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DOE OSTI2020

Neural network representability of fully ionized plasma fluid model closures

The closure problem in fluid modeling is a well-known challenge to modelers aiming to accurately describe their systems of interest. Over many years, analytic formulations in a wide range of regimes have been presented but a practical, generalized fluid closure for magnetized plasmas remains an elusive goal. Here, as a first step toward constructing a novel data-based approach to this problem, we apply ever-maturing machine learning methods to assess the capability of neural network architectures to reproduce crucial physics inherent in known magnetized plasma closures. We find encouraging results, indicating the applicability of neural networks to closure physics, but also arrive at recommendations on how one should choose appropriate network architectures for the given locality properties dictated by the underlying physics of the plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Two-dimensional turbulence in a massless fluid with a relativistic lattice Boltzmann model

We investigate a relativistic adaptation of the lattice Boltzmann method that reproduces the equations of motion for a turbulent, two-dimensional, massless hydrodynamic system. The classical lattice Boltzmann method and its extension to relativistic fluid dynamics are described. The numeric formulation is evaluated using a zero-averaged stirring force introduced into the numerics to induce turbulence, and the flow characteristics produced are compared to properties of a classical turbulent hydrodynamic flow. The model can reasonably be expected to offer quantitative simulations of electron fluid flows in graphene or Kagome lattices.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Turbulent field fluctuations in gyrokinetic and fluid plasmas

A key uncertainty in the design and development of magnetic confinement fusion energy reactors is predicting edge plasma turbulence. An essential step in overcoming this uncertainty is the validation in accuracy of reduced turbulent transport models. Drift-reduced Braginskii two-fluid theory is one such set of reduced equations that has for decades simulated boundary plasmas in experiment, but significant questions exist regarding its predictive ability. To this end, using a novel physics-informed deep learning framework, we demonstrate the first ever direct quantitative comparisons of turbulent field fluctuations between electrostatic two-fluid theory and electromagnetic gyrokinetic modeling with good overall agreement found in magnetized helical plasmas at low normalized pressure. This framework presents a new technique for the numerical validation and discovery of reduced global plasma turbulence models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Finite-difference multiple fluid solution for source-driven rotation in highly magnetized linear plasma device

The rotation profile of a magnetized plasma cylinder composed of multiple fluids is investigated analytically, expanding on previous results. The analytic steady-state solution is used as a benchmark for a time-dependent multiple-fluid finite-difference code, MITNS: Multiple-Ion Transport Numerical Solver. Magnetic field evolution is taken into account, both analytically and numerically. Its details are shown to be of importance when particles are allowed out of the domain. MITNS reproduces the asymptotic expansion results for a small parameter $δ<<<1$. For $\sqrt{m_elm_i} ~ δ << 1$ , a slightly different regime, dominated by viscosity-induced transport of ions, is found numerically and analytically. Finally, this verification supports the use of this code for more complex time-dependent calculations in the future. Additionally, we derive the angular velocity profile of each species due to radial particle and charge fluxes of various strengths.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Fluid dynamic mathematical aspects of supernova remnants

Supernovae—explosions of stars—are a central problem in astrophysics since they contain information on the entire process of stellar evolution and nucleosynthesis. Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities, developing during the supernova blast, lead to intense interfacial RT/RM mixing of the star's materials and couple astrophysical to atomic scales. This work analyzes some fluid dynamic mathematical aspects of the titanic task of supernova's blast. We handle mathematical challenges of RT/RM dynamics in supernova relevant conditions by directly linking the conservation laws governing RT/RM dynamics to symmetry-based momentum model, by exactly deriving the model parameters in the scale-dependent and scale-invariant regimes, and by exploring the special self-similar class for RT/RM interfacial mixing with variable accelerations. Here we reveal that RT/RM dynamics is strongly influenced by deterministic (the initial and the flow) conditions in the scale-dependent linear and nonlinear regimes and in the self-similar mixing regime. The theory outcomes are consistent with the observations of supernova remnants, explain the results of the scaled laboratory experiments in high energy density plasmas, and yield the design of future experiments for the accurate quantification of RT/RM dynamics in supernova relevant conditions. We find that from fluid dynamic mathematical perspectives, supernovae can be regarded as an astrophysical initial value problem. Along with the guidance of what explodes at microscopic scales, supernova remnants encapsulate information on the explosion hydrodynamics and the associated deterministic conditions at macroscopic scales. We urge such effects be considered in interpretations of the observational data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

A versatile pressure-cell design for studying ultrafast molecular-dynamics in supercritical fluids using coherent multi-pulse x-ray scattering

Supercritical fluids (SCFs) can be found in a variety of environmental and industrial processes. They exhibit an anomalous thermodynamic behavior, which originates from their fluctuating heterogeneous micro-structure. Characterizing the dynamics of these fluids at high temperature and high pressure with nanometer spatial and picosecond temporal resolution has been very challenging. The advent of hard x-ray free electron lasers has enabled the development of novel multi-pulse ultrafast x-ray scattering techniques, such as x-ray photon correlation spectroscopy (XPCS) and x-ray pump x-ray probe (XPXP). These techniques offer new opportunities for resolving the ultrafast microscopic behavior in SCFs at unprecedented spatiotemporal resolution, unraveling the dynamics of their micro-structure. However, harnessing these capabilities requires a bespoke high-pressure and high-temperature sample system that is optimized to maximize signal intensity and address instrument-specific challenges, such as drift in beamline components, x-ray scattering background, and multi-x-ray-beam overlap. We present a pressure cell compatible with a wide range of SCFs with built-in optical access for XPCS and XPXP and discuss critical aspects of the pressure cell design, with a particular focus on the design optimization for XPCS.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

Estimating the carbon footprint of computational fluid dynamics

In this study, computational resources have grown exponentially in the past few decades. These machines make possible research and design in fields as diverse as medicine, astronomy, and engineering. Despite ever-increasing computational capabilities, direct simulation of complex systems has remained challenging owing to the degrees of freedom involved. At the cusp of exascale computing, high-resolution simulation of practical problems with minimal model assumptions may soon experience a renaissance. However, growing reliance on modern computers comes at the cost of a growing carbon footprint. To illustrate this, we examine historic computations in fluid dynamics where larger computers have afforded the opportunity to simulate flows at increasingly relevant Reynolds numbers. Under a variety of flow configurations, the carbon footprint of such simulations is found to scale roughly with the fourth power of Reynolds number. This is primarily explained by the computation cost in core-hours, which is also described by similar scaling, though regional differences in renewable energy use also play a role. Using the established correlation, we examine a large database of simulations to develop estimates for the carbon footprint of computational fluid dynamics in a given year. Collectively, the analysis provides an additional benchmark for new computations where, in addition to balancing considerations of model fidelity, carbon footprint should also be considered.

42 ENGINEERING↗

DOE OSTI2024

Establishing criteria for the transition from kinetic to fluid modeling in hollow cathode analysis

Hollow cathodes for plasma switch applications are investigated via 2D3V particle-in-cell simulations of the channel and plume region. The kinetic nature of the plasma within the channel is dependent on the thermalization rate of electrons, emitted from the insert. When Coulomb collisions occur at a much greater rate than ionization or excitation collisions, the electron energy distribution function rapidly relaxes to a Maxwellian and the plasma within the channel can be described accurately via a fluid model. In contrast, if inelastic processes are much faster than Coulomb collisions, then the electron energy distribution function in the channel exhibits a notable high-energy tail, and a kinetic treatment is required. This criterion is applied to hollow cathodes from the literature, revealing that a fluid approach is suitable for most electric propulsion applications, whereas a kinetic treatment can be more critical to accurate modeling of plasma switches.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

A review of fluids under nanoconfinement: Reactivity, geomechanics, phase transitions, and flow

Due to its many industrial applications, the physics associated with the nanoconfinement of fluids has garnered great attention from the scientific community in roughly the last fifteen years. One pioneer of that research has been the Multi-Scale Fluid-Solid Interactions in Architected and Natural Materials (MUSE) Energy Frontier Research Center, which produced more than 50 journal articles from 2018 to 2023. We structure the findings of MUSE into four categories and contextualize the work with the broader literature. Here, the four categories are (1) the dependence of chemical reactions on the degree of confinement, which given the lower freedom of motion of molecules yet improved availability of reaction sites generally lead to enhancement from bulk reactions; (2) the mechanical properties of the porous matrix, which are dependent on the heterogeneity of the system in terms of both composition and structure; (3) the phase transitions under nanoconfinement, which are influenced by the pore size and morphology, surface chemistry, and substrate composition; and (4) the physical controls of slip flow, which demonstrate the importance of several factors, such as wettability. These aspects of nanoconfinement are becoming clearer, but there are other elements such as mathematical theory that are still being developed.

58 GEOSCIENCES↗

DOE OSTI2024

RASPA3

RASPA3, a molecular simulation code for computing adsorption and diffusion in nanoporous materials and thermodynamic and transport properties of fluids. It implements force field based classical Monte Carlo/molecular dynamics in various ensembles. RASPA3 is rewritten from the ground up in C++23 with speed and code readability in mind. Transition-matrix Monte Carlo is added to compute the density of states and free energies. The Monte Carlo code for rigid molecules is based on quaternions, and the atomic positions needed in the energy evaluation are recreated from the center of mass position and quaternion orientation. The expanded ensemble methodology for fractional molecules, with a scaling parameter λ between 0 and 1, now also keeps track of analytic expressions of dU/dλ, allowing independent verification of the chemical potential using thermodynamic integration. The source code is freely available under the MIT license on GitHub.

Dubbeldam, David↗

DOE OSTI2024

Initial data for first-order causal viscous conformal fluids in general relativity

We solve the Einstein constraint equations for a first-order causal viscous relativistic hydrodynamic theory in the case of a conformal fluid. For such a theory, a direct application of the conformal method does not lead to a decoupling of the equations, even for constant-mean curvature initial data. We combine the conformal method applied to a background perfect fluid theory with a perturbative argument in order to obtain the result.

Disconzi, Marcelo (ORCID:0000000234497778)↗

DOE OSTI2024

Ten-moment fluid model for low-temperature magnetized plasmas

In this paper, a one-dimensional 10-moment multi-fluid plasma model is developed and applied to low-temperature magnetized plasmas. The 10-moment model solves for six anisotropic pressure terms, in addition to density and three components of fluid momentum, which allows the model to capture finite kinetic effects. The results are benchmarked against a 5-moment model, which assumes that the gas constituents follow a Maxwellian velocity distribution function (VDF), and a particle-in-cell Monte Carlo collision model that allows for arbitrary non-Maxwellian VDFs. The models are compared in a one-dimensional, low-temperature, partially magnetized plasma test case. The 10-moment results accurately reproduce the anisotropic temperature profile in low-temperature magnetized plasmas, where shear gradients exist due to the E×B drift. We discuss the mechanisms by which the anisotropic pressure can be generated in low-temperature magnetized plasmas. In addition, the importance of a self-consistent heat flux closure to the 10-moment model is studied, showing consistency with other models only when the assumptions of the underlying model are met. The 10-moment model allows for study of electron inertia effects and non-Maxwellian VDFs without the need for kinetic methods that are more computationally expensive.

Kuldinow, Derek Amur (ORCID:0000000319730196)↗

DOE OSTI2025

Ponderomotive electron physics captured in a single-fluid extended magnetohydrodynamics model

The ponderomotive force, arising from the interaction between electromagnetic waves and plasma, plays a critical role in laser fusion, astrophysical plasmas, and laser diagnostics. Traditionally, modeling this force requires multi-fluid or particle-in-cell simulations due to its strong coupling to electron-scale dynamics. In this work, we demonstrate that a one-fluid, two-temperature extended magnetohydrodynamics (XMHD) model—augmented with a generalized Ohm's law (GOL) including electron inertia—can accurately reproduce key ponderomotive effects. We derive the ponderomotive force within this framework using a phasor-based approach and then validate its nonlinear manifestations through direct numerical simulations in the PERSEUS code, where steepening and density modulation phenomena typically associated with kinetic-scale models are reproduced. These results and prior work establish XMHD as a robust and efficient alternative for modeling nonlinear laser–plasma dynamics, bridging the gap between ideal MHD and fully kinetic approaches.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Novel approach to general curvilinear coordinates for plasma fluid applications

In general geometry, plasma fluid equations include nonlinear geometric sources associated with fictitious forces, which pose significant challenges to computer simulations. We reformulate the plasma fluid hierarchy to rigorously preserve geometry and conservation properties critical to numerical simulations, while concealing the geometric sources. In their discrete form, the reformulated models conserve mass, angular momentum, and energy naturally, by simple analogy with the continuum equations. These conservation properties have minimal requirements in discrete space, namely, the anti-symmetry of the first derivative and the orthogonality of the scalar and cross products. By decoupling magnetic geometry, coordinate systems, and numerical discretization, this enables maximum flexibility while preserving physics fidelity. As a testbed, we apply the novel representation to the resistive magnetohydrodynamic system, which involves a complete set of curvilinear operations. We verify the correctness of the approach using steady state liquid metal flows and the classic Orszag–Tang vortex.

Halpern, Federico D. [General Atomics, San Diego, ↗

DOE OSTI2012

Long range order and two-fluid behavior in heavy electron materials

The heavy electron Kondo liquid is an emergent state of condensed matter that displays universal behavior independent of material details. Properties of the heavy electron liquid are best probed by NMR Knight shift measurements, which provide a direct measure of the behavior of the heavy electron liquid that emerges below the Kondo lattice coherence temperature as the lattice of local moments hybridizes with the background conduction electrons. Because the transfer of spectral weight between the localized and itinerant electronic degrees of freedom is gradual, the Kondo liquid typically coexists with the local moment component until the material orders at low temperatures. The two-fluid formula captures this behavior in a broad range of materials in the paramagnetic state. In order to investigate two-fluid behavior and the onset and physical origin of different long range ordered ground states in heavy electron materials, we have extended Knight shift measurements to URu 2 Si 2 , CeIrIn 5 , and CeRhIn 5 . In CeRhIn 5 we find that the antiferromagnetic order is preceded by a relocalization of the Kondo liquid, providing independent evidence for a local moment origin of antiferromagnetism. In URu 2 Si 2 the hidden order is shown to emerge directly from the Kondo liquid and so is not associated with local moment physics. Lastly, our results imply that the nature of the ground state is strongly coupled with the hybridization in the Kondo lattice in agreement with phase diagram proposed by Yang and Pines.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

Universal linear and nonlinear electrodynamics of a Dirac fluid

Significance Electrons in pristine solids behave as a hydrodynamic fluid in a certain range of temperatures and frequencies. We show that the response of such a fluid to an electromagnetic field is different from what is predicted by the usual kinetic theory. Certain aspects of this response are universal, for example, a direct relation between the linear and second-order nonlinear optical conductivities. Discovery of this relation enriches our understanding of the light–matter interaction in diverse electron systems and new materials such as graphene.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Neutronics and Thermo-Fluids Simulation of Generic Pebble-Bed Fluoride-Salt-Cooled High-Temperature Reactor

The fluoride-salt-cooled high-temperature reactor (FHR) is one of the advanced reactors that has been attracting considerable interest from both the research community and the nuclear industry. To help facilitate the nuclear community's familiarity with the FHR, Kairos Power has developed a generic FHR (gFHR) benchmark. In the research performed here, this benchmark was used to assess innovative modeling methods that combine stochastic and deterministic computer codes to perform the design and analysis of the gFHR. Further, the Monte Carlo code Serpent 2 was used to generate few-group cross sections that were then used in the neutron diffusion and thermal-fluids code AGREE to perform full-core neutronics and thermal-fluids steady-state and transient core analysis. The Argonne National Laboratory code SAM was then used to model the gFHR system and to simulate the load-follow operation of the gFHR.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Fluid temperature predictions of geothermal borefields using load estimations via state observers

Fluid temperature predictions of geothermal borefields usually involves temporal superposition of its characteristic g-function, using load aggregation schemes to reduce computational times. Assuming that the ground has linear properties, it can be modeled as a linear state space system where the states are the aggregated loads. However, the application and accuracy of these models is compromised when the borefield is already operating and its load history is not registered or there are gaps in the data. This paper assesses the performance of state observers to estimate the borefield load history and obtain accurate fluid predictions. Results show that both Time-Varying Kalman Filter (TVKF) and Moving Horizon Estimator (MHE) provide predictions with average and maximum errors below 0.1 $^\circ C$ and 1 $^\circ C$ respectively. MHE outperforms TVKF in terms of n-step ahead output predictions and load history profile at the expenses of about 5 times more computational time.

Figueroa, Iago C.↗