  The saturation mechanism of Magneto-Rotational Instability (MRI) is examined
through analytical quasilinear theory and through nonlinear computation of a
single mode in a rotating disk. We find that large-scale magnetic field is
generated through the alpha effect (the correlated product of velocity and
magnetic field fluctuations) and causes the MRI mode to saturate. If the
large-scale plasma flow is allowed to evolve, the mode can also saturate
through its flow relaxation. In astrophysical plasmas, for which the flow
cannot relax because of gravitational constraints, the mode saturates through
field generation only.
