  We study the role of ambipolar diffusion (AD) on the non-linear evolution of
the MRI in protoplanetary disks using the strong coupling limit, which applies
when the electron recombination time is much shorter than the orbital time. The
effect of AD in this limit is characterized by the dimensionless number Am, the
frequency of which neutral particles collide with ions normalized to the
orbital frequency. We perform three-dimensional unstratified shearing-box
simulations of the MRI over a wide range of Am as well as different magnetic
field strengths and geometries. The saturation level of the MRI turbulence
depends on the magnetic geometry and increases with the net magnetic flux.
There is an upper limit to the net flux for sustained turbulence, corresponding
to the requirement that the most unstable vertical wavelength be less than the
disk scale height. Correspondingly, at a given Am, there exists a maximum value
of the turbulent stress alpha_max. For Am<1, the largest stress is associated
with a field geometry that has both net vertical and toroidal flux. In this
case, we confirm the results of linear analyses that show the fastest growing
mode has a non-zero radial wave number with growth rate exceeding the pure
vertical field case. We find there is a very tight correlation between the
turbulent stress (alpha) and the plasma beta=P_gas/P_mag~1/(2alpha) at the
saturated state of the MRI turbulence regardless of field geometry, and
alpha_max rapidly decreases with decreasing Am. In particular, we quote
alpha_max~0.007 for Am=1 and alpha_max~0.0006 for Am=0.1.
