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Saturation of the magnetorotational instability by stable magnetoacoustic modes

Published online by Cambridge University Press:  18 July 2013

Edward Liverts ,
Yuri Shtemler ,
Michael Mond ,
Orkan M. Umurhan  and
Dmitry V. Bisikalo
Edward Liverts
Affiliation:
Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel email: eliverts@bgu.ac.il, yshtemler@gmail.com, mond@bgu.ac.il
Yuri Shtemler
Affiliation:
Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel email: eliverts@bgu.ac.il, yshtemler@gmail.com, mond@bgu.ac.il
Michael Mond
Affiliation:
Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel email: eliverts@bgu.ac.il, yshtemler@gmail.com, mond@bgu.ac.il
Orkan M. Umurhan
Affiliation:
School of Natural Sciences, UC Merced, Merced, CA 95343, USA, and City College of San Francisco, San Francisco, CA 94112, USA email: oumurhan@ucmerced.edu
Dmitry V. Bisikalo
Affiliation:
Institute of Astronomy of the Russian Academy of Science, 48 Pyatnitskaya, Moscow, Russia email: bisikalo@inasan.rssi.ru
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Abstract

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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 Alfven-Coriolis (MRI) modes with stable magnetoacoustic waves is considered. The transition of the Alfven-Coriolis modes to instability occurs when the linearized system has zero eigenvalue of multiplicity two. 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. 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.

Keywords

Accretionmagnetohydrodynamicsinstabilities
Type
Contributed Papers
Information
Proceedings of the International Astronomical Union , Volume 8 , Symposium S294: Solar and Astrophysical Dynamos and Magnetic Activity , August 2012 , pp. 365 - 366
Copyright
Copyright © International Astronomical Union 2013 

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