Dependence of ideal MHD kink and ballooning modes on plasma shape and profiles in tokamaks

Abstract

Extensive numerical studies of ideal MHD instabilities have been carried out to gain insight into the parametric dependence of critical ..beta..'s in tokamaks. The large number of interrelated equilibrium quantities involved in establishing a critical ..beta.. 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 parameter regimes appropriate for both current and reactor-sized plasmas. A moderate dependence on the pressure profile and a strong variation with the current profile is found. The principal result is that for aspect ratio R/a approximately equal to 3, critical ..beta..'s are of the order of 2% for circular cross sections and 5% for plasmas with elongation K approximately equal to 2; somewhat higher values could be achieved with more optimal shaping. Finally, sequences of equilibria have been analyzed to compare critical ..beta.. 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 mode stability. Low-n free boundary modes appear to set a lower limit.