Axisymmetric Equilibria of Thin Plasma Accretion Disks

The equilibrium axisymmetric configurations that thin plasma accretions disks immersed in force-free external magnetic fields can sustain are identified. In the case where the plasma pressure exceeds the magnetic pressure (β ≫ 1) the fields produced by toroidal currents localized within the disk are shown to correspond to the marginally stable axisymmetric ballooning modes identified in Refs. [1] and [2]. These fields are periodic radially with a period of the order of the height of the disk. When β ̃ 1, the radial periodicity of the magnetic field has a significant influence on the radial dependence of the plasma pressure as well. Then the radial equilibrium equation can no longer be treated separately from the vertical equilibrium equation as in the case where β ≫ 1. The relevant non-linear problem has been posed but not solved yet.