The Magneto-Rotational Decay Instability in Keplerian Disks

TL;DR

This paper introduces a new saturation mechanism for the magnetorotational instability in Keplerian disks, involving three-wave resonant interactions leading to nonlinear oscillations and decay instability.

Contribution

It generalizes the decay instability concept to Keplerian disks, deriving amplitude equations and analyzing nonlinear wave interactions in MRI saturation.

Findings

Identifies a decay instability mechanism for MRI saturation.

Derives amplitude equations describing wave interactions.

Shows bounded oscillations and unbounded growth in wave amplitudes.

Abstract

The saturation of the magnetorotational (MRI) instability in thin Keplerian disks through three wave resonant interactions is introduced and discussed. That mechanism is a natural generalization of the fundamental decay instability discovered five decades ago for infinite, homogeneous and immovable plasmas. The decay instability relies on the energy transfer from the MRI to stable slow Alfv'en-Coriolis (AC) as well as magnetosonic (MS) waves. A second order forced Duffing amplitude equation for the initially unstable MRI as well as two first order equations for the other two waves are derived. The solutions of those equations exhibit bounded bursty nonlinear oscillations for the MRI as well as unbounded growth for the linearly stable slow AC and MS perturbations, thus giving rise to the magneto-rotational decay instability (MRDI).