Energy principle with global invariants: Applications

Minimum-energy equilibrium states of a pressureless cylindrical plasma are constructed subject to a recently proposed set of constraints appropriate to turbulent relaxation dominated by a tearing mode of single helicity. Stability to ideal and resistive modes is examined. It is found that the relaxed states of minimum energy are always stable to the dominant mode, as well as a class of other low m and n modes, but that there are typically high n residual instabilities in the case of the pitch branch, and a residual m=3, n=2 resistive instability is found for an otherwise stable narrow window in the tokamak branch. It is argued that the residual instabilities may be compatible with experimental observations.