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On global stability of thin ionized disks immersed in an external magnetic field

Abstract The problem of the global stability of rotating magnetized thin disks is considered. The appropriate boundary value problem (BVP) of the linearized MHD equations is solved by employing the WKB approximation to describe the dynamical development of an initial perturbation. The eigenfrequencies as well as eigenfunctions are explicitly obtained and are verified numerically. The importance of considering the initial value problem (IVP) as well as the question of global stability for finite systems is emphasized and discussed in detail. It is further shown that thin enough disks are stable (global stability) but as their thickness grows increasing number of unstable modes participate in the solution of the IVP. However it is demonstrated that due to the localization of the initial perturbation the growth time of the instability may be significantly longer than the calculated inverse growth rate of the individual unstable eigenfunctions.