Modification of Tokamak Ballooning Stability Boundaries by Alpha Populations

For T_α/T_i < 150 (where T_α is the alpha-mean energy and T_i the ion temperature), the trapped alpha precision resonance destabilizes the kinetic ballooning mode of the bulk plasma. Using a slowing down distribution and both circular and noncircular equilibrium models, the eigenfrequencies of the resonant ballooning integral equation are computed. One finds lower critical betas and a widening of the unstable region, particularly at higher electron temperature and for flat q, steep pressure profiles typical of ignited sawtoothing plasmas.