Hostname: page-component-7c8c6479df-r7xzm Total loading time: 0 Render date: 2024-03-28T13:43:28.576Z Has data issue: false hasContentIssue false

Saturation of the magnetorotational instability by stable magnetoacoustic modes

Published online by Cambridge University Press:  18 July 2013

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Contributed Papers
Copyright
Copyright © International Astronomical Union 2013 

References

Velikhov, E. P. 1959, Soviet Physics JETP, 36, 995 Google Scholar
Chandrasekhar, S. 1960, Proc. Natl. Acad. Sci., 46, 253 Google Scholar
Balbus, S. A. & Hawley, J. F. 1991, Astrophys. J., 376, 214 Google Scholar
Balbus, S. A. & Hawley, J. F. 2003, Annu. Rev. Astron. Astrophys., 41, 555 CrossRefGoogle Scholar
Knobloch, E. & Julien, K. 2005, Phys. Fluids, 17, 094106 Google Scholar
Umurhan, O. M., Menou, K., & Regev, O. 2007, Phys. Rev. Lett., 98, 034501 CrossRefGoogle Scholar
Regev, O. 1983, A&A, 126, 146 Google Scholar
Kluźniak, W. & Kita, D. 1985, arXiv:astro-ph/0006266Google Scholar
Umurhan, O. M., Nemirovsky, A., Regev, O., & Shaviv, G. 2006, A&A, 446, 1 Google Scholar
Shtemler, Y., Mond, M., & Liverts, E. 2007, Astrophys. J., 665, 1371 CrossRefGoogle Scholar
Shtemler, Y., Mond, M., & Rüdiger, G. 2009, MNRAS, 394, 1379 CrossRefGoogle Scholar
Shtemler, Y., Mond, M., & Liverts, E. 2011, MNRAS, 413, 2957 CrossRefGoogle Scholar
Liverts, E. & Mond, M. 2009, MNRAS, 392, 287 Google Scholar
Liverts, E., Shtemler, Y., & Mond, M. 2012a, AIP Proceedings no 1439, WISAP, Sulem, P.L., and Mond, M., Editors, 136Google Scholar
Liverts, E., Shtemler, Y., Mond, M., Umurhan, O. M., & Bisikalo, D. V. 2012b, Phys. Rev. Lett., 109, 224501 CrossRefGoogle Scholar