Criterion of the MHD-stability in a stellarator

Equilibrium and stability with respect to flute perturbations of a plasma confined in a stellarator with a flat circular axis with provision for members up to cubic in shift centres of magnetic surfaces have been considered. It is shown that taking account of nonlinear in shift summands leads to additional stabilization. A problem related to stabillity of ballooning modes has been analyzed and it is shown that unlike a tokamak the ballooning effect related to ''shear'' does not result in additional restrictions of limiting pressure and that the Mersier type criterium may be used for correct investigation of stability conditions