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

Abstract

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.