Abstract.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 22,500 discharges shows that more than 18% of disruptions are due to locked or quasistationary 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, β N , is observed to peak at an intermediate value, and decrease for high values. The decrease is attributed to the correlation between β 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 β 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.

Locked modes are known to be one of the major causes of disruptions, but the physical mechanisms by which locking leads to disruptions are not well understood. Here we analyze the evolution of the temperature profile in the presence of multiple coexisting locked modes during partial and full thermal quenches. Partial quenches are often observed to be an initial, distinct stage in the full thermal quench. Near the onset of partial quenches, locked island O-points are observed to align with each other on the midplane, and their widths are sufficient to overlap each other, as indicated by the Chirikov parameter. Energy conservation analysis of one partial thermal quench shows that the energy lost is both radiated in the divertor region, and conducted or convected to the divertor. Nonlinear resistive magnetohydrodynamic simulations support the interpretation of stochastic fields causing a partial axisymmetric collapse, though the simulated temperature profile exhibits less degradation than the experimental profiles. In discharges with minimum values of the safety factor above  ∼1.2, locked modes are observed to self-stabilize by inducing, possibly via double tearing modes, a minor disruption that removes their neoclassical drive. These high qmin discharges often exhibit relatively low ratios of the plasma internal inductance to the safety factor at 95% of the poloidal flux, which might imply classical stability, in agreement with the decay of the mode when the neoclassical drive is removed.

Abstract. A finite-state off-normal and fault response (ONFR) system is presented that provides the supervisory logic for comprehensive disruption avoidance and machine protection in tokamaks. Robust event handling is critical for ITER and future large tokamaks, where plasma parameters will necessarily approach stability limits and many systems will operate near their engineering limits. Events can be classified as off-normal plasmas events, e.g. neoclassical tearing modes or vertical displacements events, or faults, e.g. coil power supply failures. The ONFR system presented provides four critical features of a robust event handling system: sequential responses to cascading events, event recovery, simultaneous handling of multiple events and actuator prioritization. The finite-state logic is implemented in Matlab R /Stateflow R to allow rapid development and testing in an easily understood graphical format before automated export to the real-time plasma control system code. Experimental demonstrations of the ONFR algorithm on the DIII-D and KSTAR tokamaks are presented. In the most complex demonstration, the ONFR algorithm asynchronously applies "catch and subdue" electron cyclotron current drive (ECCD) injection scheme to suppress a virulent 2/1 neoclassical tearing mode, subsequently shuts down ECCD for machine protection when the plasma becomes over-dense, and enables rotating 3D field entrainment of the ensuing locked mode to allow a safe rampdown, all in the same discharge without user intervention. When multiple ONFR states are active simultaneously and requesting the same actuator (e.g. neutral beam injection or gyrotrons), actuator prioritization is accomplished by sorting the pre-assigned priority values of each active ONFR state and giving complete control of the actuator to the state with highest priority. This early experience makes evident that additional research is required to develop an improved actuator sharing protocol, as well as a methodology to minimize the number and topological complexity of states as the finite-state ONFR system is scaled to a large, highly constrained device like ITER.

Abstract. The toroidal phase and rotation of otherwise locked magnetic islands of toroidal mode number n=1 are controlled in the DIII-D tokamak by means of applied magnetic perturbations of n=1. Pre-emptive perturbations were applied in feedforward to "catch" the mode as it slowed down and entrain it to the rotating field before complete locking, thus avoiding the associated major confinement degradation. Additionally, for the first time, the phase of the perturbation was optimized in real-time, in feedback with magnetic measurements, in order for the mode's phase to closely match a prescribed phase, as a function of time. Experimental results confirm the capability to hold the mode in a given fixed-phase or to rotate it at up to 20 Hz with good uniformity. The controlcoil currents utilized in the experiments agree with the requirements estimated by an electromechanical model. Moreover, controlled rotation at 20 Hz was combined with Electron Cyclotron Current Drive (ECCD) modulated at the same frequency. This is simpler than regulating the ECCD modulation in feedback with spontaneous mode rotation, and enables repetitive, reproducible ECCD deposition at or near the island O-point, X-point and locations in between, for careful studies of how this affects the island stability. Current drive was found to be radially misaligned relative to the island, and resulting growth and shrinkage of islands matched expectations of the Modified Rutherford Equation for some discharges presented here. Finally, simulations predict the as designed ITER 3D coils can entrain a small island at sub-10 Hz frequencies.Page 1 of 15 AUTHOR SUBMITTED MANUSCRIPT -NF-102117. R2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Control of locked mode phase and rotation with application to modulated ECCD 2 Figure 1. Perturbed current pattern, sinusoidal in helical angle mθ − nφ, of a m/n = 2/1 magnetic island mapped onto a thin surface. Also depicted are the internal I-coils (green) and external C-coils (red) used to generate 3D fields on DIII-D.

A basic nonlinear electromechanical model is developed for the interaction between a preexisting near-saturated tearing-mode, a conducting wall, active coils internal to the wall, and active coils external to the wall. The tearing-mode is represented by a perturbed helical surface current and its island has a small but finite moment of inertia. The model is shown to have several properties that are qualitatively consistent with the experimental observations of mode-wall and mode-coil interactions. The main purpose of the model is to guide the design of a phase control system for locked modes (LMs) in tokamaks. Such a phase controller may become an important component in integrated disruption avoidance systems. A realistic feedback controller for the LM phase is designed and tested for the electromechanical model. The results indicate that a simple fixed-gain controller can perform phase control of LMs with a range of sizes, and at arbitrary misalignment relative to a realistically dimensioned background error field. The basic model is expected to be a useful minimal dynamical system representation also for other aspects of mode-wall-coil interactions.