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Paper: Convective, Absolute, and Global Instabilities in Thin Rotating Disks
Volume: 385, Numerical Modeling of Space Plasma Flows: Astronum-2007
Page: 38
Authors: Liverts, E.; Mond, M.
Abstract: The problem of the stability of rotating magnetized thin disks plays a crucial role in the dynamics of multitude of astrophysical phenomena. In particular, the magneto-rotational instability (MRI) has been considered over the last fifteen years as one of the main candidates to hold the key to the fundamental problem of outwards transport of angular momentum. Traditionally, the disk is deemed unstable if the imaginary part of the normal frequencies of the system is greater than zero for some range of wave numbers. In contrast to that practice, in frame of boundary value problem (BVP) we investigate the dynamical development of a more realistic initial perturbation, in the shape of a localized wave packet. We demonstrate that the latter’s behavior may significantly differ from that of each of its components even if some of them belong to the unstable part of the spectrum. Thus, we stress the importance of considering the initial value problem as well as the question of global instability for finite systems, and demonstrate for that purpose that a sufficiently thin disk is globally stable. Physical interpretation of the result is presented.
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