  We carry out three-dimensional magnetohydrodynamical simulations of the
magnetorotational (Balbus-Hawley) instability in weakly-ionized plasmas. We
adopt a formulation in which the ions and neutrals each are treated as separate
fluids coupled only through a collisional drag term. Ionization and
recombination processes are not considered. The linear stability of the
ion-neutral system has been previously considered by Blaes and Balbus (1994).
Here we extend their results into the nonlinear regime by computing the
evolution of Keplerian angular momentum distribution in the local shearing box
approximation. We find significant turbulence and angular momentum transport
when the collisional frequency is on order 100 times the orbital frequency. At
higher collision rates, the two-fluid system studied here behaves much like the
fully ionized systems studied previously. At lower collision rates the
evolution of the instability is determined primarily by the properties of the
ions, with the neutrals acting as a sink for the turbulence. Since in this
regime saturation occurs when the magnetic field is superthermal with respect
to the ion pressure, we find the amplitude of the magnetic energy and the
corresponding angular momentum transport rate is proportional to the ion
density. Our calculations show the ions and neutrals are essentially decoupled
when the collision frequency is less than 0.01 times the orbital frequency; in
this case the ion fluid behaves as in the single fluid simulations and the
neutrals remain quiescent. We find that purely toroidal initial magnetic field
configurations are unstable to the magnetorotational instability across the
range of coupling frequencies.

Astrophysics