Linear and Weakly Nonlinear Analysis of the Magneto-Rotational-Instability in Thin Keplerian Discs

Details Linear and Weakly Nonlinear Analysis of the Magneto-Rotational-Instability in Thin Keplerian Discs Linear and Weakly Nonlinear Analysis of the Magneto-Rotational-Instability in Thin Keplerian Discs

2012-01-13

arxiv.org/abs/1201.2847v1

Astronomy and Astrophysics

Astrophysics

Solar and Stellar Astrophysics

18 pages, 6 figures, to appear in the proceedings of the workshop "Waves and Instabilities in Space and Astrophysical plasmas"

Scientific paper

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.

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