The axisymmetric instability in weakly magnetized accretion discs

Abstract

The energy principle is used to find the global criteria for stability to axisymmetric perturbations of stationary, magnetized, differentially rotating flows, in particular accretion discs. It is found that the vertical fields usually tend to stabilize while the toroidal fields destabilize, except when the vertical fields are weak. Bounds are placed on the growth rates of the instability. Normal modes are computed for fields in slender annuli which confirm the above results.