EFFECT OF THE PARALLEL CURRENT-DENSITY ON THE LOCAL IDEAL 3-D MHD STABILITY OF THE HELIAS CONFIGURATION

The local ideal three dimensional (3-D) magneto-hydrodynamic (MHD) sta bility for the Wendelstein VTI-X (W VII-X) configuration is studied. A volume averaged beta limit of 5% is confirmed with a nearly optimal p ressure profile using two methods to calculate the parallel current de nsity: the magnetic method that uses magnetic information about the co nfiguration (in particular, the condition of charge conservation, del. j = 0, is explicitly used in the resolution) and the geometric method that uses the geometry of the configuration itself. It is shown that t he ballooning stability does not depend on the method of calculating t he parallel current. In contrast, the value of the Mercier criterion d epends sensitively on which method is used. Not only is the geometric method not sensitive to resonant surfaces (in particular. the surface l(p) = 1/6) but there is a systematic error in the Mercier criterion f or nonresonant surfaces when an insufficient number of modes is used t o calculate the equilibria numerically with a spectral method. However , this systematic error does not change the averaged beta limit of W V III-X because the ballooning stability is more stringent than the Merc ier stability for this configuration.