  The launching of magnetohydrodynamic outflows from accretion disks is
considered. We formulate a model for the local vertical structure of a thin
disk threaded by a poloidal magnetic field of dipolar symmetry. The model
consists of an optically thick disk matched to an isothermal atmosphere. The
disk is supposed to be turbulent and possesses an effective viscosity and an
effective magnetic diffusivity. In the atmosphere, if the magnetic field lines
are inclined sufficiently to the vertical, a magnetocentrifugal outflow is
driven and passes through a slow magnetosonic point close to the surface. We
determine how the rate of mass loss varies with the strength and inclination of
the magnetic field. In particular, we find that for disks in which the mean
poloidal field is sufficiently strong to stabilize the disk against the
magnetorotational instability, the mass loss rate decreases extremely rapidly
with increasing field strength, and is maximal at an inclination angle of 40-50
degrees. For turbulent disks with weaker mean fields, the mass loss rate
increases monotonically with increasing strength and inclination of the field,
but the solution branch terminates before achieving excessive mass loss rates.
Our results suggest that efficient jet launching occurs for a limited range of
field strengths, and a limited range of inclination angles in excess of 30
degrees. In addition, we determine the direction and rate of radial migration
of the poloidal magnetic flux, and discuss whether configurations suitable for
jet launching can be maintained against dissipation.
