties of a bipolar current loop

A study is made of equilibrium and stability properties of a semi-toroidal current loop imbedded in a high temperature plasma. The loop carries a toroidal current density J _t and poloidal current density J _p. By explicity including the global curvature of the loop, the net Lorentz and pressure forces acting along the major radius are calculated. Requirement of equilibrium force-balance gives rise to conditions that must be satisfied by the physical parameters and geometry. On the basis of these conditions, we deduce a class of equilibrium semi-toroidal current loops satisfying c ^#X2212;1 J × B ? ▽p = 0. It is found that the averge pressure inside the loop is less than the ambient coronal pressure in equilibrium. Furthermore, this class of equilibria is shown to be stable to a number of destructive MHD modes. The theoretical results are discussed in the context of solar bipolar current loops.