S. Kumar et al., THE AXISYMMETRICAL INSTABILITY IN WEAKLY MAGNETIZED ACCRETION DISKS, Monthly Notices of the Royal Astronomical Society, 266(2), 1994, pp. 379-385
The energy principle is used to find the global criteria for stability
to axisymmetric perturbations of stationary, magnetized, differential
ly rotating flows, in particular accretion discs. It is found that the
vertical fields usually tend to stabilize while the toroidal fields d
estabilize, except when the vertical fields are weak. Bounds are place
d on the growth rates of the instability. Normal modes are computed fo
r fields in slender annuli which confirm the above results.