The physics of neoclassical tearing modes (NTMs) is of great concern to tokamak plasma stability and performance, especially in the burning plasma regime. Whereas in many situations the seed events can be clearly identified, such as sawteeth and edge localized modes, the potential seeding mechanism of NTMs due to the resistive tearing instability driven by the impurity radiation cooling still needs more study. Recent NIMROD simulations have demonstrated that local impurity radiation cooling can drive the seed island growth and trigger the subsequent onset of NTM instability. The seed island is mainly driven by the local helical perturbation of the diamagnetic current induced by the perturbed pressure gradient as a result of the impurity radiative cooling on the rational surface. A heuristic closure for the neoclassical viscosity is adopted, and the seed island is further driven by the perturbed bootstrap current induced from the neoclassical electron viscous stress in the extended Ohm’s law. The growth rate of the NTM in simulations is found proportional to the electron neoclassical viscosity, and a theoretical neoclassical driving term is adopted to account for the nonlinear neoclassical island growth in the simulations.

Herein, we formulate, analyze, and apply a numerical method for solving a Chapman-Enskog-like (CEL) continuum kinetic model for plasmas. It is shown that centering the heat flux at the beginning of the time step and the ion temperature at the end of the time step in the kinetic equation allows for a numerically-stable time advance of the coupled fluid-kinetic system. In addition, it is shown that numerical stability is impossible to achieve without explicitly enforcing key tenets of the CEL closure approach, in particular, that the number density (n), flow (u), and temperature (T) moments of the kinetic distortion remain small in time. We show that with a method to constrain these moments, it is possible to remove both the numerical growth and numerical damping from the linear modes. We apply the results from the linear stability analysis to allow for a numerically-stable fully nonlinear axisymmetric evolution of profiles in NIMROD, wherein we observe the asymptotic evolution of the flow in a DIII-D tokamak equilibrium (based on DIII-D ITER Baseline Scenario (IBS) discharge 174446 at 3390 ms). We compare the self-consistently computed results to analytics and to results from a previously benchmarked fixed-background delta f implementation in NIMROD. Agreement with prediction is found for both the dynamics and asymptotics of the flow. This work demonstrates the first successful published benchmarking of the full CEL approach in a plasma fluid code.

Bayesian statistics offers a powerful technique for plasma physicists to infer knowledge from the heterogeneous data types encountered. To explain this power, a simple example, Gaussian Process Regression, and the application of Bayesian statistics to inverse problems are explained. The likelihood is the key distribution because it contains the data model, or theoretic predictions, of the desired quantities. By using prior knowledge, the distribution of the inferred quantities of interest based on the data given can be inferred. Because it is a distribution of inferred quantities given the data and not a single prediction, uncertainty quantification is a natural consequence of Bayesian statistics. The benefits of machine learning in developing surrogate models for solving inverse problems are discussed, as well as progress in quantitatively understanding the errors that such a model introduces.

The DIII-D tokamak has elucidated crucial physics and developed projectable solutions for ITER and fusion power plants in the key areas of core performance, boundary heat and particle transport, and integrated scenario operation, with closing the core-edge integration knowledge gap being the overarching mission. New experimental validation of high-fidelity, multi-channel, non-linear gyrokinetic turbulent transport models for ITER provides strong confidence it will achieve Q 10 operation. Experiments identify options for easing H-mode access in hydrogen, and give new insight into the isotopic dependence of transport and confinement. Analysis of 2,1 islands in unoptimized low-torque IBS demonstration discharges suggests their onset time occurs randomly in the constant beta phase, most often triggered by non-linear 3-wave coupling, thus identifying an NTM seeding mechanism to avoid. Pure deuterium SPI for disruption mitigation is shown to provide favorable slow cooling, but poor core assimilation, suggesting paths for improved SPI on ITER. At the boundary, measured neutral density and ionization source fluxes are strongly poloidally asymmetric, implying a 2D treatment is needed to model pedestal fuelling. Detailed measurements of pedestal and SOL quantities and impurity charge state radiation in detached divertors has validated edge fluid modelling and new self-consistent 'pedestal-to-divertor' integrated modeling that can be used to optimize reactors. New feedback adaptive ELM control minimizes confinement reduction, and RMP ELM suppression with sustained high core performance was obtained for the first time with the outer strike point in a W-coated, compact and unpumped small-angle slot divertor. Advances have been made in integrated operational scenarios for ITER and power plants. Wide pedestal intrinsically ELM-free QH-modes are produced with more reactor-relevant conditions, Low torque IBS with W-equivalent radiators can exhibit predator-prey oscillations in T-e and radiation which need control. High-beta(P) scenarios with q(min) > 2, q(95)-7.9, beta(N) > 4, beta(T)-3.3% and H-98y2 > 1.5 are sustained with high density ((n) over bar = 7E19 m(-3), f(G)-1) for 6 tau(E), improving confidence in steady-state tokamak reactors. Diverted NT plasmas achieve high core performance with a non-ELMing edge, offering a possible highly attractive core-edge integration solution for reactors.

Nonlinear extended magnetohydrodynamics simulations demonstrating seeding of neoclassical tearing modes (NTMs) via magnetohydrodynamics-transient-induced multimode interactions are presented. Simulations of NTMs are enabled by two recent NIMROD code developments: the implementation of heuristic neoclassical stresses and the application of transient magnetic perturbations (MPs) at the boundary. NTMs are driven unstable by the inherently pressure driven kinetic bootstrap current, which arises due to collisional viscosity between passing and trapped electrons. These simulations use heuristic closures that model the neoclassical electron and ion stresses. NTM growth requires a seed island, which is generated by a transiently applied MP in simulations. The capability is demonstrated using kinetic-based reconstructions with flow of a DIII-D ITER Baseline Scenario discharge (La Haye et al., in Proceedings IAEA FEC, 2020). The applied MP seeds a 2/1 NTM that grows in two phases: a slow growth phase followed by a faster robust growth phase. Additionally, an evolving sequence of higher order core modes are excited at first. Power transfer analysis shows that nonlinear interactions between the core modes and the 2/1 helps drive the initial slow growth. Once the induced 2/1 magnetic island reaches a critical width, the NTM transitions to faster robust growth, which is well described by the nonlinear modified Rutherford equation. This work highlights the role of nonlinear mode coupling in seeding NTMs.

New studies identify the critical parameters and physics governing disruptive neoclassical tearing mode (NTM) onset. An m/n = 2/1 mode in DIII-D that begins to grow robustly after a seeding event (edge localized mode ELM or sawtooth precursor and crash) causes the mode rotation to drop close to the plasma’s E r = 0 rest frame; this condition opens the stabilizing ion-polarization current ‘gate’ and destabilizes an otherwise marginally stable NTM. Our new experimental and theoretical insights and novel toroidal theory-based modeling are benchmarked and scalable to ITER and other future experiments. The nominal ITER rotation at q = 2 is found to be stabilizing (‘gate closed’) except for MHD-induced transients that could ‘open the gate’. Extrapolating from the DIII-D ITER baseline scenario (IBS) discharges, MHD transients are much more likely to destabilize problematic robustly growing 2/1 NTMs in ITER; this makes predictions of seeding and control of both ELMs and sawteeth imperative for more than just minimizing divertor pulsed-heat loading.

DIII-D physics research addresses critical challenges for the operation of ITER and the next generation of fusion energy devices. This is done through a focus on innovations to provide solutions for high performance long pulse operation, coupled with fundamental plasma physics understanding and model validation, to drive scenario development by integrating high performance core and boundary plasmas. Substantial increases in off-axis current drive efficiency from an innovative top launch system for EC power, and in pressure broadening for Alfven eigenmode control from a co-/counter- I p steerable off-axis neutral beam, all improve the prospects for optimization of future long pulse/steady state high performance tokamak operation. Fundamental studies into the modes that drive the evolution of the pedestal pressure profile and electron vs ion heat flux validate predictive models of pedestal recovery after ELMs. Understanding the physics mechanisms of ELM control and density pumpout by 3D magnetic perturbation fields leads to confident predictions for ITER and future devices. Validated modeling of high- Z shattered pellet injection for disruption mitigation, runaway electron dissipation, and techniques for disruption prediction and avoidance including machine learning, give confidence in handling disruptivity for future devices. For the non-nuclear phase of ITER, two actuators are identified to lower the L–H threshold power in hydrogen plasmas. With this physics understanding and suite of capabilities, a high poloidal beta optimized-core scenario with an internal transport barrier that projects nearly to Q = 10 in ITER at ∼ 8 MA was coupled to a detached divertor, and a near super H-mode optimized-pedestal scenario with co- I p beam injection was coupled to a radiative divertor. The hybrid core scenario was achieved directly, without the need for anomalous current diffusion, using off-axis current drive actuators. Also, a controller to assess proximity to stability limits and regulate β N in the ITER baseline scenario, based on plasma response to probing 3D fields, was demonstrated. Finally, innovative tokamak operation using a negative triangularity shape showed many attractive features for future pilot plant operation.

Power-transfer and fixed-point analysis of previous NIMROD simulations (Roberds et al., Phys. Plasmas, vol. 23, issue 9, 2016, 092513) improved the understanding of the effect of 3D (non-axisymmetric equilibrium) magnetic fields on sawtooth oscillations in the Compact Toroidal Hybrid (CTH) experiment. Computing the locations of order-1 fixed points, their Greene's residues, and local values for the rotational transform results in a description of CTH sawteeth consistent with Kadomtsev's model. A power-transfer analysis quantifies the distribution of energy among toroidal Fourier modes and their nonlinear interactions. The Lorentz power transfer drives sawtooth growth, and it is unambiguously interpreted as the flow of energy from toroidal mode $n'$ to mode $n$, catalysed by $\boldsymbol {B}_{n-n'}$. It has been reported previously that the CTH sawtooth frequency increases with the 3D field strength. This is attributed to an increased growth rate of the internal kink that drives sawtooth oscillations. Here, 3D fields remove energy from the kink, eliminating the possibility that these fields are an additional energy source that drives growth. Instead, 3D fields catalyse energy transfer from large-to-small scales, where magnetic reconnection is stronger. It is proposed that this energy transfer increases the reconnection rate at small scales, which is consistent with the increased growth rate observed at higher 3D field strengths.

Recent progress in the application of machine learning (ML)/artificial intelligence (AI) algorithms to improve the Equilibrium Fitting (EFIT) code equilibrium reconstruction for fusion data analysis applications is presented. A device-independent portable core equilibrium solver capable of computing or reconstructing equilibrium for different tokamaks has been created to facilitate adaptation of ML/AI algorithms. A large EFIT database comprising of DIII-D magnetic, motional Stark effect, and kinetic reconstruction data has been generated for developments of EFIT model-order-reduction (MOR) surrogate models to reconstruct approximate equilibrium solutions. A neural-network MOR surrogate model has been successfully trained and tested using the magnetically reconstructed datasets with encouraging results. Other progress includes developments of a Gaussian process Bayesian framework that can adapt its many hyperparameters to improve processing of experimental input data and a 3D perturbed equilibrium database from toroidal full magnetohydrodynamic linear response modeling using the Magnetohydrodynamic Resistive Spectrum - Feedback (MARS-F) code for developments of 3D-MOR surrogate models.

Gaussian Process Regression (GPR) is a Bayesian method for inferring profiles based on input data. The technique is increasing in popularity in the fusion community due to its many advantages over traditional fitting techniques including intrinsic uncertainty quantification and robustness to over-fitting. This work investigates the use of a new method, the change-point method, for handling the varying length scales found in different tokamak regimes. The use of the Student's t-distribution for the Bayesian likelihood probability is also investigated and shown to be advantageous in providing good fits in profiles with many outliers. To compare different methods, synthetic data generated from analytic profiles is used to create a database enabling a quantitative statistical comparison of which methods perform the best. Using a full Bayesian approach with the change-point method, Matérn kernel for the prior probability, and Student's t-distribution for the likelihood is shown to give the best results.

A non-parametric Gaussian process regression model is developed in the three-dimensional equilibrium reconstruction code V3FIT. A Gaussian process is a normal distribution of functions that is uniquely defined by specifying a mean function and covariance kernel function. Gaussian process regression assumes that an unknown profile belongs to a particular Gaussian process and uses Bayesian analysis to select the function the give the best fit to measured data. The implementation in V3FIT uses a hybrid representation where Gaussian processes are used to infer some of the equilibrium profiles and standard parametric techniques are used to infer the remaining profiles. The implementation of the Gaussian process is tested using both synthetic data and experimental data from multiple machines.

Collimated soft X-ray (SXR) emissivity measurements from multi-channel cameras on the Compact Toroidal Hybrid (CTH) tokamak/torsatron device are incorporated in the 3D equilibrium reconstruction code V3FIT to reconstruct the shape of flux surfaces and infer the current distribution within the plasma. Equilibrium reconstructions of sawtoothing plasmas that use data from both SXR and external magnetic diagnostics show the central safety factor to be near unity under the assumption that SXR iso-emissivity contours lie on magnetic flux surfaces. The reconstruction results are consistent with those using the external magnetic data and a constraint on the location of q = 1 surfaces determined from the sawtooth inversion surface extracted from SXR brightness profiles. The agreement justifies the use of approximating SXR emission as a flux function in CTH, at least within the core of the plasma, subject to the spatial resolution of the SXR diagnostics. This improved reconstruction of the central current density indicates that the current profile peakedness decreases with increasing external transform and that the internal inductance is not a relevant measure of how peaked the current profile is in hybrid discharges.