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Axisymmetric magneto-rotational instability (MRI) is studied in comparison with interchange instability (IntI) in a rotating cylindrical plasma. MRI is driven by the shear of plasma rotation, and the IntI by the density gradient with effective gravity due to the plasma rotation. The eigenmode equation for the MRI has the same form as that for the IntI. The local stability criterion is also summarized in a similar statement as “the spatial gradient of centrifugal force greater than the square of Alfven frequency causes instability.” However, the MRI is essentially different from the IntI because of the non-Hermitian property. The Keplerian rotation generates irregular singularity at the center of the disk, which yields a continuum of eigenvalues with non-orthogonal and square-integrable eigenfunctions.

MHD Stability in Flowing Plasmas: Connection between Fusion Plasma and Astrophysics Research