The stability of ideal magnetohydrodynamic ballooning modes in plasmas with internal transport barriers

Abstract

The stability and spatial structures of short wavelength ideal magnetohydrodynamic ballooning modes (i.e., those modes with moderate to large values of the toroidal mode number, n) that can exist in regions of zero or small magnetic shear are investigated. This is a situation relevant to discharges with internal transport barriers (ITBs). The generic properties of such instabilities are discussed by considering the s–α equilibrium. In regions of low s the ballooning formalism fails for large but finite, values of n. In this limit a complementary approach is developed, based on solving the recurrence relation describing the toroidal coupling of radially localized “modelets” on adjacent mode rational surfaces. This technique extends the stability analysis to lower s and finite n, capturing effects arising from the discreteness of mode rational surfaces. Consideration of equilibrium trajectories in the s–α stability diagram corresponding to profiles of ITB discharges allows one to determine the global stability of such discharges to these modes. It is shown that the stability of ITBs can be parameterized in terms of αmax, the value of the peak α, and the steepness of the barrier pressure profile relative to the shape of the q profile. Inclusion of the stabilizing effects of favorable average curvature at finite aspect ratio, ε, leads to stable high-pressure ITB configurations. The stabilizing influence of low-order rational values of qmin also emerges from the theory. The influences of the bootstrap current and plasma flow shear at ITBs are briefly discussed.