Extensive numerical studies of ideal MI'P instabilities have been carried out to gain insight into the parametric dependence of critical p's in tokamaks. The .large numrt .;; i r. tor related equilibrium quantities involved in establishirq a critir-al '.' has demanded a careful, systematic survey in order to isolate this dependence. The results of this survey establish the scaling with geometrical quantities including aspect ratio, elongation, and triangularity in the par, meter regimes appropriate for both current and reactor-sized plasmas. A :indr>vc!Lo 'InnondencR on the pressure profile and a stronc variation with the current pro Tile is found. The principal resul t is that for aspect ratio P.''a '•>, critical (3' s are of the order of r% for circular cross sections and 5% for plasmas with elongation i, "-' 2; sorewhat higher values could be achieved with more optimal shaping. Finally, sequences of equilibria have been analyzed to compare critical i' as a function of toroidal mode number n. We conclude that the infinite-n analytic ballooning theory provides a sufficient condition for ideal MHD internal node stability. Low-n free boundary modes appear to set a lower limit.

The role of shear in determining the ideal MHD stability properties of tokamaks is discussed. In particular, we assess the effects of low shear within the plasma upon pressure-driven modes. The standard ballooning theory is shown to break down, as the shear ia reduced and the growth rate is shown to be an oscillatory function of n f the toroidal mode number, treated as a continuous parameter. The oscillations are shown to depend on both the pressure and safety-factor profiles. When the 3hear is sufficiently weak, the oscillations can result in bands of unstable n values which are present even when the standard ballooning theory predicts complete stability. These instabilities are named "infernal modes." The occurrence of. these Instabilities at integer n is shown to be a sensitive function of q-axis, raising the possibility of a sharp onset AS plasma parameters evolve. DISCLArMER