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DOE OSTI2022

Normalizing flows for likelihood-free inference with fusion simulations

Fluid-based scrape-off layer transport codes, such as UEDGE, are heavily utilized in tokamak analysis and design, but typically require user-specified anomalous transport coefficients to match experiments. Determining the uniqueness of these parameters and the uncertainties in them to match experiments can provide valuable insights to fusion scientists. Here, we leverage recent work in the area of likelihood-free inference (‘simulation-based inference’) to train a neural network, which enables accurate statistical inference of the anomalous transport coefficients given experimental plasma profile input. UEDGE is treated as a black-box simulator and runs multiple times with anomalous transport coefficients sampled from priors, and the neural network is trained on these simulations to emulate the posterior. The neural network is trained as a normalizing flow model for density estimation, allowing it to accurately represent complicated, high-dimensional distribution functions. With a fixed simulation budget, we compare a single-round procedure to a multi-round approach that guides the training simulations toward a specific target observation. Finally, we discuss the future possibilities for use of amortized models, which train on a wide range of simulations and enable fast statistical inference for results during experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Experimental inference of neutral and impurity transport in Alcator C-Mod using high-resolution x-ray and ultra-violet spectra

We present experimental inferences of cross-field impurity transport coefficients for AlcatorC-Mod plasmas without edge-localized modes, leveraging a novel forward model for the entire Ca Kα spectrum, including satellite lines within the spectral range, to compare to high-resolution x-ray imaging crystal spectroscopy (XICS). These measurements are complemented by extreme ultra-violet (EUV) spectroscopy that constrains transport closer to the edge. Using new atomic data sets for both XICS and EUV analysis has enabled consideration of line ratios across both spectral ranges and has increased the accuracy of inferred transport coefficients. Inclusion of charge exchange between edge thermal neutrals and impurities is shown to be extremely important in C-Mod pedestals. Atomic D neutral densities from experimental D Lyα measurements at the midplane are compared to SOLPS-ITER simulations, finding good agreement. Bayesian inferences of impurity transport coefficients are presented for L-, EDA H-, and I-mode discharges, making use of the Aurora package for forward modeling and combining our spectroscopic constraints. Experimentally inferred diffusion profiles are found to match turbulent transport models at midradius within uncertainties, using both quasilinear gyro-fluid TGLF SAT-1 and nonlinear ion-scale gyrokinetic CGYRO simulations. Furthermore, significant discrepancies in convection are observed in some cases, suggesting difficulties in predictions of flat or hollow impurity profiles.

neutrals↗

DOE OSTI2020

Dijet Acoplanarity in CUJET3 as a Probe of the Nonperturbative Color Structure of QCD Perfect Fluids

Using the CUJET3=DGLV+VISHNU jet-medium interaction framework, we show that dijet azimuthal acoplanarity in high energy A + A collisions is sensitive to possible non-perturbative enhancement of the jet transport coefficient, $\hat{q}$(T,E), in the QCD crossover temperature T ~ 150–300 MeV range. With jet-medium couplings constrained by global RHIC& LHC χ 2 fits to nuclear modification data on R AA (p T > 20) GeV, we compare predictions of the medium induced dijet transverse momentum squared, $Q_s^2~\langle \hat{q}L\rangle~ΔΦ^2E^2$, in two models of the temperature, T, and jet energy E dependence of the jet medium transport coefficient, $\hat{q}$(T,E)). In one model, wQGP, the chromo degrees of freedom (dof) are approximated by a perturbative dielectric gas of quark and gluons dof. In the second model, sQGMP, we consider a nonperturbative partially confined semi-Quark-Gluon-Monopole-Plasma with emergent color magnetic dof constrained by lattice QCD data. Unlike the slow variation of the scaled jet transport coefficient, $\hat{q}_{wQGP}/T^3$, the sQGMP model $\hat{q}_{sQGMP}/T^3$ features a sharp maximum in the QCD confinement crossover T range. We show that the dijet path averaged medium induced azimuthal acoplanarity, Δφ 2 , in sQGMP is robustly ~ 2 times larger than in perturbative wQGP. even though the radiative energy loss in both models is very similar as needed to fit the same R AA data. Future A+A dijet acoplanarity measurements constrained together with single jet R AA and ν n measurements therefore appears to be a promising strategy to search for possible signatures of critical opalescence like phenomena in the QCD confinement temperature range.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Three-dimensional modeling of a plasma in a strong azimuthal magnetic field

Three-dimensional magnetohydrodynamic (MHD) simulations are able to model the generation of disc-shaped plasma, driven by laser ablation from a current carrying rod in a pulsed-power machine producing azimuthal magnetic fields of 2–3 MG. The plasma at such extreme conditions is unique in that the parameter space for the plasma β and Hall parameter χ transition from below unity to greater than unity at different stages of the plasma generation. In simulations, the formation of the plasma disc in the azimuthal direction, is driven by heat flux from the laser spot and depends on the set of transport coefficients used in simulations. The most recent set of transport coefficients leads to the formation of plasma ejecta at the back end of the rod, that qualitatively matches experiments. Specifically, the cross-gradient Nernst effect, which twists magnetic field, is shown to have a large effect on the shape of the back end ejecta. In the direction along the axis of the rod there is propagation of perturbations from the disc as observed in experiments. In simulations the period of temperature perturbations is in good agreement with experimental results. Furthermore, an instability due to coupling of heat flux and the magnetic field advection provides a possible explanation for perturbation growth along the axis of the rod, and the instability growth rate is consistent with experimental results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Recent progress on in-medium properties of heavy mesons from finite-temperature EFTs

Mesons with heavy flavor content are an exceptional probe of the hot QCD medium produced in heavy-ion collisions. In the past few years, significant progress has been made toward describing the modification of the properties of heavy mesons in the hadronic phase at finite temperature. Ground-state and excited-state thermal spectral properties can be computed within a self-consistent many-body approach that employs appropriate hadron-hadron effective interactions, providing a unique opportunity to confront hadronic Effective Field Theory predictions with recent and forthcoming lattice QCD simulations and experimental data. In this article, we revisit the application of the imaginary-time formalism to extend the calculation of unitarized scattering amplitudes from the vacuum to finite temperature. These methods allow us to obtain the ground-state thermal spectral functions. The thermal properties of the excited states that are dynamically generated within the molecular picture are also directly accessible. We present here the results of this approach for the open-charm and open-bottom sectors. We also analyze how the heavy-flavor transport properties, which are strongly correlated to experimental observables in heavy-ion collisions, are modified in hot matter. In particular, transport coefficients can be computed using an off-shell kinetic theory that is fully consistent with the effective theory describing the scattering processes. The results of this procedure for both charm and bottom transport coefficients are briefly discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Generation and Control of Self-Organized Nonlinear Kinetic Structures in High Energy Density Plasmas in the Presence of Intense Magnetic Fields and Ultrashort Laser Pulses

Goals were to study the interplay between electron plasma waves (EPW), KEEN waves and externally generated magnetic fields. In particular, the Weibel instability B field generation process and its interrelationship with the existence of nonlinear EPWs in high energy density plasmas. We focused on a number of models of how Kinetic, Nonlinear Electron Plasma Waves, KNL-EPW and KEEN waves create anisotropic electron velocity distribution functions, e- VDF, and how these anisotropic e- VDFs in turn drive the Weibel instability and generate B fields. Our goal is to control the SRS and SKEENS processes that generate the KNL-EPW, control the anisotropy, and thus also control the dynamics of the resulting B fields, their influence on the transport coefficients and heat transport that results, their modification of SRS itself and the reinforced anisotropy driven loop gain.

(Kinetic electrostatic electron nonlinear) KEEN wa↗

DOE OSTI2020

Effective viscosities in a hydrodynamically expanding boost-invariant QCD plasma

Background: The near-equilibrium properties of a QCD plasma can be encoded into transport coefficients such as bulk and shear viscosity. In QCD, the ratio of these transport coefficients to entropy density, ζ/$\textit{s}$ and η/$\textit{s}$, depends nontrivially on the plasma's temperature. This is unlike in conformal systems where they take constant values such as η/$\textit{s}$ = 1/(4π). Purpose: In this work, we show that in a (0 + 1)D boost-invariant fluid with no transverse expansion, a temperature-dependent ζ/$\textit{s(T)}$ or η/$\textit{s(T)}$ can be described by an equivalent effective viscosity $\langleζ/s\rangle_{\text{eff}}$ or $\langleη/s\rangle_{\text{eff}}$. This effective viscosity combines the actual temperature-dependent ζ/$\textit{s(T)}$ or η/$\textit{s(T)}$ with the temperature profile of the fluid. Further, we extend the concept of effective viscosity in systems with transverse expansion and discuss how effective viscosities can be used to identify families of ζ/$\textit{s(T)}$ and η /$\textit{s(T)}$ that lead to similar hydrodynamic evolution. Methods: The Navier-Stokes relativistic hydrodynamic equations are used to provide a first definition of effective viscosity, in (0 + 1)D and (1 + 1)D. In the (0 + 1)D case, the analysis is extended to Israel-Stewart-type second-order hydrodynamics to clarify the effect of higher-order hydrodynamics corrections on the effective viscosity. Results: In a boost-invariant fluid with no transverse expansion [(0 + 1)D], the effective viscosity is expressed as a simple integral of ζ/$\textit{s(T)}$ or η/$\textit{s(T)}$ over temperature, with a weight determined by the speed of sound of the fluid. The result is general for any equation of state with a moderate temperature dependence of the speed of sound, including the QCD equation of state. This definition of effective viscosity can be used to identify infinite families of ζ/$\textit{s(T)}$ or η/$\textit{s(T)}$ that produce essentially indistinguishable temperature profiles. In a boost-invariant cylindrical system [(1 + 1)D], a similar definition of effective viscosity is obtained in terms of characteristic trajectories in time and transverse direction. This leads to an infinite number of constraints on an infinite functional space for ζ/$\textit{s(T)}$ and η/$\textit{s(T)}$. Realistic examples are presented by using a finite number of constraints on a finite functional space. Conclusions: The definition of effective viscosity in a (0 + 1)D system clarifies how infinite families of ζ/$\textit{s(T)}$ and η/$\textit{s(T)}$ can result in nearly identical hydrodynamic temperature profiles. By extending the study to a boost-invariant cylindrical [(1 + 1)D] fluid, we identify an approximate but more general definition of effective viscosity that highlights the potential and limits of the concept of effective viscosity in fluids with limited symmetries.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Vacancy-mediated transport and segregation tendencies of solutes in fcc nickel under diffusional creep: A density functional theory study

The Nabarro-Herring (NH) diffusional creep theory postulates the vacancy-mediated transport of atoms under a stress gradient as the creep mechanism under low-stress and high-temperature conditions. In multicomponent alloys, we premise that this stress-assisted flow of vacancies to and from grain boundaries will produce elemental segregation. An observation of such segregation, validated with theoretical predictions, can provide the necessary experimental evidence for the occurrence of NH creep. Theoretical calculations of the segregation tendencies via analyzing the dominant solute diffusion mechanisms and the difference in diffusivities of the elements are therefore essential. To this end, this study applies density functional theory calculations of migration barriers and solute-vacancy binding energies as input to the self-consistent mean-field theory to assess the vacancy-mediated diffusion mechanisms, transport coefficients, and segregation tendencies of Co, Cr, Mo, Re, Ta, and W solutes in face-centered-cubic Ni. We find Co, Re, and W to be slow diffusers at high temperatures and Cr, Mo, and Ta to be fast diffusers. Further analysis shows that the slow diffusers tend to always enrich at vacancy sinks over a wide range of temperatures. In contrast, the fast diffusers show a transition from depletion to enrichment as the temperature lowers. Furthermore, our analysis of the segregation tendencies under tensile hydrostatic strains shows that slow diffusers are largely unaffected by the strain and favor enrichment. On the other hand, the fast diffusers exhibit high sensitivity to strain and their segregation tendency can transition from depletion to enrichment at a given temperature. Finally, the transport coefficients calculated in this work are expected to serve as input to mesoscale microstructure models to provide a more rigorous assessment of solute segregation under NH creep conditions.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Bottomonium suppression from the three-loop QCD potential

We compute the suppression of bottomonium in the quark-gluon plasma using the three-loop QCD static potential. The potential describes the spin-averaged bottomonium spectrum below threshold with a less than 1% error. Within potential nonrelativistic quantum chromodynamics and an open quantum systems framework, we compute the evolution of the bottomonium density matrix. The values of the quarkonium transport coefficients are obtained from lattice QCD measurements of the bottomonium in-medium width and thermal mass shift; we additionally include for the first time a vacuum contribution to the dispersive coefficient γ . Using the three-loop potential and the values of the heavy quarkonium transport coefficients, we find that the resulting bottomonium nuclear modification factor is consistent with experimental observations, while at the same time reproducing the lattice measurements of the in-medium width. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Challenges and approaches to interpretive modeling of boundary plasma and neutral transport in a closed, pumped divertor

An experimental discharge from the DIII-D tokamak is modeled using the SOLPS-ITER code suite and compared against measurements in the pumped and relatively closed upper divertor. Uncertainties of boundary plasma simulations are identified by attempting to match code inputs to experimental conditions, including iteratively solving transport coefficients to match upstream experimental profiles using varying quantities of core particle flux, different pumping models, and various assumptions of ion thermal transport. Simulated boundary conditions for particle injection at the core interface are shown to be relevant to the plasma solution at the divertor targets, even if upstream transport is modified so that plasma profiles are comparatively similar, although seperatrix density is not held constant. When upstream plasma profiles are matched to experimental measurements by varying diffusive transport coefficients, using either poloidally symmetric or ballooning structure, the model finds a majority of injected energy being transported radially off the computational domain, in conflict with experimental radiated power measurements and heat flux measurements at the divertor target. Imposing a maximum thermal diffusivity or radially shifting the experimental separatrix location of the fitted profiles to increase power conducted to the targets by increasing the upstream electron temperature does not significantly modify this result. Including a thermalizing plenum volume in the simulation domain is shown to maintain the experimental volumetric pumping rate without knowing the neutral energy distribution incident on the pump duct a priori. By modifying transport parameters to match different assumptions for ion temperature, downstream neutral pressure changes by more than a factor of two, suggesting that attention to ion thermal transport may be a critical parameter for simulations to accurately resolve recycling and neutral transport, particularly in a closed divertor geometry. In addition to quantifying various modeling uncertainties, this work motivates both further experimental study and modeling improvements to improve predictive capabilities.

divertor↗

DOE OSTI2020

Time-reversal symmetry breaking in two-dimensional nonequilibrium viscous fluids

In this work, we study the rheological signatures of departure from equilibrium in two-dimensional viscous fluids with and without internal spin. Under the assumption of isotropy, we provide the most general linear constitutive relations for stress and couple stress in terms of the velocity and spin fields. Invoking Onsager's regression hypothesis for fluctuations about steady states, we derive the Green-Kubo formulas relating the transport coefficients to time-correlation functions of the fluctuating stress. In doing so, we show that one of the nonequilibrium transport coefficients, the odd viscosity, requires time-reversal symmetry breaking in the case of systems without internal spin. However, the Green-Kubo relations for systems with internal spin also show that there is a possibility for nonvanishing odd viscosity even when time-reversal symmetry is preserved. Furthermore, we find that breakdown of equipartition in nonequilibrium steady states results in the decoupling of the two rotational viscosities relating the vorticity and the internal spin.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Kinetic Landau-fluid closures of non-Maxwellian distributions

New kinetic Landau-fluid closures, based on the cutoff Maxwellian distribution, are derived. A special static case is considered (the frequency ω=0). In the strongly collisional regime, our model reduces to Braginskii's heat flux model, and the transport is local. In the weak collisional regime, our model indicates that the heat flux is non-local and recovers the Hammett–Perkins model while the value of the cutoff velocity approaches to infinity. We compare the thermal transport coefficient χ of Maxwellian, cutoff Maxwellian and super-Gaussian distribution. The results show that the reduction of the high-speed tail particles leads to the corresponding reduction of the thermal transport coefficient χ across the entire range of collisionality, more reduction of the free streaming transport toward the weak collisional regime. In the collisionless limit, χ approaches to zero for the cutoff Maxwellian and the super-Gaussian distribution but remains finite for Maxwellian distribution. χ is complex if the cutoff Maxwellian distribution is asymmetric. The Im(χ) approaches to different convergent values in both collisionless and strongly collisional limit, respectively. It yields an additional streaming heat flux in comparison with the symmetric cutoff Maxwellian distribution. Furthermore, due to the asymmetric distribution, there is a background heat flux q0 though there is no perturbation. Furthermore, the derived Landau-fluid closures are general for fluid moment models, and applicable for the cutoff Maxwellian distribution in an open magnetic field line region, such as the scape-off-layer of Tokamak plasmas, in the thermal quench plasmas during a tokamak disruption, and the super-Gaussian electron distribution function due to inverse bremsstrahlung heating in laser-plasma studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

EOSPAC User’s Manual: V.6.5

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

EOSPAC User's Manual: Version 6.5 Second Edition (Rev. 3)

The EOSPAC utility package is a collection of interface routines, which can be used to access the SESAME data library and perform various data adjustments and interpolations on the SESAME data. The SESAME data library contains both thermodynamic (e.g., equation of state) and transport coefficients (e.g., opacity and conductivity). Note, for simplicity, the term EOS (equation of state) used herein includes both thermodynamic variables and transport coefficients. The EOSPAC utility package is designed to be used by physics codes (henceforth ”host codes”) written in multiple languages and on multiple platforms. The remainder of this manual is organized into several sections. Chapter 2 discusses conventions such as data organization and routine names. Chapter 3 provides a general overview of basic theory and models implemented within EOSPAC. Chapter 4 provides a general overview of how to use the EOSPAC interface library. Chapters 5 to 7 describe the public interfaces of EOSPAC in detail. Chapter 8 provides a brief introduction to some related tools, which may be of use to the user. Chapter 9 provides details related to some selected numerical features of EOSPAC. Chapter 10 gives examples for using the interface routines described in chapters 5 to 7. Chapter 11 provides technical support contact information. Chapter 12 contains a brief set of acknowledgments. Chapter 13 contains a list of referenced documents. Finally, chapter 14 lists the “table types: mnemonic conventions”, “table types: grouped by category, sorted by name”, “table types: eospac version 5 cross reference”, “options: setup phase”, “data information parameters”, “meta-data information parameters”, “options: interpolation phase”, and the “error codes”.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Linearised Fokker–Planck collision model for gyrokinetic simulations

We introduce a gyrokinetic, linearised Fokker–Planck collision model that satisfies conservation laws and is accurate at arbitrary collisionalities. The differential test-particle component of the operator is exact; the integral field-particle component is approximated using a spherical harmonic and a modified Laguerre polynomial expansion developed by Hirshman and Sigmar (1976 Phys. Fluids 19 1532). The numerical methods of the implementation in the δf-gyrokinetic code stella (Barnes et al 2019 J. Comput. Phys. 391 365–80) are discussed, and conservation properties of the operator are demonstrated. The collision model is then benchmarked against the collision model of the gyrokinetic solver GS2 in the limiting cases of a reduced test-particle collision operator and energy- and momentum-conserving operator. The accuracy of the full collision model is investigated by solving the parallel Spitzer-Härm problem for the transport coefficients. It is shown that retaining collisional energy flux and higher-order terms in the field-particle operator reduces errors in the transport coefficients from 10%–25% for a simple momentum- and energy-conserving model to under 1%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

CASM Monte Carlo: Calculations of the thermodynamic and kinetic properties of complex multicomponent crystals

Monte Carlo techniques play a central role in statistical mechanics approaches that connect macroscopic thermodynamic and kinetic properties to the electronic structure of a material. This paper describes the implementation of Monte Carlo techniques for the study of multicomponent crystalline materials within the Clusters Approach to Statistical Mechanics (CASM) software suite, and demonstrates their use in model systems to calculate free energies and kinetic coefficients, study phase transitions, and construct phase diagrams from first principles. Many crystal structures are complex, with multiple sublattices occupied by differing sets of chemical species, along with the presence of vacancies or interstitial species. This imposes constraints on concentration variables, the form of thermodynamic potentials, and the values of kinetic transport coefficients. The framework used by CASM to formulate thermodynamic potentials and kinetic transport coefficients accounting for arbitrarily complex crystal structures is presented and demonstrated with examples of increasing complexity. Additionally, an overview of the capabilities of the CASM software specific to Monte Carlo methods is given, and a new CASM software package is introduced, casm-flow, which helps automate the setup, submission, management, and analysis of Monte Carlo simulations.

Cluster expansion↗

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 OSTI2020

Hydrodynamic electron transport near charge neutrality

We develop the theory of hydrodynamic electron transport in a long-range disorder potential for conductors in which the underlying electron liquid lacks Galilean invariance. For weak disorder, we express the transport coefficients of the system in terms of the intrinsic kinetic coefficients of the electron liquid and the correlation function of the disorder potential. We apply these results to analyze the doping and temperature dependence of transport coefficients of graphene devices. In this work, we show that at charge neutrality, long-range disorder increases the conductivity of the system above the intrinsic value. The enhancement arises from the predominantly vortical hydrodynamic flow caused by local deviations from charge neutrality. Its magnitude is inversely proportional to the shear viscosity of the electron liquid and scales as the square of the disorder correlation radius. This is qualitatively different from the situation away from charge neutrality. In that case, the flow is predominantly potential and produces negative viscous contributions to the conductivity, which are proportional to the sum of shear and bulk viscosities and inversely proportional to the square of disorder correlation radius.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗