Statistical analysis of m/n  =  2/1 locked and quasi-stationary modes with rotating precursors at DIII-D

A database has been developed to study the evolution, the nonlinear effects on equilibria, and the disruptivity of locked and quasi-stationary modes with poloidal and toroidal mode numbers m  =  2 and n  =  1 at DIII-D. The analysis of 22500 discharges shows that more than 18% of disruptions are due to locked or quasi-stationary modes with rotating precursors (not including born locked modes). A parameter formulated by the plasma internal inductance l _i divided by the safety factor at 95% of the poloidal flux, q ₉₅, is found to exhibit predictive capability over whether a locked mode will cause a disruption or not, and does so up to hundreds of milliseconds before the disruption. Within 20 ms of the disruption, the shortest distance between the island separatrix and the unperturbed last closed flux surface, referred to as d _edge, performs comparably to $l_i/q_{95}$ in its ability to discriminate disruptive locked modes. Out of all parameters considered, d _edge also correlates best with the duration of the locked mode. Disruptivity following a m/n  =  2/1 locked mode as a function of the normalized beta, ${\beta }_{\text{N}}$, is observed to peak at an intermediate value, and decrease for high values. The decrease is attributed to the correlation between ${\beta }_{\text{N}}$ and q ₉₅ in the DIII-D operational space. Within 50 ms of a locked mode disruption, average behavior includes exponential growth of the n  =  1 perturbed field, which might be due to the 2/1 locked mode. Surprisingly, even assuming the aforementioned 2/1 growth, disruptivity following a locked mode shows little dependence on island width up to 20 ms before the disruption. Separately, greater deceleration of the rotating precursor is observed when the wall torque is large. At locking, modes are often observed to align at a particular phase, which is likely related to a residual error field. Timescales associated with the mode evolution are also studied and dictate the response times necessary for disruption avoidance and mitigation. Observations of the evolution of ${\beta }_{\text{N}}$ during a locked mode, the effects of poloidal beta on the saturated width, and the reduction in Shafranov shift during locking are also presented. (paper)