Necessary stability condition for field-reversed theta pinches

Toroidal systems of arbitrary cross section without toroidal magnetic field are analyzed via the double adiabatic fluid equations. Such systems are shown to be unstable if there exists one closed field line on which the average of (kappa)(r)(B sq) is positive, where kappa is the curvature. A similar criterion is derived for linear systems and is applied to a noncircular z-pinch.