This paper provides a comprehensive review of the TRANSP code, a sophisticated tool for interpretive and predictive analysis of tokamak plasmas, detailing its major capabilities and features. It describes the equations for particle, power, and momentum balance analysis, as well as the poloidal field diffusion equations. The paper outlines the spatial and time grids used in TRANSP and details the equilibrium assumptions and solvers. Various models for heating and current drive and radiation, including updates to the NUBEAM model, are discussed. The handling of large-scale events such as sawtooth crashes and pellet injections is examined, along with the predictive capabilities for advancing plasma profiles. The integration of TRANSP with the ITER Integrated Modeling and Analysis Suite (IMAS) is highlighted, demonstrating enhanced data access and analysis capabilities. Additionally, the paper discusses best practices and continuous integration techniques to enhance TRANSP's robustness. The suite of TRANSP tools, designed for efficient data analysis and simulation, further supports the optimization of tokamak operations and coupling with other tokamak codes. Continuous development and support ensure that TRANSP remains a major code for the analysis of experimental data for controlled thermonuclear fusion, maintaining its critical role in supporting the optimization of tokamak operations and advancing fusion research.

State-of-the-art 1D transport solvers ASTRA and TRANSP are verified, then validated across a large database of semi-randomly selected, time-dependent DIII-D discharges. Various empirical models are provided as baselines to contextualize the validation figures of merit using statistical hypothesis tests. For predicting plasma temperature profiles, no statistically significant advantage is found for the ASTRA and TRANSP simulators over a baseline empirical (two-parameter) model. For predicting stored energy, a significant advantage is found for the simulators over a baseline empirical model based on confinement time scaling. Uncertainty in the results due to diagnostic and profile fitting uncertainties is approximated and determined to be insignificant due in part to the large quantity of discharges employed in the study. Advantages are discussed for validation methodologies like this one that employ (1) large databases and (2) baselines for comparison that are specific to the intended use-case of the model.

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 edge localized mode (ELM) frequency ( f ELM ) decreased by 63% when electron cyclotron heating (ECH) deposition location is shifted from ρ = 0.4 to ρ = 0.8 in DIII-D discharges where the power ratio between neutral beam injection (NBI) and ECH ( P NBI / P ECH ) is kept at ∼1. The performance of the pedestal in the ECH heated case is compared with a pure NBI reference discharge while keeping the total input power constant. All these discharges are performed at balanced input torque conditions. Furthermore, in the pure NBI discharge a strong decoupling of the peeling–ballooning (PB) thresholds is observed. The PB decoupling is preserved when the ECH is deposited at ρ = 0.8 and P NBI / P ECH ∼ 1, while the thresholds manifest a closed stability boundary when the ECH is deposited at ρ = 0.4. The inter-ELM pedestal recovery time is considerably larger for the ECH at ρ = 0.8 case. Increased pedestal turbulence is observed in beam emission spectroscopy (BES), Doppler backscattering and magnetic diagnostics for the ECH at the ρ = 0.8 case. Strong growth of a TEM-like mode is observed in BES and the mode growth is correlated with the decrease in f ELM . In view of these observations, the increased pedestal turbulence seems to be the plausible reason behind the delayed pedestal recovery following an ELM event in the ECH at ρ = 0.8 case, and the preservation of PB decoupling through temperature pedestal profile widening. TRANSP interpretative simulations show that the ECH at the ρ = 0.8 case is more susceptible to ITG/TEM turbulence.

The objective of this study is twofold: firstly, to demonstrate the consistency between the anomalous transport results produced by updated Multi-Mode Model (MMM) version 9.0.4 and those obtained through gyrokinetic simulations; and secondly, to showcase MMM's ability to predict electron and ion temperature profiles in low aspect ratio, high beta NSTX discharges. MMM encompasses a range of transport mechanisms driven by electron and ion temperature gradients, trapped electrons, kinetic ballooning, peeling, microtearing, and drift resistive inertial ballooning modes. These modes within MMM are being verified through corresponding gyrokinetic results. The modes that potentially contribute to ion thermal transport are stable in MMM, aligning with both experimental data and findings from linear CGYRO simulations. The isotope effects on these modes are also studied and higher mass is found to be stabilizing, consistent with the experimental trend. The electron thermal power across the flux surface is computed within MMM and compared to experimental measurements and nonlinear CGYRO simulation results. Specifically, the electron temperature gradient modes (ETGM) within MMM account for 2.0 MW of thermal power, consistent with experimental findings. It is noteworthy that the ETGM model requires approximately 5.0 ms of computation time on a standard desktop, while nonlinear CGYRO simulations necessitate 8.0 h on 8 K cores. MMM proves to be highly computationally efficient, a crucial attribute for various applications, including real-time control, tokamak scenario optimization, and uncertainty quantification of experimental data.

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.

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.

A new model for electron temperature gradient (ETG) modes is developed as a component of the multi-mode anomalous transport module [Rafiq et al., Phys Plasmas 20, 032506 (2013)] to predict a time-dependent electron temperature profile in conventional and low aspect ratio tokamaks. This model is based on two-fluid equations that govern the dynamics of low-frequency short- and long-wavelength electromagnetic toroidal ETG driven drift modes. A low collisionality NSTX discharge is used to scan the plasma parameter dependence on the ETG real frequency, growth rate, and electron thermal diffusivity. Electron thermal transport is discovered in the deep core region where modes are more electromagnetic in nature. Several previously reported gyrokinetic trends are reproduced, including the dependencies of density gradients, magnetic shear, β and gradient of β (β′), collisionality, safety factor, and toroidicity, where β is the ratio of the plasma pressure to the magnetic pressure. The electron heat diffusivity associated with the ETG mode is discovered to be on a scale consistent with the experimental diffusivity determined by power balance analysis.

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.

The extended-MHD NIMROD code (Sovinec C.R. and King J.R. 2010 J. Comput. Phys. 229 5803) is used to simulate the dynamics of an edge harmonic oscillation (EHO) in quiescent H-mode (QH-mode) DIII-D (Luxon J.L. 2002 Nucl. Fusion 42 614) discharge 163 518. EHOs observed in non-linear MHD simulations have n = 1 and n = 2 as dominant modes akin the DIII-D experiment. Kinetic equilibrium reconstructions during the time of the fully-developed EHO include the effect of the MHD profile relaxation and are found below the stability boundary. This paper discusses methods to include additional instability drives to the experimental equilibria in order to trigger EHO formation. The experimental equilibrium for the DIII-D discharge 163 518 is modified to include two levels of instability drive by increasing the experimental pressure gradient. In order to do a more direct comparison of the simulation results with the experiment, a synthetic BES diagnostic is used to compute cross-correlation and cross-power spectral densities associated with the simulated density perturbations. It is shown that the amplitude of the experimental density perturbations is between the computed density perturbation amplitude for the two levels of instability drive. The synthetic cross-power spectral density shows a transition from a double to a single peak in frequency when the BES analysis shifts from near the LCFS towards the steep gradient region of the pedestal. This observation is similar to the experiment, but the first peak frequency for the weak instability drive is found below the experimental frequencies, and the second peak for the strong instability drive is found above the experimental peak frequencies. However, these peak frequencies are in agreement with the local flow estimate and a MHD turbulence bursty behavior in the simulations with the strong instability drive.

We present a detailed mathematical analysis of the tensor Ponderomotive Force calculation in 3D, from fundamental principles. We are primarily interested in applications of this to tokamak configurations with ICRF, helicon, and/or LH RF sources. The tensor analysis includes force terms in both the poloidal plane and in the toroidal plane, which can result in either perpendicular force x B poloidal-plane convection or parallel force that can lead to rarefaction, or other toroidal displacements when coupled with an equilibrium code. We also present the implementation of the tensor ponderomotive force calculation in a 3D finite-difference time-domain (FDTD) simulation tool (VSim [1]) which can model 3D antenna and launcher geometry. We verify the implementation on a simple test case. We also discuss processing the 3D vector force for use in equilibrium and turbulence codes.

The Multi-Mode anomalous transport model is validated employing experimental data for superconducting KSTAR NBI heated tokamak discharges that represent a high beta poloidal, high beta normalized, and ITB long pulse scenarios. The Multi-Mode model computes the anomalous transport driven by the ITG, TEM, ETG, KBM, RBM, and PB modes. In addition, recent modification to the model allows the computation of the anomalous transport driven by the microtearing modes. The validation study is carried out using integrated modeling simulations that employ the numerical PT-SOLVER in the TRANSP code and that utilizes the KSTAR experimental boundary and initial conditions. The equilibrium data is interpolated from EFIT reconstruction. NBI heating and current drive are obtained using NUBEAM. Neoclassical transport is calculated using the Chang-Hinton model. The predicted evolving temperature profiles are compared with the corresponding KSTAR experimental data. The comparison is quantified by calculating the RMS deviations and Offsets.

DIII-D research is addressing critical challenges in preparation for ITER and the next generation of fusion devices through focusing on plasma physics fundamentals that underpin key fusion goals, understanding the interaction of disparate core and boundary plasma physics, and developing integrated scenarios for achieving high performance fusion regimes. Fundamental investigations into fusion energy science find that anomalous dissipation of runaway electrons (RE) that arise following a disruption is likely due to interactions with RE-driven kinetic instabilities, some of which have been directly observed, opening a new avenue for RE energy dissipation using naturally excited waves. Dimensionless parameter scaling of intrinsic rotation and gyrokinetic simulations give a predicted ITER rotation profile with significant turbulence stabilization. Coherence imaging spectroscopy confirms near sonic flow throughout the divertor towards the target, which may account for the convection-dominated parallel heat flux. Core-boundary integration studies show that the small angle slot divertor achieves detachment at lower density and extends plasma cooling across the divertor target plate, which is essential for controlling heat flux and erosion. The Super H-mode regime has been extended to high plasma current (2.0 MA) and density to achieve very high pedestal pressures (similar to 30 kPa) and stored energy (3.2 MJ) with H-98y2 approximate to 1.6-2.4. In scenario work, the ITER baseline Q = 10 scenario with zero injected torque is found to have a fusion gain metric beta(TE) independent of current between q(95) = 2.8-3.7, and a lower limit of pedestal rotation for RMP ELM suppression has been found. In the wide pedestal QH-mode regime that exhibits improved performance and no ELMs, the start-up counter torque has been eliminated so that the entire discharge uses approximate to 0 injected torque and the operating space is more ITER-relevant. Finally, the high-beta(N) (<= 3.8) hybrid scenario has been extended to the high-density levels necessary for radiating divertor operation, achieving similar to 40% divertor heat flux reduction using either argon or neon with P-tot up to 15 MW.