Influence of Trapped Thermal Particles on Internal Kink Modes in High-Temperature Tokamaks

The effects of thermal trapped particles on the n = 1 internal kink mode are studied using drift kinetic theory. Strong modifications of the magnetohydrodynamic (MHD) results are found, and marginal stability generally occurs at nonzero rotation frequency. For equal electron and ion temperatures, the trapped particles increase the marginal poloidal beta at q = 1 substantially above the MHD value. For unequal electron and ion temperatures, the drift resonance with the hotter species becomes increasingly destabilizing and for sufficiently unequal temperatures, this leads to instability below the ideal-MHD threshold. Treatment of trapped thermal particles requires consideration of the effects of an electrostatic potential. The potential is weakly stabilizing for the internal kink mode. Furthermore, finite beta couples unstable, nearly electrostatic, trapped particle modes to the internal kink mode. At high beta, thermal fluctuations of the trapped particle modes can lead to significant internal kink displacements.