Non-Dissipative Saturation of the Magnetorotational Instability in Thin Disks

Abstract

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.

4 pages, 3 figures; Phys. Rev. Lett. accepted

References in corpus (2)

• A weakly nonlinear analysis of the magnetorotational instability in a model channel flow
• Spectral and algebraic instabilities in thin Keplerian discs under poloidal and toroidal magnetic fields

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• Study of MRI in stratified viscous plasma configuration
• Explosive magnetorotational instability in Keplerian disks
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