Non-Dissipative Saturation of the Magnetorotational Instability in Thin
  Disks
  A new non-dissipative mechanism is proposed for the saturation of the
axisymmetric magnetorotational (MRI) instability in thin Keplerian disks that
are subject to an axial magnetic field. That mechanism relies on the energy
transfer from the MRI to stable magnetosonic (MS) waves. Such mode interaction
is enabled due to the vertical stratification of the disk that results in the
discretization of its MRI spectrum, as well as by applying the appropriate
boundary conditions. A second order Duffing-like amplitude equation for the
initially unstable MRI modes is derived. The solutions of that equation exhibit
bursty nonlinear oscillations with a constant amplitude that signifies the
saturation level of the MRI. Those results are verified by a direct numerical
solution of the full nonlinear reduced set of thin disk magnetohydrodynamics
equations.
