Axisymmetric equilibria of a gravitating plasma with incompressible flows

It is found that the ideal magnetohydrodynamic equilibrium of an axisymmetr ic gravitating magnetically confined plasma with incompressible flows is go verned by a second-order elliptic differential equation for the poloidal ma gnetic flux function containing five flux functions coupled with a Poisson equation for the gravitation potential, and an algebraic relation for the p ressure. This set of equations is amenable to analytic solutions. As an app lication, the magnetic-dipole static axisymmetric equilibria with vanishing poloidal plasma currents derived recently by Krasheninnikov et at. (1999) are extended to plasmas with finite poloidal currents, subject to gravitati ng forces from a massive body (a star or black hole) and inertial forces du e to incompressible sheared flows. Explicit solutions are obtained in two r egimes: (a) in the low-energy regime beta (o) approximate to gamma (o) appr oximate to delta (o) approximate to epsilon (o) << 1, where beta (o), gamma (o), delta (o), and epsilon (o) are related to the thermal, poloidal-curre nt, flow and gravitating energies normalized to the poloidal-magnetic-field energy, respectively, and (b) in the high-energy regime beta (o) approxima te to gamma (o) approximate to delta (o) approximate to epsilon (o) >> 1. I t turns out that in the high-energy regime all four forces, pressure-gradie nt, toroidal-magnetic-field, inertial, and gravitating contribute equally t o the formation of magnetic surfaces very extended and localized about the symmetry plane such that the resulting equilibria resemble the accretion di sks in astrophysics.