Linear and weakly nonlinear analysis of the magneto-rotational-instability in thin keplerian discs

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Abstract

The linear instability of thin, vertically-isothermal Keplerian discs, under the influence of axial magnetic field is investigated. Solutions of the stability problem are found explicitly by asymptotic expansions in the small aspect ratio of the disc. It is shown that the perturbations are decoupled into in-plane and vertical modes. Exact expressions for the growth rates as well as the number of unstable modes are derived. Those are the discrete counterpart of the continuous infinite homogeneous cylinder magnetorotational (MRI) spectrum. In addition, a weakly nonlinear analysis of the MRI is performed. It is shown that near the instability threshold the latter is saturated by the stable magnetoacoustic modes.

Original languageEnglish
Title of host publicationWaves and Instabilities in Space and Astrophysical Plasmas
Pages136-153
Number of pages18
DOIs
StatePublished - 1 Dec 2012
EventWorkshop on Waves and Instabilities in Space and Astrophysical Plasmas - Eilat, Israel
Duration: 19 Jun 201124 Jun 2011

Publication series

NameAIP Conference Proceedings
Volume1439
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceWorkshop on Waves and Instabilities in Space and Astrophysical Plasmas
Country/TerritoryIsrael
CityEilat
Period19/06/1124/06/11

Keywords

  • Accretion
  • Instabilities
  • Magnetohydrodynamics

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