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DOE OSTI2025

Power balance and divertor asymmetries in the Super-X divertors of MAST-U using SOLPS-ITER

Spherical tokamaks (STs) present unique challenges and opportunities in the area of particle and power exhaust, intensified due to their more compact sizes. Substantial efforts are underway in STs to determine the limits in dissipative operational regimes and advanced divertor solutions, including at MAST-U which provides access to the Super-X divertor configuration. Power balance, and upper/lower divertor asymmetries have been studied using SOLPS-ITER simulations of the MAST-U Super-X divertor. A set of simulations with experimentally inferred transport coefficients with E x B and diamagnetic drifts activated, consisting of density and power scans, and high field side vs low field side gas puff locations, have been used for code experimentation to uncover trends beyond the current experimental parameter space. The upper biased asymmetry (U:L > 1) of the ratio of the peaks of the plasma energy flux densities at the outer targets increases with heating power and decreases with gas puff strength, going from symmetric to up to a factor of 15. The upper target electron temperature has been found to be a good ordering quantity for the magnitude of this asymmetry for all heating powers, gas puff strength, and gas puff locations. The lower divertor biased asymmetry (U:L < 1) of the radiation patterns processed through SOLPS-based bolometry synthetic diagnostics is in qualitative agreement with resistive bolometry experimental results, and it is in quantitative agreement with the trend of the total volume radiation within the divertors of SOLPS. However, radiation measurements alone are not sufficient to infer the magnitude of the asymmetry of the peaks of the power loads at the targets.

MAST-U↗

DOE OSTI2026

Statistical inference of anomalous thermal transport with uncertainty quantification for interpretive 2D SOL models

The critical task of inferring anomalous cross-field transport coefficients is addressed in simulations of boundary plasmas with fluid models. A workflow for parameter inference in the UEDGE fluid code is developed using Bayesian optimization with parallelized sampling and integrated uncertainty quantification. In this workflow, transport coefficients are inferred by maximizing their posterior probability distribution, which is generally multidimensional and non-Gaussian. Uncertainty quantification is integrated throughout the optimization within the Bayesian framework that combines diagnostic uncertainties and model limitations. As a concrete example, we infer the anomalous electron thermal diffusivity $\chi_\perp$ from an interpretive 2D model describing electron heat transport in the conduction-limited region with radiative power loss. The workflow is first benchmarked against synthetic data and then tested on H-, L-, and I-mode discharges to match their midplane temperature and divertor heat flux profiles. We demonstrate that the workflow efficiently infers diffusivity and its associated uncertainty, generating 2D profiles that match 1D measurements. Future efforts will focus on incorporating more complicated fluid models and analyzing transport coefficients inferred from a large database of experimental results.

Bayesian optimization↗

DOE OSTI2026

Towards self-consistent integrated modeling of the tokamak pedestal, scrape-off layer, and divertor using SOLPS-ITER and EPED

A predictive, self-consistent integrated model of the tokamak edge plasma and neutral system has been developed and validated against experimental data from DIII-D, spanning from the divertor target and scrape-off layer to the top of the pedestal. The model uses the SOLPS-ITER fluid boundary plasma and neutral code to constrain the EPED prediction of the pedestal height and width by taking the separatrix temperature and density calculated from SOLPS as inputs to EPED. An empirical proxy function based on data from a subset of these discharges is then used to infer the ratio of density at the pedestal top to that at the separatrix based on the electron temperature at the divertor target. This allows the density at the top of the pedestal to be provided to EPED as well, so that knowledge of this quantity is no longer required a priori, while SOLPS radial transport coefficients are needed instead. The gas puff rate provided to SOLPS is then a primary model input for this forward model coupling (along with radial transport coefficients, which are kept fixed through each scan in this study). Comparisons with measurements from DIII-D density scans through a range of target conditions find significant pedestal pressure degradation as the density is increased towards detachment in three different divertor configurations, consistent with the experimental data in these ballooning-limited pedestal regimes.

core-edge integration↗

DOE OSTI2024

Particle control via cryopumping and its impact on the edge plasma profiles of Alcator C-Mod

At the high n e proposed for high-field fusion reactors, it is uncertain whether ionization, as opposed to plasma transport, will be most influential in determining n e at the pedestal and separatrix. A database of Alcator C-Mod discharges is analyzed to evaluate the impact of source modification via cryopumping. The database contains similarly-shaped H-modes at fixed I P = 0.8 MA and B t = 5.4 T, spanning a large range in P net and ionization. Measurements from an edge Thomson scattering system are combined with those from a midplane-viewing Ly α camera to evaluate changes to n e and T e in response to changes in ionization rates, S ion ∙ $n^{sep}_e$ and $T^{ped}_e$ are found to be most sensitive to changes to $S^{sep}_{ion}$, as opposed to $n^{ped}_e$ and $T^{sep}_e$. Dimensionless quantities, namely α MHD and v*, are found to regulate attainable pedestal values. Select discharges at different values of P net and in different pumping configurations are analyzed further using SOLPS-ITER. It is determined that changes to plasma transport coefficients are required to self-consistently model both plasma and neutral edge dynamics. Pumping is found to modify the poloidal distribution of atomic neutral density, n 0 , along the separatrix, increasing n 0 at the active X-point. Opaqueness to neutrals from high n e in the divertor is found to play a role in mediating neutral penetration lengths and hence, the poloidal distribution of neutrals along the separatrix. Pumped discharges thus require a larger particle diffusion coefficient than that inferred purely from 1D experimental profiles at the outer midplane.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

Exploring Li-Ion Transport Properties of Li 3 TiCl 6 : A Machine Learning Molecular Dynamics Study

We performed large-scale molecular dynamics simulations based on a machine-learning force field (MLFF) to investigate the Li-ion transport mechanism in cation-disordered Li 3 TiCl 6 cathode at six different temperatures, ranging from 25°C to 100°C. In this work, deep neural network method and data generated by ab − initio molecular dynamics (AIMD) simulations were deployed to build a high-fidelity MLFF. Radial distribution functions, Li-ion mean square displacements (MSD), diffusion coefficients, ionic conductivity, activation energy, and crystallographic direction-dependent migration barriers were calculated and compared with corresponding AIMD and experimental data to benchmark the accuracy of the MLFF. From MSD analysis, we captured both the self and distinct parts of Li-ion dynamics. The latter reveals that the Li-ions are involved in anti-correlation motion that was rarely reported for solid-state materials. Similarly, the self and distinct parts of Li-ion dynamics were used to determine Haven’s ratio to describe the Li-ion transport mechanism in Li 3 TiCl 6 . Obtained trajectory from molecular dynamics infers that the Li-ion transportation is mainly through interstitial hopping which was confirmed by intra- and inter-layer Li-ion displacement with respect to simulation time. Ionic conductivity (1.06 mS/cm) and activation energy (0.29eV) calculated by our simulation are highly comparable with that of experimental values. Overall, the combination of machine-learning methods and AIMD simulations explains the intricate electrochemical properties of the Li 3 TiCl 6 cathode with remarkably reduced computational time. Thus, our work strongly suggests that the deep neural network-based MLFF could be a promising method for large-scale complex materials.

Selvaraj, Selva Chandrasekaran (ORCID:000000029023↗

DOE OSTI2025

Quarkonium Polarization Kinetic Equation from Open Quantum Systems and Effective Field Theories

Recent measurements of polarization phenomena in relativistic heavy ion collisions have aroused a great interest in understanding dynamical spin evolution of the QCD matter. In particular, the spin alignment signature of J/ψ has been recently observed in Pb-Pb collisions at LHC, which may infer nontrivial spin transport of quarkonia in quark gluon plasmas. Motivated by this, we study the spin-dependent in-medium dynamics of quarkonia by using the potential nonrelativistic QCD (pNRQCD) and the open quantum system framework. By applying the Markovian approximation and Wigner transformation, we systematically derive the Boltzmann transport equation for vector quarkonia with polarization dependence in the quantum optical limit. As opposed to the previous study for the spin-independent case where the collision terms depend on chromoelectric correlators, the new kinetic equation incorporates gauge invariant correlators of chromomagnetic fields that determine the recombination and dissociation terms with polarization dependence at the order we are working in the multipole expansion. In the quantum Brownian motion limit, the Lindblad equation with new transport coefficients defined in terms of the chromomagnetic field correlators have also been derived. Our formalism is generic and valid for both weakly-coupled and strongly-coupled quark gluon plasmas. It may be further applied to study spin alignment of vector quarkonia in heavy ion collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Multi-fidelity equations of state and transport coefficient datasets for pulsed-power applications

Reliably simulating experiments relevant to the National Nuclear Security Administration (NNSA) requires a detailed description of material properties across a wide range of conditions. Such properties include the equations of state, charged-particle transport coefficients, and optical properties like the opacity. Together, these properties make up the material models used in radiation-magnetohydrodynamic simulations of nuclear fusion experiments. Many of these models do not incorporate uncertainties in the data used to produce them. It is unknown whether these uncertainties significantly impact the interpretation of simulation results and diagnostics. The purpose of this work is to quantify how such uncertainties impact simulations of pulsed-power experiments. We accomplished this task by first assessing discrepancies between approaches used to generate the data. This included bringing together members of the high-energy-density community spanning the three NNSA laboratories and multiple universities. Then, using these data, we developed a general framework that systematically incorporates physical uncertainties within the material models suitable for uncertainty quantification analyses. The framework utilizes machine learning, Bayesian inference, and incorporates multi-fidelity datasets. We demonstrated the framework by quantifying the impact that material model uncertainties have on simulations of pulsed-power experiments underway on Z at Sandia National Laboratories. As a result of this work, we discovered that modest uncertainties in material models (roughly 20%) correspond to significant uncertainties in the outputs from simulations. Our framework has enabled rapid construction of material models through an automated procedure and allows for the generation of material models of interest to the NNSA.

36 MATERIALS SCIENCE↗

DOE OSTI2024

ETHOS: An automated framework to generate multi-fidelity constitutive data tables and propagate uncertainties to hydrodynamic simulations

Accurate constitutive data, such as equations of state and plasma transport coefficients, are necessary for reliable hydrodynamic simulations of plasma systems such as fusion targets, planets, and stars. Here, we develop a framework for automatically generating transport-coefficient tables using a parameterized model that incorporates data from both high-fidelity sources (e.g., density functional theory calculations and reference experiments) and lower-fidelity sources (e.g., average-atom and analytic models). The framework incorporates uncertainties from these multi-fidelity sources, generating ensembles of optimally diverse tables that are suitable for uncertainty quantification of hydrodynamic simulations. We illustrate the utility of the framework with magnetohydrodynamic simulations of magnetically launched flyer plates, which are used to measure material properties in pulsed-power experiments. We explore how changes in the uncertainties assigned to the multi-fidelity data sources propagate to changes in simulation outputs and find that our simulations are most sensitive to uncertainties near the melting transition. The presented framework enables computationally efficient uncertainty quantification that readily incorporates new high-fidelity measurements or calculations and identifies plasma regimes where additional data will have high impact.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Implementing Superresolution of Nonstationary Tides with Wavelets: An Introduction to CWT_Multi

Abstract Tides are often nonstationary due to nonastronomical influences. Investigating variable tidal properties implies a trade-off between separating adjacent frequencies (using long analysis windows) and resolving their time variations (short analysis windows). Previous continuous wavelet transform (CWT) tidal methods resolved tidal species. Here, we present CWT_Multi, a MATLAB code that 1) uses CWT linearity (via the “response coefficient method”) to implement superresolution, i.e., resolving tidal constituents beyond the Rayleigh criterion; 2) provides a Munk–Hasselmann constituent selection criterion appropriate for superresolution; and 3) introduces an objective, time-variable form of inference (“dynamic inference”) based on time-varying data properties. CWT_Multi resolves tidal species on time scales of days, and multiple constituents per species with fortnightly filters. It outputs astronomical phase lags and admittances, analyzes multiple records, and provides power spectra of the signal(s), residual(s), and reconstruction(s); confidence limits; and signal-to-noise ratios. Artificial data and water levels from the Lower Columbia River Estuary (LCRE) and San Francisco Bay Delta (SFBD) are used to test CWT_Multi and compare it to harmonic analysis programs NS_Tide and UTide. CWT_Multi provides superior reconstruction, detiding, dynamic analysis utility, and time resolution of constituents (but with broader confidence limits). Dynamic inference resolves closely spaced constituents (like K 1 , S 1 , and P 1 ) on fortnightly time scales, quantifying impacts of diel power peaking (with a 24-h period, like S 1 ) on water levels in the LCRE. CWT_Multi also helps quantify the impacts of high flows and a salt barrier closing on tidal properties in the SFBD. On the other hand, CWT_Multi does not excel at prediction, and results depend on analysis details, as for any method applied to nonstationary data. Significance Statement Ocean tides, especially in coastal and estuarine systems, are often nonstationary, in the sense that the mean and standard deviation of tidal properties vary over time, usually in response to some nontidal process. We introduce here a MATLAB code, CWT_Multi, that uses wavelet transforms to resolve both tidal species and constituents on time scales from a few days to months. Our code accommodates multiple scalar time series and has typical tidal analysis features like constituent selection and inference, plus two forms of uncertainty analyses. It is flexible, allowing the user to adapt analysis properties to diverse datasets. CWT_Multi is applicable to many problems involving time-variable tides, including sea level rise, compound flooding, sediment transport, and wetland habitat analyses. Application to vector data is a straightforward extension, but further development of our uncertainty analysis is merited. Because nonstationary tidal analysis is rapidly advancing, we also define the features of a “well-formed” analysis code.

Lobo, Matthew↗