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 beta is driven slowly through its instability threshold. The MHD perturbation grows faster than exponentially, approximately as exp[(t/tau)(3/2)]. Its characteristic growth time tau similar to(3/2)(2/3)<(gamma)over cap>(-2/3)(MHD)gamma(h)(-1/3) is a hybrid of the ideal MHD incremental growth rate <(gamma)over cap>(MHD) and the heating rate gamma(h). This simple model agrees well with the observed growth of disruption precursors in high beta 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 greater than or equal to 10(-4) s are significantly slower than the typical ideal MHD time scale of less than or equal to 10(-5) s. (C) 1999 American Institute of Physics. [S1070-664X(99)01508-6].