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DOE OSTI2025

An experimentally informed design process for future inertial confinement fusion facilities

The achievement of ignition in the laboratory has renewed interest in defining the requirements for a future high-gain inertial confinement fusion (ICF) facility. Our best chance of predicting future ICF performance is with 3-D radiation hydrodynamic simulations that have been benchmarked against experimental data, but their high computational cost is prohibitive for use in practical design studies. We introduce a hierarchical approach where 3-D simulations are tuned to match experimental measurements and used to train 3-D degradation models in 1-D simulations allowing for accurate predictions over the entire OMEGA direct-drive database. A genetic algorithm was used in combination with the trained 1-D simulations to search for optimal direct-drive implosion designs at driver energies ranging from 20 kJ to 10 MJ. As the fidelity of 3-D codes improves, this approach will provide a viable experimentally informed tool for defining the next ICF facility.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Modeling cross-beam energy transfer with sector ray tracing

Ray-based cross-beam energy transfer (CBET) models are an essential feature of the radiation-hydrodynamic codes used to simulate inertial confinement fusion implosions, but full 3D ray-based CBET calculations can have a prohibitively high computational cost. Sector ray tracing can be used to reduce the cost by orders of magnitude in cases where the coronal plasma and laser drive can be approximated as spherically symmetric. An extension of sector ray tracing (section ray tracing) can be used to relax the assumption of a spherically symmetric drive while still retaining most of the computational savings of a sector ray trace. We discuss the foundations of sector and section ray tracing and compare them to full ray tracing.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Resolving discrepancies in bang-time predictions for indirect-drive ICF experiments on the NIF: Insights from the Build-A-Hohlraum campaign

This study investigated discrepancies between measured and simulated x-ray drive in Indirect-Drive Inertial Confinement Fusion (ID-ICF) hohlraums at the National Ignition Facility. Despite advances in radiation-hydrodynamic simulations, a consistent “drive deficit” remains. Experimentally measured ID-ICF capsule bang-times are systematically 400–700 ps later than simulations predict. The Build-A-Hohlraum (BAH) campaign explored potential causes for this discrepancy by systematically varying hohlraum features, including laser entrance hole (LEH) windows, capsules, and gas fills. Overall, the agreement between simulated and experimental x-ray drive was found to be largely unaffected by these changes. The data allow us to exclude some hypotheses put forward to potentially explain the discrepancy. Errors in the local thermodynamic equilibrium (LTE) atomic modeling, errors in the modeling of LEH closure, and errors due to a lack of plasma species mix physics in simulations are shown to be inconsistent with our measurements. Instead, the data support the hypothesis that errors in NLTE emission modeling are a significant contributor to the discrepancy. X-ray emission in the 2–4 keV range is found to be approximately 30% lower than in simulations. This is accompanied by higher than predicted electron temperatures in the gold bubble region, pointing to errors in non-LTE modeling. Introducing an opacity multiplier of 0.87 on energy groups above 1.8 keV improves agreement with experimental data, reducing the bang-time discrepancy from 300 to 100 ps. These results underscore the need for refined NLTE opacity models to enhance the predictive power of hohlraum simulations.

Band emission↗

DOE OSTI2025

Evaluating nonlocal heat transport in directly driven chromium spheres using x-ray spectroscopy

We report on experiments investigating heat transport in laser-generated plasmas using directly driven chromium spheres. The spheres are fielded at the OMEGA laser facility and are driven with laser intensities of 5×10 14 Wcm −2 . Plasma conditions in the corona and scattered light are measured experimentally and compared against predictions from two-dimensional (2D) radiation-hydrodynamic simulations using different heat transport models. Spectroscopic analysis of x-ray self-emission is used as an additional diagnostic. X-ray emission is integrated over a large region of the plasma, probing regions that are not observed by localized optical Thomson scattering. In particular, x-ray emission peaks near the plasma critical density, so emission from optically thin lines provides information on plasma conditions where nonlocal transport is most likely to be significant. Three common heat transport models are considered: local transport with flux limiters f = 0.15 and f = 0.03, and the nonlocal Schurtz–Nicolai–Busquet (SNB) model. Consistent with previous work, both the high-flux (f = 0.15) and SNB models show good agreement with experimentally measured plasma conditions in the corona despite overpredicting laser absorption, whereas the low-flux (f = 0.03) model fails to match any experimental data. Conditions inferred from x-ray self-emission line ratios support this conclusion during the period of laser peak power, although synthetic spectra for all models fail to match the experiment during the transient portions of the pulse. For these reasons, the low-flux model is again rejected.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

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 OSTI2025

Detailed simulations of the first deuterium-tritium-filled double shell implosions on the National Ignition Facility

The first indirectly driven, liquid DT-filled double shell inertial confinement fusion (ICF) implosions have recently been successfully performed on the National Ignition Facility (NIF). Double shells are a class of alternative designs that use a low-Z outer shell to compress a foam cushion that accelerates a high-Z inner shell to efficiently compress a liquid DT core. Double shells are challenging to fabricate, field, and model. Important engineering features enabling double shell fabrication include a fill-tube penetrating all shells and a carefully designed and very narrow (few μm) step-joint in the ablator. Due to the higher density materials involved, high Atwood number instabilities are also important at many material interfaces. In this paper, numerical simulations of double shell implosions using the Los Alamos National Laboratory multi-physics radiation-hydrodynamics code xRAGE will be discussed. An extensive effort has been under way for several years to develop the code capabilities for ICF simulations in a common modeling framework to allow ease of simulation setup and standardization of the computational methodology. This paper will present a wide range of simulation results capturing, quantifying, and comparing the impact of all these degradation mechanisms on implosion performance. Brief comparisons with recent experimental results and suggestions for future improvements will also be discussed. Our results suggest that capsule surface roughness and the step-joint gap have the largest impact on implosion performance. Initial experimental data may suggest that the sensitivity to the step-joint gap could provide the dominant explanation for DT-filled double shell experiments that have been fielded on NIF thus far.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

A platform to measure isentropes from proton-heated warm dense matter on short pulse laser facilities

We describe the development of an experimental platform that measures the release isentrope of materials heated isochorically to temperatures of a few electron volts, using short-pulse laser-produced protons to heat the sample and long-pulse laser-produced x rays to perform streaked x-ray radiography. The density profiles derived from the radiography data are integrated to generate pressure–density isentropes, independent of prior knowledge of the equation of state of the sample material. In order to understand the sensitivities of isentrope extraction from radiography data, we analyze synthetic radiographs generated by a radiation hydrodynamics code. Noise reduction and high spatial resolution are critical for isentrope reconstruction, as demonstrated by the analysis of a proof-of-principle shot day on the OMEGA-EP facility. In conclusion, the data demonstrate the feasibility of the platform for characterizing isentropes, and we discuss the necessary improvements to enhance precision in differentiating between equation-of-state models.

Equations of state↗

DOE OSTI2025

Determining the nanostructure of polymer foams using 3D ptycho-tomography for inertial fusion energy applications

Polymer foams play a critical role in contemporary inertial fusion energy (IFE) target designs by enhancing energy yield and optimizing implosion dynamics. However, the lack of high-resolution characterization of the nanostructure of these foams restricts progress in fusion science. In this work, we demonstrate the first high-resolution three-dimensional (3D) reconstruction of a low-density, Si-doped polymer foam fabricated via two-photon polymerization, using ptychographic x-ray computed tomography (PXCT) at an x-ray free electron laser (XFEL). This imaging method reconstructs two-dimensional (2D) attenuation and phase information at multiple sample angles that are combined into a 3D density map used to extract local mass density and determine structural dimensions. We achieve a 2D spatial resolution of 19 ± 3 nm on a high-contrast Ronchi pattern target and 78.7 ± 3 nm for low-contrast polymer foams, marking a significant advancement for XFEL-based ptychography of low-density materials. Furthermore, our experimental results reveal an average foam strut thickness of 1.17 ± 0.4 μm, consistent with fabrication expectations, and a reconstructed average mass density of 0.35 g/cc, aligning closely with the predicted density of 0.29 g/cc. These findings provide important insights for improving foam design and refining radiation hydrodynamics modeling in future IFE experiments. Our study establishes PXCT at an XFEL as a powerful tool for high-resolution characterization of fusion-relevant materials, paving the way for enhanced target performance in IFE research.

Hancock, Levi [Colorado State Univ., Fort Collins,↗

DOE OSTI2025

Single-shot in-line x-ray phase-contrast imaging of void-shockwave interactions in fusion energy materials

Recent breakthroughs in nuclear fusion, specifically the report of reactions exceeding scientific breakeven at the National Ignition Facility (NIF), highlight the potential of inertial fusion energy (IFE) as a sustainable and virtually limitless energy source. However, further progress in IFE requires characterization of defects in ablator materials and how they affect fuel capsule compression. Voids within the ablator can degrade energy yield, but their impact on the density distribution has primarily been studied through simulations, with limited high-resolution experimental validation. To address this, we used the x-ray free-electron laser (XFEL) at the matter in extreme conditions (MECs) instrument at the Linac coherent light source (LCLS) to capture 2D x-ray phase-contrast (XPC) images of a void-bearing sample with a composition similar to inertial confinement fusion (ICF) ablators. By driving a compressive shockwave through the sample using MEC's long-pulse laser system, we analyzed how voids influence shockwave propagation and density distribution during compression. To quantify this impact, we extracted phase information using two phase retrieval algorithms. First, we applied the contrast transfer function (CTF) method, paired with Tikhonov regularization and a fast optimization approach to generate an initial phase estimate. We then refined the result using a projected gradient descent (PGD) method that works directly with the sample's refractive index. Comparing these results with radiation adaptive grid Eulerian (xRAGE) radiation hydrodynamic simulations enables identification of model validation needs or improvements. By calculating phase maps in situ, it becomes possible to reconstruct areal density maps, improving understanding of laser-capsule interactions and advancing IFE research.

Hodge, D. S. [Colorado State Univ., Fort Collins, ↗

DOE OSTI2025

Laser wavelength dependence of particle acceleration mechanisms in high intensity laser–solid density plasma interactions

We investigate the generation of relativistic electrons and the subsequent ion acceleration due to target-normal sheath acceleration when ultra-intense (⁠ I > 10 18 W/cm 2 ⁠) short pulse (⁠ τ L < 10ps⁠) lasers are incident onto solid density targets as laser wavelength is varied. Scaling laws for the hot electron temperature, T hot ⁠, and the maximum ion energy, E max ⁠, are recast as a function of laser wavelength. These predictions are compared to results from particle-in-cell computer simulations in a variety of geometries, including cases where realistic plasma density profiles as determined by a radiation hydrodynamics code are used. It is found that the wavelength dependence observed in simulation is less pronounced than what is predicted from the well-established scaling laws. An assessment of how switching to longer laser wavelengths, specifically 2 μm Tm:YLF technology, would impact current high energy density science applications and diagnostics is made.

Electromagnetism↗

DOE OSTI2025

X-ray spectroscopy of multi-temperature plasmas using the differential emission measure formalism

We present a theoretical construct that nominally underlies spectroscopic data analysis of multi-temperature plasmas, known as the differential emission measure (DEM). From a data analytic perspective, the DEM formalism is used to derive temperature distributions from line spectra that are formed in the presence of temperature gradients and by time integrations of evolving plasmas. From a modeling perspective, DEMs are convenient intermediaries between radiation hydrodynamics simulations and spectroscopic measurements acquired in the laboratory. The DEM concept and its associated methodologies were originally developed by spectroscopists working with astrophysical data. We borrow from these earlier investigations. In this manuscript, intended primarily as a tutorial, we discuss the basic concepts, but also augment various aspects of the theory by the way of extension and example, including a detailed treatment of various weighting and averaging schemes, intended to mitigate ambiguities that often arise when reporting temperature information. We focus on high-temperature plasmas that are not in local thermodynamic equilibrium and the x-ray spectra that they produce, although the core ideas presented here are applicable to spectroscopy in other energy bands. A few examples involving the derivation and manipulation of model DEMs in simple geometries are provided.

Liedahl, Duane A. [Lawrence Livermore National Lab↗

DOE OSTI2026

Studies of localized mix and asymmetry caused by the stalk in inertial fusion experiments at OMEGA

In an inertially confined fusion experiment, a capsule of fusion fuel is compressed to high temperatures and densities using lasers, creating a hot plasma in which thermonuclear fusion reactions take place. To achieve efficient conversion of laser energy to fuel heating, the implosion must be as spherically symmetric as possible. One common source of asymmetry that degrades performance is the stalk and glue spot that hold the capsule in place before the experiment. The exact nature and magnitude of this perturbation had not been previously quantified. In this work, inertially confined fusion experiments were executed with an additional stalk on the capsule to measure and quantify the effect of the stalk and glue spot on the symmetry and performance. It is found that the stalk drives low-mode asymmetry by shadowing the laser drive on the part of the shell near the glue spot, enhancing the hot-spot velocity toward the stalk by 40–80 km/s and elongating the hot-spot along the stalk axis. It is also found that localized mix due to the additional stalk has a negligible effect on implosion performance. Two-dimensional radiation-hydrodynamic simulations using the xRAGE code reproduce the direction of the experimentally observed change to hot-spot velocity and implosion performance metrics, but not the observed elongation, suggesting that this feature results from an interaction between stalk perturbations and other preexisting asymmetry seeds, such as laser drive asymmetry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Wetted-foam target stability for laser-direct-drive inertial confinement fusion

Using highly resolved three-dimensional radiation-hydrodynamic simulations, the effects of wetted-foam (WF) ablators in direct-drive inertial confinement fusion cryogenic implosions on the OMEGA laser were investigated. The performance of these implosions was compared with that of implosions using targets with solid-plastic ablators. Simulations considering WF ablators as a homogeneous material show no mitigation of the effects of laser imprint, where the absence of this mitigation can be attributed to the use of picket pulses. Heterogeneous random-structure WF ablators introduce large short-wavelength perturbations, which are seeded by WF inhomogeneities. These perturbations exceed the perturbations seeded by the imprint and cause an additional reduction in implosion performance when the average pore size in the WF exceeds ~0.2 μm. Foam-seeded perturbations are expected to be less damaging in more stable high-adiabat (⁠ ≳ 5⁠) implosions. Here, the perturbations introduced by the WF ablators can be substantially reduced by using a foam matrix with a layered structure instead of a random one. Further study of the effects of WFs in ignition designs of the MJ laser energy scale is required in the perspective of future inertial fusion energy mass production.

Igumenshchev, I. V. [University of Rochester, NY (↗

DOE OSTI2026

Robustness of inertial fusion energy relevant implosions to low-mode asymmetries

Inertial confinement fusion implosions for power production need to be robust. Degradation sources need to be understood and considered for an economic power plant. In this work, the impact of low-mode asymmetries on yield is studied using 2D radiation hydrodynamics simulations for inertial fusion energy relevant implosions. First, a high-gain indirectly driven capsule design is developed. This design is subsequently degraded with low-mode drive asymmetries. The results show that yield is constant with increasing amounts of asymmetry until a cliff is reached where the yield quickly drops below ignition. Robustness arises because the degraded hotspot still has enough time to get to ignition before capsule decompression. This robustness occurs even though the asymmetry couples less energy to the hotspot and causes decompression to occur sooner. The robustness is linked to the generalized Lawson parameter, χ⁠. The value of χ steadily decreases with increasing asymmetry. Once χ is close to one, the hotspot is no longer able to ignite before the capsule decompresses. A simple piston model is used to predict where the robustness cliff is for any design. The trade-off between yield and robustness is also demonstrated.

Physics - Plasma physics↗

DOE OSTI2022

Combinatorial sputter deposition of ultrathick Au-Bi alloy films

We report gold-bismuth alloys are of interest as catalysts and catalytic sensing systems, electrochemical sensors, superconductors, and hohlraums for magnetically assisted inertial confinement fusion implosions. Radiation-hydrodynamics simulations with the Lasnex code of laser-driven hohlraums predict higher x-ray drive from Au-Bi alloys compared with cases of Au-Ta or pure Au and Bi hohlraums. Here, we use direct current magnetron sputtering in Ar gas, with co-sputtering from two elemental targets, to deposit Au-Bi alloys with Bi content of 9–77 at.% and thicknesses up to ~20 µm. Films are characterized by a combination of x-ray diffraction, Rutherford backscattering, scanning electron microscopy, substrate-curvature-based residual stress, and electronic transport measurements. Experiments are complemented by Monte Carlo simulations of ballistic sputtering and gas phase transport of depositing species and Ar gas atoms. Results show that all films are polycrystalline, with three distinct compositional regimes dominated by Au, Au 2 Bi, and Bi crystallographic phases. A metallic behavior of the temperature dependence of electrical resistivity is observed for all the films. Films with Bi content above ~30 at.% exhibit porosity, which is tolerable to hohlraum x-ray drive based on Lasnex simulations.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Simulation studies of the interaction of laser radiation with additively manufactured foams

The interaction of laser radiation with foams of various porosities and low densities has been the subject of several numerical and experimental studies. In all cases, the modeling of low-Z under-dense foams as uniform gases of equivalent average density using standard radiation-hydrodynamics codes has resulted in heat-front velocities that are considerably faster than those observed experimentally. It has been theoretically conjectured that this difference may be attributed to the breakdown of the foam’s morphology, leading to a dynamics of filament expansion where the ion and electron energy partitions are significantly different from those calculated using the uniform gas model. We found that 3D computer simulations employing a disconnected representation of the foam’s microstructure which allowed for the dynamics of foam element heating, expansion, and stagnation largely supported the theoretical picture. Simulations using this model for laser experiments on under-dense 2 mg cc -1 SiO 2 aerogel foams reproduced the experimental data fairly well. We used the validated model in simulations of low-density structured foam-like materials (produced via additive manufacturing) with a variety of morphologies. We found that the log-pile configurations were consistent with the analytical propagation model of Gus’kov et al. Further validation of the model was obtained by simulating experiments performed at the Jupiter Laser Facility using the log-pile and octet-truss foam morphologies. Simulations of the foam-laser interaction using a wave propagation code showed that the microstructure was able to enhance stimulated Brillouin scattering (SBS) by concentrating the light energy into density holes. In turn, this promotes laser filamentation, reducing SBS and bringing the predicted values closer to the experimental data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

3D simulations of inertial confinement fusion implosions part 2: systematic flow anomalies and impact of low modes on performances in OMEGA experiments

We present the first 3D radiation-hydrodynamic simulations of directly driven inertial confinement fusion implosions with an inline package for polarized crossed-beam energy transfer, which were used to assess the impact of the current distributed polarization rotators (DPRs) on OMEGA as well as other known sources of asymmetry. Applied to OMEGA implosions, the simulations predict bang times with no need for ad hoc multipliers, as well as yields—if you separately account for the impacts of imprint and fuel age. The magnitude of the flow is well reproduced when the low mode sources are large, whereas the modeling of the stalk is thought to be required to match the flow magnitude in the remaining cases. For the cases explored in more detail, polarized cross-beam energy transfer (CBET)—the only known systematic drive asymmetry, brought the results closest to the measured flow vectors. The remaining discrepancies are shown to be stemming from the limited knowledge of the laser pointing modes. For typical current levels of beam mispointing, power imbalance, target offset, and asymmetry caused by polarized CBET, low modes degrade the yield by more than 40%. The current strategy of attempting to compensate the mode-1 asymmetry with a preimposed target offset recovers only about one-third of the losses caused by the low modes due to the dynamic nature of the multiple asymmetries and the presence of low modes other than l = 1. Furthermore, addressing the root causes of the drive asymmetries is apt to be more beneficial. To that end, one possible solution to the specific issue of polarized CBET (10 µm DPRs) is shown to work well.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

3D simulations of inertial confinement fusion implosions part 1: inline modeling of polarized cross beam energy transfer and subsequent drive anomalies on OMEGA and NIF

Inertial confinement fusion experiments are sensitive to cross-beam energy transfer (CBET), a laser-plasma instability that redistributes laser energy in the coronal plasma through self-generated ion acoustic wave (IAW) gratings. The detailed CBET coupling depends on the polarization state of the crossing wavefields. CBET itself can also scramble the beam polarizations by inducing ellipticity through the IAW grating, and rotating the seed polarization toward that of the pump. We develop a ray-based model that describes the polarized CBET coupling and that is compatible with the framework of 3D inline radiative hydrodynamics simulations. The model is implemented in the ASTER/IFRIIT code and verified against an academic test case and an offline polarized CBET post-processor. It is then applied to the detailed configuration of the distributed polarization rotator system on OMEGA, where results highlight how polarized CBET induces significant low modes in the collisional absorption source term. Finally, the modeling is applied to a simple indirect-drive configuration, comparing CBET calculations with 96 unpolarized or polarized beams with 24 unpolarized quads. It is shown that these cases produce similar power amplification per cone of beams grouped with similar polar angles. However, the 96 beam geometry itself is found to reduce azimuthal variations in quad power after the interaction and favors beams with larger polar angles within the cones, an effect that is amplified by the polarized CBET. Application of the model to inline calculations of OMEGA implosions are presented in a companion paper.

3D inline modeling↗