Saturation of MRI via parasitic modes

Understanding the physical mechanisms that play a role in the saturation of the magnetorotational instability (MRI) has been an outstanding problem in accretion physics since the early 90's. Here, we present the summary of a study of the parasitic modes that feed off exact viscous, resistive MRI modes. We focus on the situation in which the amplitude of the magnetic field produced by the MRI is such that the instantaneous growth rate of the fastest parasitic mode matches that of the fastest MRI mode. We argue that this "saturation" amplitude provides an estimate of the magnetic field that can be generated by the MRI before the secondary instabilities suppress its growth significantly. We show that there exist two regimes, delimited by a critical Elsasser number of order unity, in which saturation is achieved via secondary instabilities that correspond to either Kelvin-Helmholtz or tearing modes.