Non-Dissipative Saturation of the Magnetorotational Instability in Thin Disks

TL;DR

This paper introduces a novel non-dissipative mechanism for MRI saturation in thin Keplerian disks, involving energy transfer to stable magnetosonic waves due to vertical stratification and boundary conditions, supported by analytical and numerical evidence.

Contribution

It proposes a new saturation mechanism for MRI based on mode interaction with magnetosonic waves, derived from a Duffing-like amplitude equation and validated through numerical simulations.

Findings

MRI spectrum becomes discrete due to vertical stratification.

The amplitude equation predicts bursty oscillations at saturation.

Numerical solutions confirm the theoretical saturation level.

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.