Nondissipative Saturation of the Magnetorotational Instability in Thin Disks

Edward Liverts, Yuri Shtemler, Michael Mond, Orkan M. Umurhan, and Dmitry V. Bisikalo

Phys. Rev. Lett. 109, 224501 – Published 28 November 2012

Abstract

A new nondissipative 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 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.

Received 27 June 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.224501

Authors & Affiliations

Edward Liverts^*, Yuri Shtemler^†, and Michael Mond^‡

Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

Orkan M. Umurhan^§

School of Natural Sciences, University of California Merced, Merced, California 95343, USA
City College of San Francisco, San Francisco, California 94112, USA

Dmitry V. Bisikalo^∥