  Given the important role turbulence plays in the settling and growth of dust
grains in protoplanetary disks, it is crucial that we determine whether these
disks are turbulent and to what extent. Protoplanetary disks are weakly ionized
near the mid-plane, which has led to a paradigm in which largely laminar
magnetic field structures prevail deeper in the disk, with angular momentum
being transported via magnetically launched winds. Yet, there has been little
exploration on the precise behavior of the gas within the bulk of the disk. We
carry out 3D, local shearing box simulations that include all three
low-ionization effects (Ohmic diffusion, ambipolar diffusion, and the Hall
effect) to probe the nature of magnetically driven gas dynamics 1-30 AU from
the central star. We find that gas turbulence can persist with a generous yet
physically motivated ionization prescription (order unity Elsasser numbers).
The gas velocity fluctuations range from 0.03-0.09 of the sound speed $c_s$ at
the disk mid-plane to $\sim c_s$ near the disk surface, and are dependent on
the initial magnetic field strength. However, the turbulent velocities do not
appear to be strongly dependent on the field polarity, and thus appear to be
insensitive to the Hall effect. The mid-plane turbulence has the potential to
drive dust grains to collision velocities exceeding their fragmentation limit,
and likely reduces the efficacy of particle clumping in the mid-plane, though
it remains to be seen if this level of turbulence persists in disks with lower
ionization levels.
