The behaviour of the diamagnetic current modified MRI in different rotation profiles

Magnetohydrodynamic turbulence driven by magnetorotational instability (MRI) has been widely accepted as an efficient mechanism for transporting angular momentum radially outward in the discs. Previously, we have shown the triggering effect of the magnetization currents and the gradients produced by these currents on MRI for Keplerian discs. In this work, we examine the properties of the diamagnetic current modified MRI for the discs where the epicyclic frequencies deviate from Keplerian behaviour. We show that the diamagnetic effect modifies the instability both for an increasing and for a decreasing angular momentum with radius. The novel unstable region produced by magnetization effects still exists even if dΩ /dR > 0, where Ω(R) is the angular velocity. Inclusion of the diamagnetic effect increases the maximum dimensionless growth rate sm = 0.25 which was found from the classical MRI to sm = 0.59 for an outwardly increasing angular velocity profile with κ > 4Ω , where κ is the epicyclic frequency. Moreover, the maximum dimensionless growth rate is obtained as sm = 8.58 for a an outwardly decreasing angular velocity profile with 0 < κ < Ω . Decreasing the magnetic field strength which is already weak, leads to more rapid growth in any differential rotation profile.