SATURATION OF THE MAGNETOROTATIONAL INSTABILITY BY STABLE MAGNETOACOUSTIC MODES

Liverts Eduard, eliverts@bgu.ac.il, Ben Gurion University of the Negev, Israel
Shtemler Yuri, yshtemler@gmail.com, Ben Gurion University of the Negev
Mond Michael, mond@bgu.ac.il, Ben Gurion University of the Negev
Umurhan Orkan, mumurhan@ccsf.edu, City College of San Francisco

Abstract
The magnetorotational instability (MRI) of thin, vertically-isothermal Keplerian discs, under the influence of an axial magnetic field is investigated near the instability threshold. The nonlinear interaction of in-plane Alfv?en-Coriolis (MRI) modes with stable vertical magnetoacoustic waves is considered. The transition of the Alfv?en-Coriolis modes to instability occurs when the linearized system has zero eigenvalue of multiplicity two. Such transition is characteristic of the Takens-Bogdanov type bifurcation. As a result the nonlinear ordinary differential equation that describes the evolution of the amplitude of the MRI mode near the threshold is of second order as opposed to first order equations (like the Landau-Ginzburg one) that characterize systems that bifurcate through a simple zero eigenvalue. Numerical solutions of that amplitude equation reveal that the MRI is saturated to bursty periodical oscillations due to the transfer of energy to the stable magnetosonic modes.