  We carry out a series of local, vertically stratified shearing box
simulations of protoplanetary disks that include ambipolar diffusion and a net
vertical magnetic field. The ambipolar diffusion profiles we employ correspond
to 30AU and 100AU in a minimum mass solar nebula (MMSN) disk model, which
consists of a far-UV-ionized surface layer and low-ionization disk interior.
These simulations serve as a follow up to Simon et al. (2013), in which we
found that without a net vertical field, the turbulent stresses that result
from the magnetorotational instability (MRI) are too weak to account for
observed accretion rates. The simulations in this work show a very strong
dependence of the accretion stresses on the strength of the background vertical
field; as the field strength increases, the stress amplitude increases. For gas
to magnetic pressure ratios of 1e4 and 1e5, we find accretion rates between
1e-8 and 1e-7 solar masses per year. These accretion rates agree with
observational constraints, suggesting a vertical magnetic field strength
between 60 and 200 microgauss at 30AU and 10 and 30 microgauss at 100AU in a
MMSN disk. Furthermore, the stress has a non-negligible component due to a
magnetic wind. For sufficiently strong vertical field strengths, MRI turbulence
is quenched, and the flow becomes largely laminar, with accretion proceeding
through large scale correlations in the radial and toroidal field components as
well as through the magnetic wind. In all simulations, the presence of a low
ionization region near the disk mid-plane, which we call the ambipolar damping
zone, results in reduced stresses there.
