Session TI01: MFE: Disruptions and Equilibria

Root Cause of Disruptive NTMs in DIII-D ITER Baseline Scenario Plasma

DIII-D experiments identify the rotation profile flattening as the direct cause of the majority of disruptive m,n=2,1 tearing modes in low-torque ITER baseline scenario plasmas, while long pulse stable operation is achieved when the differential rotation is preserved. 

The observed exponential onset time distribution and constant onset rate of these islands is consistent with the wait time of Poisson point processes [1]. This behavior indicates the existence of a threshold for instability growth that is crossed with uniform temporal probability occurring from a transient imbalance of stabilizing and destabilizing mechanisms, such as differential rotation and MHD triggering. The probabilistic onset with constant rate clarifies that these modes do not favor any phase of the current relaxation in the pressure flattop. Moreover, the magnetic perturbation amplitude of these islands grows linearly in time, in accordance with the bootstrap current dominated asymptotic limit of the modified Rutherford equation, regardless of how far the current relaxation has evolved by the onset time. This shows that changes in the classical tearing stability due to the current relaxation do not affect the 2,1 tearing mode evolution either. The majority of the mode triggers are consistent with non-linear 3-wave coupling between the sawtooth precursor, the 3,2 island and the equilibrium when the differential rotation between the q=1 and q=2 rational surfaces approaches zero [2]. This flattening is caused by n>1 islands whose amplitude shows chaotic behavior possibly due to non-linear couplings between these core islands and the equilibrium current, pressure and rotation profiles through phase-space resonances of energetic ions. We present shot programs where long pulse stable operation was achieved by avoiding large core n>1 modes and preserving the favorable differential rotation. Machine learning analysis of multi-scenario database of over 13,000 discharges shows the importance of differential rotation in the onset and avoidance of disruptive 2,1 tearing instabilities is general in low edge safety factor H-mode plasmas [3].   

Non-disruptive tokamak operation far beyond traditional safety factor and density limits

Non-disruptive tokamak plasmas have been produced in the Madison Symmetric Torus (MST) at low field (B_T = 0.13 T) with edge safety factor 0.6 < q(a) < 2, below the traditional disruptive stability limit of q(a) = 2 [Phys. Plasmas 29, 080704 (2022)]; and (separately) with density up to 10 times the Greenwald limit, n_G. Achievable values of q(a) and n/n_G appear to be limited only by hardware and not by instabilities. Low-q(a) operation is possible due to MST’s thick, conductive, close-fitting shell with resistive wall time 800 ms that inhibits resistive wall modes during the 50 ms discharges, and high-voltage, high-bandwidth feedback power supplies capable of sustaining the plasma current in the presence of large resistance and/or rapid MHD dynamics. Plasmas with 1 < q(a) < 2 and q(a) < 1 have been studied previously in other devices, but our work is novel in that steady, controlled equilibria are obtained with detailed internal diagnosis. Measurements reveal self-organized q(r) profiles with q(0) near unity, irregular fluctuations, and decreased confinement for 1 < q(a) < 2; and strong, coherent helical structures for q(a) ≤ 1. Nonlinear MHD simulations conducted with q(a) ≥ 1.5 using the NIMROD code also find q(0) near unity. The capability for n > n_G is thought to be enabled by the advanced power supplies, and the thick shell may also play a role. While other devices have obtained n/n_G as high as 2, the values n/n_G ~ 10 reported here are unprecedented. In the range 1 < n/n_G < 2 the Ohmic power and impurity radiation scale strongly with density, but for n/n_G > 2 the current profile collapses and the scalings weaken. These results may help inform future tokamak design efforts in order to mitigate the disruption problem and extend operational stability boundaries.   

The critical role of the avalanche source in understanding wall damage from runaway electrons

Subcritical energetic electrons (SEEs) produced by the runaway electron (RE) avalanche source at energies below the runaway threshold are found to be the primary contributor to surface heating of plasma-facing components (PFCs) during final loss events. This finding is supported by theoretical analysis, computational modeling with the Kinetic Orbit Runaway electrons Code (KORC), and qualitative agreement with DIII-D experimental observations. The avalanche source generates significantly more secondary electrons below the runaway threshold, which thermalize rapidly when well-confined. However, during a final loss event, the RE beam impacts the first wall, and SEEs are deconfined before they can thermalize. Additionally, because the energy deposition length decreases faster than energy, the deposited energy density, and thus the maximum PFC surface temperature change, is larger for SEEs than REs. KORC simulations employ an analytic first wall to model particle deconfinement onto a non-axisymmetric wall composed of individual tiles. PFC surface heating is calculated using a 1D model extended to include an energy-dependent deposition length scale. Simulations of DIII-D qualitatively agree with infrared (IR) imaging only when SEEs from the avalanche source are included. These results demonstrate that SEEs are the dominant contributor to PFC surface heating and indicate that the avalanche source plays a critical role in the PFC damage caused during final loss events. The prominence of SEEs also has important implications for interpreting IR imaging, one of the primary diagnostics for RE-wall interaction diagnosis, despite REs dominating the energy and current density. This result improves predictions of wall damage due to post-disruption REs to estimate material lifetime and design RE mitigation systems for ITER and future reactors.   

Simulation of DIII-D disruption with pellet injection and runaway electron beam

The injection of a frozen impurity pellet as a disruption mitigation system (DMS) for the next generation of large tokamaks, including ITER, is a promising method for reducing the thermal and electromagnetic loads from a potential disruption without generating enough high-energy (runaway) electrons to damage the device. The effectiveness of this system has been tested on many experiments, with encouraging results. To further study its effects, we have modeled one such DMS experiment on DIII-D using the M3D-C1 nonlinear 3D extended MHD code (Jardin et al 2012 J. Comput. Sci. Discovery). Our model includes the injection and ablation of an argon pellet, impurity ionization and recombination, radiation, and the formation and evolution of runaway electrons, including both Dreicer and avalanche sources. We have found that our model provides reasonable agreement with the experimental results, in terms of the timescale of the thermal and current quench, and the magnitude of the runaway electron plateau formed during the mitigation. This provides a partial validation of the M3D-C1 DMS model, and further highlights the potential of using frozen impurity pellet injection for disruption mitigation in the next generation of large tokamaks. Disclaimer: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.   

Runaway electron dynamics in shattered pellet mitigated ITER disruptions

Disruptions and associated runaway electron beams represent an outstanding challenge in reactor-scale tokamaks. We have systematically explored the parameter space of disruption mitigation through shattered pellet injection in ITER with a focus of runaway electron dynamics, using the disruption modeling tool DREAM. The analysis provides a rather comprehensive coverage of experimentally feasible scenarios: We consider plasmas representative of both non-activated and high-performance DT operation, use different thermal quench onset criteria and transport levels, a wide range of injected deuterium and neon quantities, as well as single-stage and two-stage injection of pellets with various characteristic shard sizes. In addition, we consider the effect of the drift of pure hydrogen pellet clouds, as well as injections that fail to reach the plasma before the thermal quench. We find that two-stage injection helps hydrogen assimilation and reduces the hot-tail generation mechanism, providing the best performing cases. It also allows a robust elimination of the runaway current in reduced plasma current scenarios. However, we find megaampere scale runaway currents in 15 MA discharges, even in non-activated scenarios. .   

EFIT-AI neural network surrogates for magnetic, MSE, and kinetic equilibrium reconstruction

.Artificial neural network (NN) surrogate models have been developed and trained on magnetic, magnetic + motional stark effect (MSE), and kinetic DIIII-D equilibria to accelerate tokamak equilibrium reconstructions for offline, between-shot, and real-time applications. Adaptation of the ML/AI algorithms has been facilitated through the recently developed device-independent portable equilibrium solver and a large EFIT database of DIII-D magnetic, MSE and kinetic equilibria[1]. The main model comprises a fully connected NN coupled to a convolutional NN that together enforce the toroidal force-balance constraint by concurrently learning the poloidal flux and toroidal current density on the EFIT spatial grid. In addition, the NN surrogates also predict pressure, current, P', FF', and safety factor (q) profiles, and important plasma parameters such as the internal inductance, normalized beta, and magnetic axis location. Models are optimized for both architecture and hyperparameters, as well as inference speed, which has been clocked at real-time EFIT-like speeds. 

 

The NN surrogates for the magnetic EFITs show generalizability to previously-unseen negative-triangularity shapes, by incorporating the spatial correlation among various magnetic sensors in DIII-D into the NN input vector. The magnetic + MSE surrogates show improved predictions of the q profiles, and certain plasma parameters like the internal inductance. Finally, the kinetic surrogates show additional improvements in accurately reproducing EFIT-predicted internal current and pressure profiles. These results suggest the possibility of using a surrogate model as a real-time tool for plasma control and other applications.