Hydromagnetic Stability of the Bennett Pinch

The hydromagnetic energy principle is applied to the derivation of a sufficient condition for the hydromagnetic stability of the linear Bennett pinch. The instabilities can be divided into unlocalized modes in which the most dangerous ones are the kink mode and localized modes. A sufficient condition for stability of the kink mode is βz < (9/25) (r0/R)2 for (r0/R)2<3.75 where βz is the toroidal β and r0 and 2πR are the mean radius and the length of the pinch, respectively. The linear Bennett pinch is unstable for localized Suydam modes. But these unstable modes can be stabilized if the pinch is bent into a torus. The above stability condition against the kink instability may be considered as a sufficient condition for stability of a toroidal Bennett pinch.