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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Robust Solar Receivers Using MAX Phase Materials

This work was supported by the U.S. Department of Energy’s Office of Energy Efficiency and Renewable Energy under the Solar Energy Technologies Office Award Number 35928. The objective of the proposed effort was to develop and optimize additive manufacturing technologies for low-cost fabrication of high-temperature receivers using MAX phase-based materials (Ti 3 SiC 2 and Ti 3 AlC 2 ). MAX phase materials are a group of ternary metal carbides and nitrides where M stands for an early transition metal element, A is a group 13–16 element, and X is C and/or N. In Phase 1, the binder jetting additive manufacturing process was used to synthesize and characterize the Ti 3 SiC 2 MAX phase material. The typical process involved first producing a TiC preform using binder jetting followed by infiltration of the preform with silicon melt to form Ti 3 SiC 2 in situ. The reaction-infiltrated samples showed formation of MAX phase in the sample core; however, the surface showed cracking. Various process conditions—cooling rates, hold times, Si proportion, etc.—were varied to minimize the surface cracking. The fabricated MAX phase core was characterized by microstructure analysis and evaluations of mechanical properties such as hardness and thermal shock. In Phase 2, the focus included fabrication of Ti 3 SiC 2 MAX phase materials by spark plasma sintering (SPS) and synthesis of Ti 3 AlC 2 MAX phase materials by the Al melt infiltration process. It is expected that Al infiltration will not cause sample cracking, since Al does not expand during solidification. In addition, other processing approaches were investigated to fabricate the MAX phase materials, such as SPS with a graphite bedding approach for producing short-length Ti 3 AlC 2 MAX phase tubes for demonstration of prototypical Concentrating Solar Power receiver tubes. Fabricated samples underwent thermo-mechanical testing to validate the materials for the solar receiver application at temperatures >1000°C. In Phase 3, the effort focused on the development and optimization of the Ti-Al-C MAX phase composite material using the Al melt infiltration approach. We started with optimization of precursor powders and making preform structures by either pressing them in a die or using the binder jetting additive manufacturing process followed by Al melt infiltration. In addition, we investigated the formation of preform structures by cold isostatic pressing followed by Al melt infiltration for making Ti-Al-C MAX phase composite. Thermo-mechanical characterizations, such as creep, strength, and thermal shock, were conducted to establish the structures’ performance.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Mass spectrometric investigations into 3D printed parts to assess radiopurity as ultralow background materials for rare event physics detectors

The mass concentrations of 232 Th and 238 U in several 3D printing filaments and printed polymer parts are reported as measures of their radiopurity. In order to minimize background signals in rare event physics detectors, radiopure polymers are necessary as dielectric and structural materials in their construction. New data are reported for polyvinylidene fluoride (PVDF), polyphenylene sulfide (PPS), and two forms of polyetherimide (PEI, branded ULTEM 1010 and 9085). Data for starting filaments and both simple and complex printed parts are reported. PVDF filaments and simple printed beads, were found to have values of approximately 30 and 50 pg g -1 for 232 Th and 238 U, respectively, while a more complex spring clip part had slightly elevated 232 Th levels of 65 pg g -1 , with 238 U remaining at 50 pg g -1 . PPS filament was found to have concentrations of 270 and 710 pg g -1 for 232 Th and 238 U, respectively, and were not chosen to be printed as those levels were already higher than other material options. ULTEM 1010 filaments and printed complex spring clip parts were found to have concentrations of around 5 and 7 pg g -1 for 232 Th and 238 U, respectively, illustrating no significant contamination from the printing process. ULTEM 9085 filaments were found to have concentrations of around 9 and 5 pg g -1 for 232 Th and 238 U, respectively, while the printed complex spring clip part was found to have slightly elevated concentrations of 25 and 7 pg g -1 for 232 Th and 238 U, respectively. All these results were obtained using a novel dry ashing method in crucibles constructed of ultralow background electroformed copper or, when applicable, microwave assisted wet ashing digestion. Samples and process blanks were spiked with 229 Th and 233 U as internal standards prior to dry/wet ashing and determinations were made by inductively coupled plasma mass spectrometry (ICP-MS). In order to maintain high radiopurity levels, pre-cleaning the filaments before printing and post-cleaning the parts is recommended, although the printing process itself has shown to contribute very minute amounts of radiocontaminants.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Software For Advanced Large-scale Analysis Of Magnetic Confinement For Numerical Design, Engineering & Research (salamander)

As magnetic confinement fusion energy gains traction internationally to enable abundant energy production, designing components for fusion systems is a pressing challenge. During the planned lifetime of a fusion device, components evolve in extreme environments and must withstand large, repeated thermal loads and bombardment by 14 MeV neutrons, plasma ions, and neutral particles (deuterium, tritium, and helium), corrosive conditions, etc. All these physical processes take place simultaneously, interact in intricate ways, and impose important constraints that can affect performance. Experimental data is rare and costly to obtain, making design particularly challenging. Predictive computational frameworks must be an integral part of an accelerated and cost-effective design process by modeling fusion system performance in simulated environments. To better understand component degradation and operational impacts on their performance, the Software for Advanced Large-scale Analysis of MAgnetic confinement for Numerical Design, Engineering & Research (SALAMANDER) is designed as an open-source, fully integrated, multiphysics, multiscale, NQA-1 compliant framework facilitating 3D, high-fidelity fusion system modeling. To that end, SALAMANDER is a MOOSE-based framework, and therefore leverages MOOSE upstream libraries such as PETSc and libMesh to deliver sophisticated finite element, finite volume, and nonlinear solver technology for fusion energy simulations. SALAMANDER couples MOOSE physics module capabilities—such as thermal hydraulics, heat conduction, Navier-Stokes, and thermomechanics—with tritium transport via TMAP8, neutronics via Cardinal, and nascent particle-in-cell capabilities. Direct simulation Monte Carlo methods will be used to address neutral transport near the walls. By coupling all these physics in an integrated application, SALAMANDER will enable high-fidelity modeling of irradiation levels and plasma exposure conditions of plasma facing components and their impact on heat and tritium distributions, as well as the resulting mechanical constraints experienced by the plasma facing components and performance of blanket systems. Furthermore, SALAMANDER will be particularly suited for engineering studies thanks to the stochastic tool module readily available in MOOSE, allowing for extended uncertainty quantification and risk analysis studies. It is also able to use computer-aided design (CAD) meshes to model complex geometries, which is indispensable for fusion systems. SALAMANDER therefore supports design, safety, engineering, and research projects for magnetic confinement fusion systems

Simon, Pierre-Clement [Idaho National Laboratory (↗
DOE OSTI2025

The Langdon effect in laser plasmas: Absorption and conduction

A plasma heated by inverse bremsstrahlung absorption of laser light develops a non-Maxwellian electron distribution function, called the Langdon effect [A. B. Langdon, Phys. Rev. Lett. 44, 575 (1980)]. These non-Maxwellian distributions are sufficiently long-lived to impact the absorption processes itself as well as the transport of heat by electrons. The theory of the Langdon effect in a homogeneous plasma is reviewed to clarify some aspects of Langdon's derivation as well as to confirm that the widely used super-Gaussian approximation works fairly well to describe the shape of the distribution function and reduction of the absorption rate. The Langdon effect on thermal conduction in an inhomogeneous plasma is developed by considering perturbations in a homogeneous absorbing plasma, which develops a heat flux due to both temperature and density gradients. A practical theory of the heat flux is developed by fitting the results of Vlasov–Fokker–Planck simulations, which avoids several approximations that compromised the usefulness of past theoretical predictions, most critically, the effect of electron–electron collisions on the fluxes. The present fits parameterize the coefficients of the temperature gradient (thermal conductivity) and the density gradient for a plasma of any ionization state and for any laser intensity where the theory of the Langdon effect remains locally valid. It is expected that this generalized theory of heat flow in an absorbing plasma will improve the predictive capability of radiation-hydrodynamics simulations of laser-produced plasmas, especially those formed in inertial confinement fusion experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

A low power flexible dielectric barrier discharge disinfects surfaces and improves the action of hydrogen peroxide

There is an urgent need for disinfection and sterilization devices accessible to the public that can be fulfilled by innovative strategies for using cold atmospheric pressure plasmas. Here, we demonstrate a successful novel combination of a flexible printed circuit design of a dielectric barrier discharge (flex-DBD) with an environmentally safe chemical reagent for surface decontamination from bacterial contaminants. Flex-DBD operates in ambient air, atmospheric pressure, and room temperature without any additional gas flow at a power density not exceeding 0.5 W/cm 2 . The flex-DBD activation of a 3% hydrogen peroxide solution results in the reduction in the bacterial load of a surface contaminant of > 6log 10 in 90 s, about 3log 10 and 2log 10 better than hydrogen peroxide alone or the flex-DBD alone, respectively, for the same treatment time. We propose that the synergy between plasma and hydrogen peroxide is based on the combined action of plasma-generated OH · radicals in the hydrogen peroxide solution and the reactive nitrogen species supplied by the plasma effluent. A scavenger method verified a significant increase in OH · concentration due to plasma treatment. Novel in-situ FTIR absorption spectra show the presence of O 3 , NO 2 , N 2 O, and other nitrogen species. Ozone dissolving in the H 2 O 2 solution can effectively generate OH · through a peroxone process. The addition of the reactive nitrogen species increases the disinfection efficiency of the hydroxyl radicals and other oxygen species. Hence, plasma activation of a low concentration hydrogen peroxide solution, using a hand-held flexible DBD device results in a dramatic improvement in disinfection.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Elucidating key reducing species beyond ions in hydrogen plasma smelting reduction of iron ore

Hydrogen plasma smelting reduction (HPSR) of iron ore has attracted significant attention over the past decade due to its high-temperature operation, rapid plasma mediated reduction kinetics, and simpler density-based separation of molten iron product, compared to H2-based solid-state reduction. All of these attributes enable processing of low-grade ores for downstream use in electric-arc furnaces, as virgin iron with low gangue content is required for high quality steel and improved furnace operation. While positive ions exist within the plasma arc, this work demonstrates that near the anodic ore surface, hydrogen radicals and vibrationally excited hydrogen species dominate and their densities correlate well with observed reduction rates. Species concentrations in the transferred plasma arc and at the plasma-ore interface are evaluated using coupled thermal plasma and near-wall non-equilibrium plasma models. The thermal plasma model is validated against experimental voltage data and spectroscopic measurements of plasma temperature and density for varying current inputs. Modeling of the near surface thermochemical non-equilibrium and micrometer scale anode sheath layer reveals, in addition to the expected H + , significant concentrations of ArH + and H$^+_3$ ions, typically not observed in thermal plasmas under thermodynamic equilibrium. Our results show that the inverted sheath structure at the anodic ore surface strongly suppresses reactive positive ion fluxes, while non-equilibrium electron-impact processes generate abundant hydrogen radicals and vibrationally excited species. These findings highlight the critical role of non-equilibrium effects in hydrogen arc-driven iron ore reduction and advance understanding beyond prevailing hypotheses centered on hydrogen ion-driven mechanisms.

08 HYDROGEN↗
DOE OSTI2020

In-situ spectroscopic ellipsometry for real-time characterization of the effects of high-flux helium plasmas on tungsten surfaces

Tungsten samples were exposed to He plasmas generated by an RF source (Γ i = 3.5 x 10 16 He cm -2 s -1 , ion energy = 92 eV.) The range of exposure conditions selected here is conducive to the growth of nearsurface He bubbles, and at higher fluence, the formation of W nanotendrils ranging between 50 — 100 nm in diameter. The evolution of these surface features was probed using a fixed-angle ellipsometer (280 — 1000 nm wavelength range) with direct line-of-sight to the sample. Over the parameter space explored here, changes in the two angles (p, S) that define the polarization of the reflected light followed a distinct trajectory with increasing plasma fluence. Ex-situ ellipsometry of 22 additional tungsten specimens tested at a wide range of plasma fluences and temperatures mapped onto these in-situ results well. We used helium ion microscopy and focused ion beam profiling to provide a direct calibration of the ellipsometry measurements. Our results indicate that for a reproducible process such as the growth helium-induced surface morphologies, ellipsometry is a practical in-situ diagnostic to study how fusion plasmas modify materials. To study more general effects of plasmas on surfaces, including co-deposition and sputtering, different approaches to modelling the optical properties of the exposed surfaces are also considered.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Heating and acceleration of ions with Kappa distribution functions by low‐frequency Alfvén wave

Abstract Heating and acceleration of ions with Kappa distribution functions (with parameter ) in low‐beta plasmas, by a low‐frequency Alfvén wave, is investigated using test‐particle simulations, yielding interesting new results. As long as the Alfvén wave amplitude is sufficiently large, the computed net heating energy of ions becomes independent of the wave frequency and amplitude, always approaching the same value of . The eventual energy of ions is dictated only by the initial ion energy and the ratio of the magnetic field energy density to the plasma density. The heating effect of the Kappa ions increases with . During the heating process, the ions are picked up by the Alfvén wave and pitch angle scattered, forming a quasi‐isotropic spherical shell velocity distribution. The Kappa ions are accelerated in the parallel direction, reaching a bulk flow speed roughly equal to the local Alfvén speed. Higher ‐value in the initial Kappa distribution leads to faster saturation. The above results may explain certain features of the ion heating and acceleration in the solar wind and corona.

Li, Kehua↗
DOE OSTI2026

Exploding Bridgewire (EBW) Detonators: An Example of Synergistic Multiphysics

Exploding bridgewire (EBW) detonators are highly temporally reproducible explosive devices that require the rapid discharge of a high‐voltage capacitance to operate and so are immune to most of the accidental hazards associated with traditional electric detonators. They have been demonstrated to be safe enough for use in high‐consequence explosive applications. Despite continued use for over 82 years, understanding the exact mechanism of operation has remained elusive. Various researchers have ascribed either deflagration‐to‐detonation (DDT) or shock‐to‐detonation (SDT) phenomena observed in other explosive events to explain the science behind the successful engineering; however, a rigorous justification has been absent. Previously, we have demonstrated a complex interaction in EBW detonators between large electrical currents, non‐equilibrium thermodynamic material states, plasma physics, powder compaction phenomena, shock physics, photochemistry, and rapid conventional explosive chemical reaction processes. Specifically, we have made progress in understanding the complex multiphysics that operates in these detonators and demonstrating that it is a serendipitous synergy between UV light emitted from the arc formed as the bridge is electrically exploded and the accompanying short‐duration shock transmitted into the explosive powder bed that allows these devices to function at practical capacitor sizes and charge voltages. This insight not only places the topic on a firmer scientific footing but potentially enables new approaches to safe detonator design.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Efficient numerical integration of thermal interaction rates

In many problems in particle cosmology, interaction rates are dominated by 2 ↔ 2 scatterings, or get a substantial contribution from them, given that 1 ↔ 2 and 1 ↔ 3 reactions are phase-space suppressed. We describe an algorithm to represent, regularize, and evaluate a class of thermal 2 ↔ 2 and 1 ↔ 3 interaction rates for general momenta, masses, chemical potentials, and helicity projections. A key ingredient is an automated inclusion of virtual corrections to 1 ↔ 2 scatterings, which eliminate logarithmic and double-logarithmic IR divergences from the real 2 ↔ 2 and 1 ↔ 3 processes. We also review thermal and chemical potential induced contributions that require resummation if plasma particles are ultrarelativistic.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Meso-Scale Electrodynamic Coupling of the Earth Magnetosphere-Ionosphere System

Within the fully integrated magnetosphere-ionosphere system, many electrodynamic processes interact with each other. We review recent advances in understanding three major meso-scale coupling processes within the system: the transient field-aligned currents (FACs), mid-latitude plasma convection, and auroral particle precipitation. (1) Transient FACs arise due to disturbances from either dayside or nightside magnetosphere. As the interplanetary shocks suddenly compress the dayside magnetosphere, short-lived FACs are induced at high latitudes with their polarity successively changing. Magnetotail dynamics, such as substorm injections, can also disturb the current structures, leading to the formation of substorm current wedges and ring current disruption. (2) The mid-latitude plasma convection is closely associated with electric fields in the system. Recent studies have unraveled some important features and mechanisms of subauroral fast flows. (3) Charged particles, while drifting around the Earth, often experience precipitating loss down to the upper atmosphere, enhancing the auroral conductivity. Recent studies have been devoted to developing more self-consistent geospace circulation models by including a better representation of the auroral conductance. It is expected that including these new advances in geospace circulation models could promisingly strengthen their forecasting capability in space weather applications. The remaining challenges especially in the global modeling of the circulation system are also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Driven electrostatic phase space vortices in a 1D weakly dissipative Vlasov–Poisson system

In this paper, the effect of collisions on driven electrostatic phase space vortices is analyzed by means of Eulerian simulation for two different collision models. It was demonstrated recently that in the absence of collisions, at late times, steady state phase space vortices manifest to form a plateau in the resonant region of the particle velocity distribution function, due to trapping of particles supporting multiextrema giant phase space vortices (PSVs). In the presence of collisions, over long time, this multiextrema plateau are found to smooth out, since collisions drive the velocity distribution toward Maxwellian, irrespective of how weak the collisions are as long as they are non-zero. In these conditions, kinetic processes and collisionality are found to be in competition, and the evolution of the plasma is found, therefore, to be a result of nontrivial combination of these two effects. An attempt has been made by means of numerical simulations to study the effect of weak collisionality on the electrostatic driven phase space vortices with two types of collision operators: (1) Bhatnagar–Gross–Krook (Krook) collision operator, where the colliding particles can be treated as isolated pairs and, (2) Fokker–Planck (FP) type collision operator (Zakharov–Karpman) in one dimension, where many weak collisions lead to particle diffusion in velocity space. It is shown that depending on the collision model used, the nature of smoothing in velocity space of giant PSVs results in qualitatively very different phase space structures. However, irrespective of the collision model used, excess density fractions over 10% are retained.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Transient magnetic field diffusion considerations relevant to magnetically assisted indirect drive inertial confinement fusion

We report application of a magnetic field to an indirect drive inertial confinement fusion target requires diffusion of the field through the high-Z and electrically conducting Hohlraum. The onset of the external field generates eddy currents in the Hohlraum wall that result in (1) a reduction of the peak field at the capsule, (2) heating of the Hohlraum wall through Ohmic dissipation, and (3) wall movement due to the inward force from the eddy current interacting with the field. Heating of the wall causes an increase in blackbody radiation which can preheat the capsule and frozen deuterium–tritium fuel, while wall motion leads to potential misalignment of the lasers at the Hohlraum wall. Limiting these detrimental effects sets requirements on the tolerable magnitude of each effect. We present a nonlinear model for B-field diffusion through an infinitely long thin-walled cylinder with a temperature dependent resistivity, to show that a 15 μm thick wall of pure gold fails to meet these requirements. A new Hohlraum material made from an alloy of Au and Ta has a measured resistivity of ≥60 times that of Au and is shown with the nonlinear model to meet the requirements for magnetization. We compare the nonlinear model to simulations of the actual Hohlraum target using a finite element code which includes temperature-dependent Hohlraum resistivity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Upgrades to the ion cyclotron emission diagnostic on the DIII-D tokamak

The ion cyclotron emission diagnostic on the DIII-D tokamak comprises seven single-turn loops that measure high-frequency (1–100 MHz) magnetic field fluctuations that are often excited by energetic particles in the plasma. The raw voltage signals induced in the loops in response to these fluctuations travel through a series of cables, isolation transformer DC blocks, low-pass filters, and finally a digitizer before being analyzed in frequency space. The diagnostic has been recently upgraded, most notably to include four additional graphite tile loops and a new eight-channel digitizer. The previous three loops are all on the low-field side of the tokamak. The measurement capabilities of the system have been expanded by the addition of a new horizontally oriented loop on the low-field side, an additional toroidal loop on the low-field side, and two toroidal loops on the high-field side. These loops will be used to provide approximate mode polarization, improved toroidal mode number calculations, and information on modes in inward-shifted plasmas, respectively.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Characterization of thermal transport and evolution of Au plasma in ICF experiments by Thomson scattering

Here, this paper demonstrates the capability of optical Thomson scattering (OTS) to measure thermal transport, and provides support to radiation hydrodynamic and kinetic simulations of electron thermal transport and plasma evolution. OTS theory and plasma simulations are applied to the interpretation of experimental measurements of laser-produced plasma from spherical gold targets on the OMEGA laser facility. The dynamical form factor, S($\vec{k}$, ω), of electron density fluctuations that is used in the fitting of Thomson scattering spectra includes ion–ion collisions and effects of non-Maxwellian distribution functions. OTS measurements and their interpretation are consistent with the nonlocal transport model in radiation hydrodynamic simulations as well as with kinetic simulations in the second half of the probe pulse duration. In particular, the reversal of heat transport during cooling is observed to be consistent with simulations, while some discrepancies are noted during the initial heating of the Au targets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

X-ray source characterization and sample heating on x-ray diffraction experiments at the National Ignition Facility

X-ray diffraction is a powerful measurement technique for determining material properties, and it is now possible to perform these experiments at pressures exceeding 1 TPa [Rygg et al., Rev. Sci. Instrum. 91, 043902 (2020)] at the National Ignition Facility (NIF). The x-ray source for these experiments is the quasi-monochromatic Heα emission from metal foils heated to multi-keV temperatures. A critical aspect for understanding the sample's thermodynamic state is the amount of heating caused by absorption of the probe x-rays. In this work, we characterize the performance of the Ge foil x-ray source over more than 60 NIF x-ray diffraction experiments. We use this information to constrain the level of diffraction sample heating from the x-ray source and discuss the impact on the thermodynamic state.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Staircases of passive and active scalar concentration in cellular flow

This paper develops a unified model for staircase formation in both passive and active scalar systems, building upon prior numerical studies by offering new heuristic and physical insights. While prior studies primarily reported numerical results, they did not explore the underlying unifying physics that governs both types of scalar transport; this work addresses that gap by identifying shared mechanisms across both cases. Results of studies of passive and active scalar staircase formation in cellular flows are presented. Staircase formation in cellular flows occurs due to the interplay of fast mixing within cells and slow transport across the inter-cell boundary. The cell boundary emerges as a de facto transport barrier. Special attention is focused on the effects of cellular fluctuations and noise upon staircase structure. A forced, fluctuating vortex array model is used to drive the underlying flow structure. Cellular Peclet number and staircase profile curvature are identified as figures-of-merit to quantify the resiliency of layering. These are related to simple, multi-scatterer scalar random walk models. Results for Peclet number and curvature scaling with flow excitation are presented. We also study staircases of magnetic potential evolving in two-dimensional magnetohydrodynamics as examples of layering of active scalar concentration. Formation of magnetic potential staircases is indeed observed. Flux expulsion inhibits the intercellular transport of magnetic potential and strengthens staircase barriers. Magnetic staircases can be supported against resistive decay by magnetic potential noise forcing. Implications for staircase formation in magnetic confinement experiments are discussed.

Control theory↗
DOE OSTI2025

Analysis of streaked images of x-ray self-emission in laser-driven spherical implosions

Imaging of x-ray self-emission provides a powerful in situ measurement of the spatial and temporal evolution of high-energy-density plasmas. However, interpretation of these measurements requires detailed understanding of the data-generating process. This work presents a case study in the interpretation of x-ray self-emission data for the specific application of streaked one-dimensional slit imaging of spherical laser-driven implosions. A comprehensive generative model of the streaked slit-imaging diagnostic is developed including detailed treatments of the radiation transfer, photometrics, and photostatistics associated with the measurement. The model is used to generate realistic synthetic streaked images and to analyze experimental streaked images to extract important physical quantities of interest. An example analysis of streaked images from implosion experiments on the OMEGA laser is presented, where the model developed in this work is used to constrain the trajectory and peak velocity of the implosion using Bayesian inference.

Bayesian inference↗