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The temporal behavior of axisymmetric magneto-rotational instability in a thin accretion disk is analyzed via the Wentzel-Kramars-Brillouin (WKB) method. The height of the thin disk is used as a small parameter. It is found that the oscillation of the envelope of the mode accelerates with time because of the density distribution in the direction of the disk height.

WKB Analysis of Axisymmetric Magneto-Rotational Instability in a Thin Accretion Disk