Growth of Ideal Magnetohydrodynamic Modes Driven Slowly Through Their Instability Threshold: Application to Disruption Precursors

The growth of an ideal magnetohydrodynamic (MHD) instability in a high-temperature plasma is calculated in the case where the plasma β is driven slowly through its instability threshold. The MHD perturbation grows faster than exponentially, approximately as exp[(t/τ)3/2]. Its characteristic growth time τ∼(32)2/3γ̂MHD−2/3γh−1/3 is a hybrid of the ideal MHD incremental growth rate γ̂MHD and the heating rate γh. This simple model agrees well with the observed growth of disruption precursors in high β DIII-D [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] discharges having strongly peaked pressure profiles, where the observed growth times of ⩾10−4 s are significantly slower than the typical ideal MHD time scale of ⩽10−5 s.