Ion dynamics and the magnetorotational instability in weakly-ionized discs

The magnetorotational instability (MRI) of a weakly ionized, differentially rotating, magnetized plasma disk is investigated in the multi-fluid framework. The disk is threaded by a uniform vertical magnetic field and charge is carried by electrons and ions only. The inclusion of ion dynamics causes significant modification to the conductivity tensor in a weakly ionized disk. The parallel, Pedersen and Hall component of conductivity tensor become time dependent quantities resulting in the AC and DC part of the conductivity. The conductivity may change sign leading to the significant modification of the parameter window in which MRI may operate. The effect of ambipolar and Hall diffusion on the linear growth of the MRI is examined in the presence of time dependent conductivity tensor. We find that the growth rate in ambipolar regime can become somewhat larger than the rotational frequency, especially when the departure from ideal MHD is significant. Further, the instability operates on large scale lengths. This has important implication for the angular momentum transport in the disk.