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DOE OSTI2026

A novel conditional formulation of the Vlasov–Ampère equations: a conservative, positivity, asymptotic and Gauss law preserving scheme

We propose a novel reformulation of the Vlasov–Ampère equations for plasmas that reveals discrete symmetries that enables simultaneous conservation of mass, momentum and energy; preservation of Gauss’s law; positivity of the distribution function; and consistency with quasi-neutral asymptotics. The approach employs variable and coordinate transformations to yield a coupled system comprising a modified Vlasov equation and associated moment–field equations. The modified Vlasov equation advances a conditional distribution function that excludes mass, momentum and energy densities, which are instead evolved through moment equations enforcing the relevant symmetries, conservation laws and involution constraints. This reformulation aligns naturally with a recent slow-manifold reduction technique, which separates fast electron time scales and simplifies the treatment of the quasi-neutral limit within the reduced moment–field subsystem. Using this framework, we develop a numerical method for the reduced 1D1V subsystem that, for the first time in the literature, satisfies all key physical constraints while maintaining a quasi-neutral asymptotic behaviour. The advantages of the method are demonstrated on canonical electrostatic test problems, including the multiscale ion acoustic shock wave.

1D1V↗

DOE OSTI2025

The Effects of Shockwave Pressures on Ultrafast Vibrational Energy Transfer in BNFF, a Hydrogen-Free Energetic Material

Energy conversion in energetic materials from shock-wave-induced lattice compression to bond breaking critically depends on vibrational coupling and energy transfer between intra- and intermolecular vibrations, though the details of the mechanisms remain unknown. Herein, we indirectly tune the strength of intermolecular interactions in 3,4-bis(3-nitrofurazan-4-yl)furoxan (BNFF), a hydrogen-free energetic material characterized by van der Waals interactions, by applying high static pressure using a diamond anvil cell and monitoring vibrational energy transfer (VET) with ultrafast broadband infrared pump–probe spectroscopy. As BNFF is compressed from ambient pressure to 9 GPa, we find that VET accelerates by ∼ 0.9 ps/GPa. Density functional theory is applied in tandem with experiments to assign mode character and elucidate VET pathways. In conclusion, we find that furazan ring O–N–O vibrations, which are high-frequency detonation-relevant vibrational modes, experience increased sensitivity to lattice compression under shockwave pressures. These findings provide new mechanistic insight into how intermolecular interactions govern the rate and selectivity of VET.

Energy transfer↗

DOE OSTI2021

Hydrodynamic instability at impact interfaces and planetary implications

Abstract Impact-induced mixing between bolide and target is fundamental to the geochemical evolution of a growing planet, yet aside from local mixing due to jetting – associated with large angles of incidence between impacting surfaces – mixing during planetary impacts is poorly understood. Here we describe a dynamic instability of the surface between impacting materials, showing that a region of mixing grows between two media having even minimal initial topography. This additional cause of impact-induced mixing is related to Richtmyer-Meshkov instability (RMI), and results from pressure perturbations amplified by shock-wave refraction through the corrugated interface between impactor and target. However, unlike RMI, this new impact-induced instability appears even if the bodies are made of the same material. Hydrocode simulations illustrate the growth of this mixing zone for planetary impacts, and predict results suitable for experimental validation in the laboratory. This form of impact mixing may be relevant to the formation of stony-iron and other meteorites.

58 GEOSCIENCES↗

DOE OSTI2021

High-energy emission from a magnetar giant flare in the Sculptor galaxy

Magnetars are the most highly magnetized neutron stars in the cosmos (with magnetic field 10 13 –10 15 G). Giant flares from magnetars are rare, short-duration (about 0.1 s) bursts of hard X-rays and soft γ rays. Owing to the limited sensitivity and energy coverage of previous telescopes, no magnetar giant flare has been detected at gigaelectronvolt (GeV) energies. Here, we report the discovery of GeV emission from a magnetar giant flare on 15 April 2020 (refs. 3,4 and A. J. Castro-Tirado et al., manuscript in preparation). The Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope detected GeV γ rays from 19 s until 284 s after the initial detection of a signal in the megaelectronvolt (MeV) band. Our analysis shows that these γ rays are spatially associated with the nearby (3.5 megaparsecs) Sculptor galaxy and are unlikely to originate from a cosmological γ-ray burst. Thus, we infer that the γ rays originated with the magnetar giant flare in Sculptor. Furthermore, we suggest that the GeV signal is generated by an ultra-relativistic outflow that first radiates the prompt MeV-band photons, and then deposits its energy far from the stellar magnetosphere. After a propagation delay, the outflow interacts with environmental gas and produces shock waves that accelerate electrons to very high energies; these electrons then emit GeV γ rays as optically thin synchrotron radiation. This observation implies that a relativistic outflow is associated with the magnetar giant flare, and suggests the possibility that magnetars can power some short γ-ray bursts.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Femtosecond laser produced periodic plasma in a colloidal crystal probed by XFEL radiation

With the rapid development of short-pulse intense laser sources, studies of matter under extreme irradiation conditions enter further unexplored regimes. In addition, an application of X-ray Free-Electron Lasers (XFELs) delivering intense femtosecond X-ray pulses, allows to investigate sample evolution in IR pump - X-ray probe experiments with an unprecedented time resolution. Here we present a detailed study of the periodic plasma created from the colloidal crystal. Both experimental data and theory modeling show that the periodicity in the sample survives to a large extent the extreme excitation and shock wave propagation inside the colloidal crystal. This feature enables probing the excited crystal, using the powerful Bragg peak analysis, in contrast to the conventional studies of dense plasma created from bulk samples for which probing with Bragg diffraction technique is not possible. X-ray diffraction measurements of excited colloidal crystals may then lead towards a better understanding of matter phase transitions under extreme irradiation conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Quantifying motion blur by imaging shock front propagation with broadband and narrowband X-ray sources

Time-integrated radiography using MeV Bremsstrahlung X-ray sources is the norm for imaging during system-level testing of components and structures under dynamic condition. One source of error in the analysis of the time-integrated radiography data sets stems from motion blur which smears out sharp interfaces to a greater degree with longer exposure times, which become necessary to provide sufficient signal-to-noise with low X-ray penetration of objects of interest. To quantify motion blur, a 1D shock wave through PMMA was investigated experimentally at The Dynamic Compression Sector at The Advanced Photon Source (DCS@APS) with tapered broadband and 25.46 ± 1.06 keV narrowband X-rays. Four cameras with different exposure times were used for each experiment to compare the effect that exposure time has on motion blur. In addition, our methodology to accurately simulate motion blur in terms of transmission and shape is presented and compared to our experimental results and quantified. There is a high level of agreement between the experimental and simulation results across the range of data sets investigated in this study with a percent difference range of 0.29–1.31% for the four shots. The methodology of this work serves as a steppingstone towards a physically validated model that could be used in conjunction with experimental results to deconvolve physical parameters, densities, and interfaces of interest in a way that would not be possible with experimental results alone.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

The staged Z-pinch as a potential fusion energy source

A staged Z-pinch is a fusion concept where a high atomic number liner compresses a fusion fuel (deuterium–deuterium or deuterium–tritium) target. Here, we report new results from Lagrangian, Eulerian, and Arbitrary Lagrangian–Eulerian simulations, which confirm that, with proper treatment of the vacuum region outside from the pinch, fusion energy production >1 MJ can be expected without alpha heating and significantly higher if alpha heating is included. It is shown that shock waves play an important role in preheating the target plasma and in piling up liner mass at the liner/target interface. This results in higher ram pressure just before the pinch stagnation time and ultimately in higher energy density target plasma.

Ruskov, E. (ORCID:0000000336724580)↗

DOE OSTI2020

Many-body reactive force field development for carbon condensation in C/O systems under extreme conditions

In this paper, we describe the development of a reactive force field for C/O systems under extreme temperatures and pressures, based on the many-body Chebyshev Interaction Model for Efficient Simulation (ChIMES). The resulting model, which targets carbon condensation under thermodynamic conditions of 6500 K and 2.5 g cm –3 , affords a balance between model accuracy, complexity, and training set generation expense. We show that the model recovers much of the accuracy of density functional theory for the prediction of structure, dynamics, and chemistry when applied to dissociative condensed phase systems at 1:1 and 1:2 C:O ratios, as well as molten carbon. Our C/O modeling approach exhibits a 104 increase in efficiency for the same system size (i.e., 128 atoms) and a linear system size scalability over standard quantum molecular dynamics methods, allowing the simulation of significantly larger systems than previously possible. We find that the model captures the condensed-phase reaction-coupled formation of carbon clusters implied by recent experiments, and that this process is susceptible to strong finite size effects. Overall, we find the present ChIMES model to be well suited for studying chemical processes and cluster formation at pressures and temperatures typical of shock waves. We expect that the present C/O modeling paradigm can serve as a template for the development of a broader high pressure–high temperature force-field for condensed phase chemistry in organic materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Spatiotemporal evolution of emission and absorption signatures in a laser-produced plasma

Here we report spatiotemporal evolution of emission and absorption signatures of Al species in a nanosecond (ns) laser-produced plasma (LPP). The plasmas were generated from an Inconel target, which contained ~0:4 wt. % Al, using 1064 nm, ≈6 ns full width half maximum pulses from an Nd:YAG laser at an Ar cover gas pressure of ≈34 Torr. The temporal distributions of the Al I (394.4 nm) transition were collected from various spatial points within the plasma employing time-of-flight (TOF) emission and laser absorption spectroscopy, and they provide kinetics of the excited state and ground state population of the selected transition. The emission and absorption signatures showed multiple peaks in their temporal profiles, although they appeared at different spatial locations and times after the plasma onset. The absorption temporal profiles showed an early time signature representing shock wave propagation into the ambient gas. We also used emission and absorption spectral features for measuring various physical properties of the plasma. The absorption spectral profiles are utilized for measuring linewidths, column density, and kinetic temperature, while emission spectra were used to measure excitation temperature. A comparison between excitation and kinetic temperature was made at various spatial points in the plasma. Our results highlight that the TOF measurements provide a resourceful tool for showing the spatiotemporal LPP dynamics with higher spatial and temporal resolution than is possible with spectral measurements but are difficult to interpret without additional information on excitation temperatures and linewidths. The combination of absorption and emission TOF and spectral measurements thus provides a more complete picture of LPP spatiotemporal dynamics than is possible using any one technique alone.

(140.3440) Laser-induced breakdown, (280.4788) Opt↗

DOE OSTI2022

An Eulerian crystal plasticity framework for modeling large anisotropic deformations in energetic materials under shocks

Here, this paper demonstrates a novel Eulerian computational framework for modeling anisotropic elastoplastic deformations of organic crystalline energetic materials (EM) under shocks. While Eulerian formulations are advantageous for handling large deformations, constitutive laws in such formulations have been limited to isotropic elastoplastic models, which may not fully capture the shock response of crystalline EM. The present Eulerian framework for high-strain rates, large deformation material dynamics of EM incorporates anisotropic isochoric elasticity via a hypo-elastic constitutive law and visco-plastic single-crystal models. The calculations are validated against atomistic calculations and experimental data and benchmarked against Lagrangian (finite element) crystal plasticity computations for shock-propagation in a monoclinic organic crystal, octahydro-1,3,5,7-tetranitro-1,3,5,7 tetrazocine (β-HMX). The Cauchy stress components and the resolved shear stresses calculated using the present Eulerian approach are shown to be in good agreement with the Lagrangian computations for different crystal orientations. The Eulerian framework is then used for computations of shock-induced inert void collapse in β-HMX to study the effects of crystal orientations on hotspot formation under different loading intensities. The computations show that the hotspot temperature distributions and the collapse profiles are sensitive to the crystal orientations at lower impact velocities (viz., 500 m/s); when the impact velocity is increased to 1000 m/s, the collapse is predominantly hydrodynamic and the role of anisotropy is modest. The present methodology will be useful to simulate energy localization in shocked porous energetic material microstructures and other situations where large deformations of single and polycrystals govern the thermomechanical response.

42 ENGINEERING↗

DOE OSTI2023

Invited article: X-ray phase contrast imaging in inertial confinement fusion and high energy density research

X-ray phase contrast imaging (XPCI) provides enhanced image contrast beyond absorption-based x-ray imaging alone due to refraction and diffraction from gradients in the object material density. It is sensitive to small variations in density, such as internal voids, cracks, grains, defects, and material flow, as well as to stronger density variations such as from a shock wave. Beyond its initial use in biology and materials science, XPCI is now routinely used in inertial confinement fusion (ICF) and high energy density (HED) research, first to characterize ICF capsules and targets, and later applied in dynamic experiments, where coherent x-ray sources, ultrafast x-ray pulses, and high temporal and spatial resolution are required. In this Review article, XPCI image formation theory is presented, its diverse use in ICF and HED research is discussed, the unique requirements for ultrafast XPCI imaging are given, as well as current challenges and issues in its use.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Study of ablation and shock generation across three orders of magnitude of laser intensity with 100 ps laser pulses

The laser ablation and subsequent shock generation in solid targets plays an important role in a variety of research topics from equation of state models for materials to inertial confinement fusion. One of the long-standing issues is the knowledge of ablation depth in the picosecond time regime. Here, we report on a direct technique for determining the ablation depth in aluminum using x-ray diffraction data from Linac Coherent Light Source at the Stanford Linear Accelerator Center. This technique gives a direct measurement of the shock wave propagation in the bulk target, enabling an ability to discern early timescale physics from late timescale effects not available in postmortem analysis. We find that the ablation depths only vary by 0.2 μm across three orders of magnitude of laser intensity, while the pressure increased by a factor of 10 following a square root dependence on laser pulse energy. We further observe that the ablation depth in this intensity range (10 11 –10 13 W/cm 2 in intensity, corresponding to 0.8–80 J/cm 2 in fluence) cannot be modeled by a universal scaling law, given the complexity of the mechanisms governing laser ablation in this intensity regime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

A point-particle-based hydride shell-shedding model for ejecta particle transport in reactive environments

A shock wave passing over a rough or perturbed metal surface will induce a limiting case of Richtmyer–Meshkov instability and will cause small particles to eject from the surface and transport into the surrounding medium. These particles are known as ejecta and can be either solid or liquid in nature. Recent experiments have shown that liquid cerium ejecta clouds exhibit unexpected non-monotonic acceleration behaviors as well as temperature plateaus after a brief temperature rise if they are transporting in a chemically reactive, hydrogen-based medium while they act as expected in an inert medium. This work details a point-particle model developed for reactive cerium ejecta transport, which attempts to account for these new physics through the behavior of a developing solid hydride shell, which is believed to form as a product of the reaction. The overall model incorporates the effects of the reaction on the particle properties as well as the effects of potential shedding of the shell into sub-micrometer scale flakes and potential phase change of the hydride if the ejecta particles reach the melt point of the hydride layer. The model is tested by performing simulations of the original motivating experiments and comparing quantities, such as ejected mass, velocimetry, and temperature profiles, against the experimental data. While the model is able to capture many general features of the observed anomalies, some inaccuracies still exist. These point to both missing physics in the model (such as a deuterium adsorption mechanism on the hydride layer) as well as a lack of knowledge of certain material properties (such as the strength of cerium hydride to determine dynamic fracture thicknesses) needed to fully reduce the uncertainties in the model by up to an order of magnitude and perform a true attempt at model validation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Transfer learning for analysis of collective and non-collective Thomson scattering spectra

Thomson scattering (TS) diagnostics provide reliable, minimally perturbative measurements of fundamental plasma parameters, such as electron density (⁠n e ) and electron temperature (⁠T e ⁠). Deep neural networks can provide accurate estimates of ⁠n e and T e when conventional fitting algorithms may fail, such as when TS spectra are dominated by noise, or when fast analysis is required for real-time operation. Although deep neural networks typically require large training sets, transfer learning can improve model performance on a target task with limited data by leveraging pre-trained models from related source tasks, where select hidden layers are further trained using target data. We present five architecturally diverse deep neural networks, pre-trained on synthetic TS data and adapted for experimentally measured TS data, to evaluate the efficacy of transfer learning in estimating n e and T e in both the collective and non-collective scattering regimes. We evaluate errors in n e and T e estimates as a function of training set size for models trained with and without transfer learning, and we observe decreases in model error from transfer learning when the training set contains ≲ 200 experimentally measured spectra.

Artificial neural networks↗

DOE OSTI2025

Development, Verification, and Validation of an OpenFOAM-Based Solver for Modeling Inertial Fusion Energy Chambers

Our work seeks to introduce a computational tool tailored to the physics of inertial fusion energy chambers, in particular, those concepts based on thick liquid walls. In this approach, the structural materials are protected by several neutron mean-free-paths of renewable liquid and thus will be able to survive much longer than un-shielded walls, with virtually all structures lasting for the life of the plant and enabling the use of commercially available and qualified materials. The OpenFOAM-based solver named rhoCentralFoam has been used as a starting point. rhoCentralFoam belongs to the standard OpenFOAM solver toolset. It is a high-speed, explicit compressible flow solver with shock-capturing capability. While the main features have been retained, the solver had to be restructured to make use of tabular data for equations of states, a necessary addition to model the complex thermo-physical properties of ionized gasses. This entailed the need to change the independent state variables used by the solver, resulting in a new thermodynamic library and slightly different solution algorithm. Moreover, a radiation heat transfer model based on the P-1 approximation was added to the solver. The solver is verified against an analytical solution from the Sedov-Taylor-Neumann test problem to showcase the ability of the hydrodynamic solvers to handle strong shocks, whereas the P-1 model was verified using a simple one-dimensional problem with an analytical solution. Additionally, a validation case involving shock-wave propagation through jet array is presented, and the results are compared with experimental data from the open literature. Lastly, in order to showcase the utility of the solver for practical cases, we applied the refined solver to two representative scenarios: gas venting within the HYLIFE-II chamber and the compression of the gas following the partial ablation of the liquid wall.

Chamber dynamics↗

DOE OSTI2021

Filamentary surface plasma discharge flow length and time scales

Nanosecond surface dielectric barrier discharges (ns-SDBDs) are a class of plasma actuators that utilize a high-voltage pulse of nanosecond duration between two surface-mounted electrodes to create an electrical breakdown of air, along with rapid heating. These actuators usually produce multiple filaments when operated at high pulse frequencies, and the rapid heating leads to the formation of shock waves and complex flow fields. In this work we replicate a single filament of the ns-SDBDs and characterize the induced flow using velocity measurements from particle image velocimetry and density measurements from background-oriented schlieren. The discharge is produced by a high voltage electrical pulse between two copper electrodes on an acrylic base. A hot gas kernel characterizes the flow field formed close to the electrodes that expands and cools over time and a vortex ring that propagates away from the surface while entraining cold ambient fluid. The gas density deficit inside the kernel displays a power-law decay over time. Based on the observations, we develop a simplified theoretical model based on vortex-driven cooling and perform a scaling analysis to obtain the induced flow length and time scales. The results show that the cooling process's time scales correspond to a circulation-based time scale of the vortex ring, and the length scale of the kernel corresponds to the vortex ring radius. Furthermore, these findings can guide the choice of optimal filament spacing and pulse frequencies in the design, deployment, and operation of ns-SDBDs for flow control.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Analysis of the density field around a supersonic conical projectile using quantitative schlieren

Quantitative schlieren imaging is a flow measurement technique that is capable of measuring density fields throughout refractive flowfields. The technique was applied here to measure the density field surrounding supersonic conical projectiles in free flight. Shock waves attached to a supersonic conical projectile offer a simple geometry with the well-established Taylor–Maccoll analytical flow solution to which these experimental measurements were compared. The schlieren images recorded a projection of the index of refraction field surrounding the 10° half-angle cones which was converted to density first through an Abel inversion and then the Gladstone–Dale law. Three Abel inversion methods—two-point, three-point, and arbitrary ray axisymmetric projection (ARAP)—were applied to deconvolute the three-dimensional flow within the constrained axisymmetric flow field. The resulting reconstructed density profiles were compared to the Taylor–Maccoll solution, parameterized by cone geometry and Mach number. The experimental density fields demonstrated strong agreement with the theoretical profiles. Experimental consistency was confirmed across various projectile speeds, demonstrating quantitative schlieren’s capability to accurately reconstruct the density of the flow field, even within the resolution constraints imposed by high-speed imaging. In conclusion, an assessment of experimental uncertainties in the density reconstruction was performed.

Abel Inversion↗

DOE OSTI2021

The effects of laser pulse length and collisional ionization on the acceleration of titanium ions

Abstract The interaction of a relativistic laser pulse ( > 10 18 W cm −2 µ m 2 ) with foil targets can accelerate ions to energies of tens of MeV u −1 with optimized laser and target parameters. We report the results on simulations of the interaction of a 6.0 × 10 20 W cm −2 laser pulse incident on ultrathin (10–500 nm) titanium foils to investigate the roles of laser pulse duration and ionization mechanisms in the acceleration of titanium ions. While holding peak intensity constant, two laser pulse durations were investigated, 140 and 650 fs. The optimum thickness is dependent on pulse duration, as it requires the concurrence of target transparency with the incidence of the peak laser intensity. The collisional processes do not play a significant role in Ti ion beam generation from the 140 fs laser pulse duration at the optimum thickness (30 nm). However, for the 650 fs laser optimum, collisions improve the conversion efficiency of highly energetic ( > 10 MeV u −1 ), high charge titanium (Ti 21 − 22 + ) by a factor of 20, and the titanium ion cutoff energy by ∼15%. This improvement is due to the fact that collisional ionization increases the electron density of the plasma, which delays the time of relativistic transparency, causing collisions to decrease the optimum foil thickness from 150 to 100 nm. Additionally, collisional ionization increases the charge-to-mass ratio of the titanium, and injects more electrons into the accelerating sheath field. At the optimum thickness, target normal sheath acceleration is the dominant mechanism of acceleration, with additional contributions from radiation pressure and shock wave acceleration.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗