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NASA NTRS1983

The atmosphere of a dirty-clathrate cometary nucleus - A two-phase, multifluid model

The dynamical and thermal structure of a dirty-clathrate cometary nucleus' gas atmosphere is presently given a self-consistent, transonic multifluid solution in which, although the heavy neutron and ion species are treated as a single fluid in the collision-dominated region, the photoproduced H is treated separately. The thermal profile of the atmosphere thus obtained is entirely different from those predicted by the earlier, single-fluid models as well as the multifluid models which assumed equipartition of energy between electrons and ions. While the electron gas, like the neutrals and the ions, cools due to expansion, its main mode of energy loss in the inner coma is by way of inelastic collisions with the predominant H2O molecule. The high electron temperature in the outer coma also decreases the efficiency of electron removal by dissociative recombination, thereby increasing electron density throughout the coma.

Marconi, M. L.↗

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↗

NASA NTRS1982

Electrostriction in liquid He-4

The two-fluid model of liquid He-4 is extended to include effects of applied electric fields. New terms that account for electrostriction in equations of motion for superfluid and normal fluid are derived with the aid of a variational principle subject to the assumption that the Clausius-Mossotti relation for the dielectric constant is applicable. Corresponding additions to conservation laws for momentum and energy are presented.

Jackson, H. W.↗

NASA NTRS1995

Three-fluid solar wind model with Alfven waves

We present a study of a three-fluid solar wind model. with continuity, momentum and separate energy equations for protons. alpha particles and electrons. Allowing separate coronal heat sources for all three species, we study the flow properties of the solar wind as a function of heat input, Alfven wave energy input, and alpha particle abundance.

Esser, Ruth↗

DOE OSTI2026

A filter-dependent granular temperature model from large-scale CFD-DEM data

The computational study of strongly-coupled, gas–solid flows at scales relevant to most environmental and engineering applications requires the use of ‘coarse-grained’ methodologies such as the two-fluid model, particle-in-cell approach or the multiphase Reynolds Averaged Navier–Stokes equations. While these strategies enable computations at desirable length- and time-scales, they rely heavily on models to capture important flow physics that occur at scales smaller than the mesh. To date, the models that do exist are based on a limited set of flow conditions, such as very dilute particle phase. To this end, we leverage a large-scale repository of CFD-DEM data to develop filter-size dependent models for the mean variance in particle volume fraction, a quantity commonly used to assess the degree of clustering, and the granular temperature, a key quantity for accurately predicting gas–solid flows. In conclusion, because of its filter-size dependence, the granular temperature model can be directly translated to coarse-grained approaches and tied directly to grid size.

AMReX↗

DOE OSTI2019

Hydrodynamical instabilities in the superfluid interior of neutron stars with background flows between the components

The interiors of mature neutron stars are expected to host superfluid neutrons that can flow relative to the normal component tracked by electromagnetic emission. Hence, analogously to the hydrodynamic description of terrestrial superfluids like 4 He, the system is best described by means of a two-fluid model. In this work, we study wave propagation in the crust and core of a neutron star by conducting a local plane-wave analysis of the two-fluid hydrodynamic equations for a homogeneous macroscopic element of nuclear matter. We explicitly account for a background flow between the two components (as would be expected in the presence of pinning of superfluid vortex lines) and the entrainment coupling, and we consider both standard (Hall-Vinen) and isotropic (Gorter-Mellink) forms of the mutual friction. We find that for standard mutual friction there are families of unstable inertial and sound waves both in the case of a counter-flow along the superfluid vortex axis and for counterflow perpendicular to the vortex axis and find that entrainment leads to a quantitative difference between instabilities in the crust and core of the star. For isotropic mutual friction, we find no unstable branches of the dispersion law and speculate that instabilities in a straight vortex array may be linked to glitching behavior, which then ceases until the turbulence has decayed.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Continuum gyrokinetic simulations of edge plasmas in single-null geometries

The first continuum gyrokinetic calculations of electrostatic ion scale turbulence are presented for the case of a diverted tokamak geometry. The simulation model solves the long-wavelength limit of the full-F gyrokinetic equation for ion species coupled to the quasi-neutrality equation for electrostatic potential variations, where a fluid model is used for an electron response. Furthermore, in order to facilitate simulations of highly-anisotropic microturbulence in the presence of strong magnetic shear and a magnetic X-point, a numerical algorithm utilizing a locally field-aligned multiblock coordinate system has been developed and implemented in the 5D finite-volume code COGENT. In this approach, the toroidal direction is divided into blocks, such that within each block, the cells are field-aligned and a non-matching grid interface is allowed at block boundaries. The toroidal angle corresponds to the “coarse” field-aligned coordinate, whereas the poloidal cross section, comprised of the radial and poloidal directions, is finely gridded to resolve short-scale perpendicular turbulence structures and to support accurate re-mapping (interpolation) at block boundaries. The 5D simulations explore cross-separatrix ion scale turbulence in the presence of a self-consistent radial electric field and address the effects of magnetic-shear stabilization in the X-point region.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Improved melt model for power flow

Accelerators that drive z-pinch experiments transport current densities in excess of 1 MA/cm 2 in order to melt or ionize the target and implode it on axis. These high current densities stress the transmission lines upstream from the target, where rapid electrode heating causes plasma formation, melt, and possibly vaporization. These plasmas negatively impact accelerator efficiency by diverting some portion of the current away from the target, referred to as “current loss”. Simulations that are able to reproduce this behavior may be applied to improving the efficiency of existing accelerators and to designing systems operating at ever higher current densities. The relativistic particle-in-cell code CHICAGO ® is the primary code for modeling power flow on Sandia National Laboratories’ Z accelerator. We report here on new algorithms that incorporate vaporization and melt into the standard power-flow simulation framework. Taking a hybrid approach, the CHICAGO® kinetic/multi-fluid treatment has been expanded to include vaporization while the quasi-neutral equation-of-motion has been updated for melt at high current-densities. For vaporization, a new one-dimensional substrate model provides a more accurate calculation of electrode thermal, mass, and magnetic field diffusion as well as a means of emitting absorbed contaminants and vaporized metal ions. A quasi-fluid model has been implemented expressly to mimic the motion of imploding liners for accurate inductance histories. For melt, a multi-ion Hall-MHD option has been implemented and benchmarked against Alegra MHD. This new model is described with sufficient detail to reproduce these algorithms in any hybrid kinetic code. Physics results from the new code are also presented. A CHICAGO ® Hall-MHD simulation of a radial transmission line demonstrates that Hall physics, not included in Alegra, has no significant impact on the diffusion of electrode material. When surface contaminant desorption is mocked in as a hydrogen surface plasma, both the surface and bulk-material plasmas largely compress under the influence of the j × B force. Similar results are seen in Alegra, which also shows magnetic and material diffusion scaling with peak current. Test vaporization simulations using MagLIF and a power-flow experimental geometry show Fe + ions diffuse only a few hundred µm from the electrodes, so present models of Z power flow remain valid.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Integrated modeling of boron powder injection for real-time plasma-facing component conditioning

An integrated modeling framework for investigating the application of solid boron (B) powder injection for real-time surface conditioning of plasma-facing components (PFCs) in tokamak environments is presented. Utilizing the DIII-D impurity powder dropper (IPD) setup, this study simulates B powder injection scenarios ranging from milligrams to tens of milligrams per second, corresponding to boron flux rates of 10 20 –10 21 B/s in standard L-mode conditions. The comprehensive modeling approach combines EMC3-EIRENE for simulating the deuterium plasma background and the Dust Injection Simulator (DIS) for the ablation and transport of the boron powder particles. EMC3 trace impurity fluid modeling results show substantial boron transport to the inboard lower divertor, predominantly influenced by the main ion plasma flow. The dependency on powder particle size (5-250 µm) was found to be insignificant for the scenario considered. The effects of erosion and redeposition were considered to reconcile the discrepancies with experimental observations, which saw substantial deposition on the outer divertor plasma-facing components. For this purpose, the WallDYN3D code was updated to include boron sources within the plasma domain and integrated into the modeling framework. The mixed-material migration modeling shows evolving boron deposition patterns, suggesting the formation of mixed B-C layers or predominantly B coverage depending on the powder mass flow rate. While the modeling outcomes at lower B injection rates tend to align with DIII-D experimental observations, the prediction of near-pure boron layers at higher rates has yet to be experimentally verified in the carbon environment of the DIII-D tokamak. The extensive reach of boron layers found in the modeling suggests the need for modeling that encompasses the entire wall geometry for more accurate experimental correlations. This integrated approach sets a precedent for analyzing and applying real-time in-situ boron coating techniques in advanced tokamak scenarios, potentially extendable to ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

A physics-informed and hierarchically regularized data-driven model for predicting fluid flow through porous media

This paper presents a new deep learning data-driven model for predicting structure dependent pore-fluid velocity fields in rock. The model is based on a Convolutional Auto-Encoder (CAE) artificial neural network capable of learning from image data generated by direct numerical simulations of fluid flow through pore-structures, such as by Lattice Boltzmann or molecular dynamics methods. The main novelty of the model in comparison to previous CAE-based data-driven approaches consists of three parts. The first is a methodology for decomposing the full-domain of the porous media into sub-regions, or “sub-domains”, in order to reduce the overall size of the CAE, batch process the sub-domains in parallel, and enable the CAE to learn local and generalizable nonlinear mappings of pore-fluid velocities. The second consists of embedding the finite difference solutions of the incompressible Navier-Stokes and continuity equations into convolutional layers prior to the CAE in order to provide the CAE with knowledge of fluid dynamics physics (PhyFlow). The third main novelty is that the training of the CAE is regularized with a hierarchical loss function that encourages the learning of fluid flow patterns (in a way similar to ranked modes in principal component analysis), ranking from most to least important. This is shown to increase the stability in learning, reduce over-fitting, and promote interpretability of the CAE neural network layers (HierCAE). The comprehensive new data-driven model, which we call the PhyFlow-HierCAE model, is shown to exhibit improved accuracy and generalizability of flow field predictions over conventional CAE models, attributable to the embedded physical knowledge and the hierarchical regularization, as well as realize orders of magnitude speed-ups in computation times as a surrogate for the direct numerical simulations. Examples of training and forward predictions on unseen pore-structures are provided and evaluated for data from Lattice Boltzmann and molecular dynamics simulations of pore-fluid flow. The model is shown to be a fast and accurate emulator (or “surrogate”) for predicting effective permeability of unseen pore-structures based on learning from relatively small direct numerical simulation datasets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Modeling the effect of MHD activity on runaway electron generation during SPARC disruptions

Magnetohydrodynamic (MHD) instabilities and runaway electrons (REs) interact in several ways, making it important to self-consistently model these interactions for accurate predictions of RE generation and the design of mitigation strategies, such as massive gas injection (MGI). Using M3D-C1 – an extended MHD code with a RE fluid model – we investigate the effects of 3-D nonlinear MHD activity, material injection, and 2-D axisymmetric vertical displacement events (VDEs) on RE evolution during disruptions on SPARC – a high-field, high-current tokamak designed to achieve a fusion gain Q > 1. Several cases, comprising different combinations of neon (Ne) and deuterium (D 2 ) injection, are considered. Here, our results demonstrate key effects that arise from the self-consistent RE + MHD coupling, such as an initial increase in RE generation due to MHD instability growth, decreased saturation energies of the m/n = 1/1 mode driving sawteeth-like activity, RE losses in stochastic magnetic fields, and subsequent RE confinement and plateau formation due to re-healing of flux surfaces. Large RE plateaus (>5 MA) are obtained with Ne-only injection (2-5 × 10 21 atoms), while combined D 2 + Ne injection (2 × 10 21 Ne atoms; 1.8 × 10 22 D 2 molecules) produces a lower RE current (<2 MA). With D 2 + Ne injection, a post thermal quench "cold" VDE terminates the RE beam, preventing a steady plateau. These simulations couple REs, 3-D MHD instabilities, MGI, and axisymmetric VDEs for the first time in SPARC disruption simulations and represent a crucial step in understanding RE generation and mitigation in high-current devices like SPARC.

Datta, Rishabh [Massachusetts Inst. of Technology ↗

DOE OSTI2021

NRC Multiphysics Analysis Capability Deployment (FY2021 - Part 2)

This report details the progress and activities of Idaho National Laboratory (INL) on the Nuclear Regulatory Commission (NRC) project “Development and Modeling Support for Advanced Non-Light Water Reactors.” Task 4b was completed for this report. INL developed a sample problem showing how to use Serpent 2 to calculate macroscopic cross sections for use in Griffin for a typical sodium fast reactor Unprotected Loss of Flow (ULOF) transient. The complicating factor is the relatively large axial gradient of the coolant (and hence fuel) temperature and its evolution during the transient. A 3D Griffin model of the Advanced Burner Test Reactor (ABTR) is coupled to the System Analysis Module (SAM) to perform the ULOF transient. The model includes various explicit feedback mechanisms for fast reactors, including Doppler, radial expansion from the displacement of the support plate, and axial expansion from the displacement of the fuel pins. The results for the ULOF transient are consistent with published values. We observed small effects in the transient results that arise from the superhomogenization equivalence correction of uniform and nonuniform temperature data sets, but they diminish as more dominant reactivity mechanisms are added to the model. Potential improvements to the neutronics model include: adding the differential control rod and sodium feedback mechanisms, implementing cross section re-homogenization based on the partial volume of the various materials, and enhancing the kinetics parameters. Furthermore, the fluids model only includes four subchannels to represent the entire active core due to performance limitations in SAM when attempting to model one subchannel per assembly.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

A conservative implicit-PIC scheme for the hybrid kinetic-ion fluid-electron plasma model on curvilinear meshes

We report that the hybrid kinetic-ion fluid-electron plasma model is widely used to study challenging multi-scale problems in space and laboratory plasma physics. Here, a novel conservative scheme for this model employing implicit particle-in-cell techniques is extended to arbitrary coordinate systems via curvilinear maps from logical to physical space. The scheme features a fully non-linear electromagnetic formulation with a multi-rate time advance - including sub-cycling and orbit-averaging for the kinetic ions. By careful choice of compatible particle-based kinetic-ion and mesh-based fluid-electron discretizations in curvilinear coordinates, as well as particle-mesh interpolations and implicit midpoint time advance, the scheme is proven to conserve total energy for arbitrary curvilinear meshes. In the electrostatic limit, the method is also proven to conserve total momentum for arbitrary curvilinear meshes. Although momentum is not conserved for arbitrary curvilinear meshes in the electromagnetic case, it is for an important subset of Cartesian tensor-packed meshes. The scheme and its novel conservation properties are demonstrated for several challenging numerical problems using different curvilinear meshes, including a merging flux-rope simulation for a space weather application, and a helical m = 1 mode simulation for magnetic fusion energy application.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Fluid-like shock compression of dilute polymer nanocomposites

The shock Hugoniot of heterogenous mixtures of discrete particles has been experimentally investigated for porous agglomerates and fluids, while the study of full-density solids has been primarily limited to compressed powders and high-dimensional composites. By dispersing ceria nanoparticles in a polyethylene matrix, we are able to examine the hydrodynamic behavior of a nonporous, heterogenous solid in thermal equilibrium during weak shock compression. Phase-driven discontinuities in the Hugoniot particle velocity–shock velocity (u−D) relationship of pure polyethylene are replicated in the nanocomposites but are shifted to lower velocity and to higher pressure with higher particle concentration. The results are explained using an isothermal, two-velocity fluid model under the hydrodynamic approximation. The model, which assumes a theoretical equation-of-state for ceria and either a low-order or high-order fit to the measured polyethylene Hugoniot, reasonably predicts the Hugoniot for two different polyethylene/ceria nanocomposites. Using the model, the mixture Hugoniot is shown to be insensitive to the Hugoniot of the stiffer constituent when the moduli are sufficiently disparate, while dependence on particle density and volume fraction is preserved through fluid-like motion.

Moore, Nathan W. [Sandia National Laboratories (SN↗

DOE OSTI2025

Simulation Center for Runaway Electron Avoidance and Mitigation (SCREAM SciDAC) (Technical Final Report)

Runaway electrons can severely damage the plasma facing components on ITER during a major disruption and pose a major risk for tokamak fusion. It has been recognized that an adequate disruption mitigation system (DMS) is essential for the safe operation of ITER. The United States is responsible for the design and implementation of the disruption mitigation system on ITER, and in July 2016 the Simulation Center for Runaway Electron Avoidance and Mitigation (SCREAM) was launched by DOE, in a joint Fusion Energy Sciences (FES) and Advanced Scientific Computing Research (ASCR) collaboration. SCREAM was a comprehensive theory and simulation SciDAC center that provided physics guidance in the avoidance and mitigation of runaway electrons, and in tandem with domestic and international experiments, helped establish the qualitative and quantitative bases for safe operational scenarios and viable mitigation techniques. The SCREAM center assembled a national team of experts in runaway electron physics, tokamak disruptions, magnetohydrodynamic (MHD) simulation, and advanced algorithms and computing. The team combined advanced simulation and analysis capability facilitated by direct participation of ASCR SciDAC institutes with theoretical models and code development by FES scientists to focus on the runaway risk for ITER and tokamaks in general. The research scope was focussed on integrated simulations of kinetic runaway electrons, including MHD and fluid models of impurity transport, within a research plan guided by theory. The specific research tasks were (1) establish the fundamental physics of runaway generation, saturation, and dynamical evolution in a tokamak; (2) examine the critical path toward runaway avoidance; and (3) investigate the viability and effectiveness of the leading candidate schemes for runaway mitigation. In all three areas, members of the team carried out scoping studies that established the readiness for rapid and critical advances, especially in the deployment and further development of large-to extreme-scale simulation tools. Our multi-pronged computational approach included (1) relativistic Fokker-Planck solvers with discretization in phase space, (2) self-consistent particle-in-cell techniques, (3) particle-based Monte-Carlo, and (4) MHD-particle hybrid simulations. Cross-check between these different methods provided an additional means for verification and further bolstered the fidelity of our physics prediction. Validation against experimental results brings confidence to the predictive capability for ITER and frequently leads to new ideas for understanding and mitigating the thermal quench driven runaway electron phenomenon.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Theory-based scaling laws of near and far scrape-off layer widths in single-null L-mode discharges

Abstract Theory-based scaling laws of the near and far scrape-off layer (SOL) widths are analytically derived for L-mode diverted tokamak discharges by using a two-fluid model. The near SOL pressure and density decay lengths are obtained by leveraging a balance among the power source, perpendicular turbulent transport across the separatrix, and parallel losses at the vessel wall, while the far SOL pressure and density decay lengths are derived by using a model of intermittent transport mediated by filaments. The analytical estimates of the pressure decay length in the near SOL is then compared to the results of three-dimensional, flux-driven, global, two-fluid turbulence simulations of L-mode diverted tokamak plasmas, and validated against experimental measurements taken from an experimental multi-machine database of divertor heat flux profiles, showing in both cases a very good agreement. Analogously, the theoretical scaling law for the pressure decay length in the far SOL is compared to simulation results and to experimental measurements in TCV L-mode discharges, pointing out the need of a large multi-machine database for the far SOL decay lengths.

Physics↗

DOE OSTI2024

Effects of alpha-ion stopping on ignition and ignition criteria in inertial confinement fusion experiments

With the advent of ignited plasmas at the National Ignition Facility (NIF), alpha physics has become a driving factor in theoretical understanding and experimental behavior. In this communication, we explore aspects of direct alpha-ion heating through comparison of the consequences from the one-fluid and two-fluid models in the hydrodynamic approach. We show that the case with all alpha energy deposited in electrons raises the ignition criteria by ∼4 keV or ∼0.2 g/cm2 in the hotspot relative to the case with all alpha energy deposited in ions. In the case of the recently ignited NIF implosion, 30% of the 3.5 MeV α energy is deposited into the DT fuel ions, for which there is negligible difference between the one-fluid and two-fluid ignition criteria. However, changes in the ion stopping fraction through profile effects and alternate stopping power models could lead to ignition curve shifts of ∼1 keV.

Physics↗

DOE OSTI2022

Modelling of electrostatic ion-scale turbulence in divertor tokamaks with the gyrokinetic code $\mathrm{COGENT}$

Here, continuum gyrokinetic simulations of electrostatic ion scale turbulence are presented for the case of a diverted (single-null) tokamak geometry. The simulation model, implemented in the finite-volume code COGENT, solves the long-wavelength limit of the full-F gyrokinetic equation for ion species coupled to a vorticity equation for electrostatic potential variations, where a fluid model is used for an electron response. The model describes the ion scale ion temperature gradient (ITG) and resistive drift modes as well as neoclassical ion physics effects. Different turbulence regimes are observed depending on the plasma profiles, and the roles of a self-consistent background electric field and an X-point geometry are explored. In particular, increasing the pedestal density gradient and the corresponding radial electric field is demonstrated to suppress the ITG turbulence, whereas the same edge plasma background can still be destabilized by the resistive modes when the plasma resistivity is increased. The effects of X-point geometry are assessed by comparing cross-separatrix simulations with counterpart calculations performed for a toroidal annulus geometry. For the simulation parameters considered, similar global behaviour is observed in both cases, whereas strong local suppression of turbulence fluctuations is demonstrated near the X-point for the case of a single-null geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗