  Activity of the nuclei of galaxies and stellar mass systems involving disk
accretion to black holes is thought to be due to (1) a small-scale turbulent
magnetic field in the disk (due to the magneto-rotational instability or MRI)
which gives a large viscosity enhancing accretion, and (2) a large-scale
magnetic field which gives rise to matter outflows and/or electromagnetic jets
from the disk which also enhances accretion. An important problem with this
picture is that the enhanced viscosity is accompanied by an enhanced magnetic
diffusivity which acts to prevent the build up of a significant large-scale
field. Recent work has pointed out that the disk's surface layers are
non-turbulent and thus highly conducting (or non-diffusive) because the MRI is
suppressed high in the disk where the magnetic and radiation pressures are
larger than the thermal pressure. Here, we calculate the vertical ($z$)
profiles of the stationary accretion flows (with radial and azimuthal
components), and the profiles of the large-scale, magnetic field taking into
account the turbulent viscosity and diffusivity due to the MRI and the fact
that the turbulence vanishes at the surface of the disk. The stationary
solutions we find indicate that a weak ($\beta > 1$) large-scale field does not
diffuse away as suggested by earlier work.
