Magnetorotational Instability in Collisional Weakly Ionized Plasma with Distinct Species Velocities

Abstract In a differential rotating system, we use the incompressible multifluid model to investigate the dynamics of a weakly ionized plasma placed in a vertical background magnetic field with radial shearing. The equilibrium current is taken into account. The differences in velocities between charged species and neutrals are supposed to be related to the collisions. The analytical expression of the general local dispersion relation is derived and the effect of the shearing magnetic field is demonstrated in three different limiting cases. Momentum transfer to neutrals is neglected in the first case, and the instability criteria are provided with the involvement of magnetic field shearing. In the magnetohydrodynamic (MHD) case, the previous results are reproduced when setting the equilibrium current density to zero, and the magnetic field structure is depicted to restrain/reinforce the instability in the Keplerian system with decaying/increasing shearing. In the last case, the finite collisions with weak ionization and ion Hall effects generate another unstable vertical mode compared with the MHD case and also alleviate the unstable waves propagated between the horizontal and vertical directions.