Resistive stability of 2/1 modes near 1/1 resonance

The stability of resistive modes is examined using reconstructions of experimental equilibria in the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)], revealing the important physics in mode onset as discharges evolve to instability. Experimental attempts to access the highest β in tokamak discharges, including 'hybrid' discharges, are typically terminated by the growth of a large 2/1 tearing mode. Model equilibria, based on experimental reconstructions from one of these discharges with steady state axial q0≅1, are generated varying q0 and pressure. For each equilibrium, the PEST-III code [A. Pletzer, A. Bondeson, and R. L. Dewar, J. Comput. Phys. 115, 530 (1994)] is used to determine the ideal magnetohydrodynamic solution including both tearing and interchange parities. This outer region solution must be matched to the resistive inner layer solutions at the rational surface to determine resistive mode stability. From this analysis it is found that the approach to q=1 simultaneously causes the 2/1 mode to become unstable and the nonresonant 1/1 displacement to become large, as the ideal β limit rapidly decreases toward the experimental value. However, the 2/2 harmonic on axis, which is also large and is coupled to the saturated steady state 3/2 mode, is thought to contribute to the current drive sustaining q0 above 1 in these hybrid discharges. Thus, the approach to the q=1 resonance is self-limiting in this context. This work suggests that sustaining q0 slightly above 1 will avoid the 2/1 instability and will allow access to significantly higher β values in these discharges