Saturation of the magnetorotational instability

An analytical theory is developed that describes asymptotically exactly the process of nonlinear saturation of the magnetorotational instability in a model problem employing a linear shear flow in a uniformly rotating channel. The theory shows that the instability saturates by modifying the shear responsible for it. The saturation process requires both viscous and Ohmic dissipation. The theory also describes the approach from small-amplitude perturbations to the final strongly nonlinear saturated state.