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At least 955 records · Page 53

Direct Observation of Ammonia Storage in UiO-66 Incorporating Cu(II) Binding Sites

The presence of active sites in metal–organic framework (MOF) materials can control and affect their performance significantly in adsorption and catalysis. However, revealing the interactions between the substrate and active sites in MOFs at atomic precision remains a challenging task. Here, we report the direct observation of binding of NH 3 in a series of UiO-66 materials containing atomically dispersed defects and open Cu(I) and Cu(II) sites. While all MOFs in this series exhibit similar surface areas (1111–1135 m 2 g –1 ), decoration of the -OH site in UiO-66-defect with Cu(II) results in a 43% enhancement of the isothermal uptake of NH 3 at 273 K and 1.0 bar from 11.8 in UiO-66-defect to 16.9 mmol g –1 in UiO-66-Cu II . A 100% enhancement of dynamic adsorption of NH 3 at a concentration level of 630 ppm from 2.07 mmol g –1 in UiO-66-defect to 4.15 mmol g –1 in UiO-66-Cu II at 298 K is observed. In situ neutron powder diffraction, inelastic neutron scattering, and electron paramagnetic resonance, solid-state nuclear magnetic resonance, and infrared spectroscopies, coupled with modeling reveal that the enhanced NH 3 uptake in UiO-66-Cu II originates from a {Cu(II)···NH 3 } interaction, with a reversible change in geometry at Cu(II) from near-linear to trigonal coordination. This work represents the first example of structural elucidation of NH 3 binding in MOFs containing open metal sites and will inform the design of new efficient MOF sorbents by targeted control of active sites for NH 3 capture and storage.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Outer shell symmetry for double shell capsules with aluminum ablators

Double shell targets are a promising potential avenue to obtain robust neutron yield at current laser facilities. Similar to single shell designs, double shells require the symmetric implosion of an ablator in order to uniformly compress and heat a fuel volume, with the goal of achieving thermonuclear burn. Significant differences between double and single shells include the usage of an aluminum ablator as well as a reverse ramp laser pulse. In addition, double shells require a different convergence than single shells for fuel ignition. Numerical implosion studies at various energies with comparisons to experimental outcomes are required to gain confidence that simulations can capture the ablator shape from subscale to full scale. The current work builds on previous implosion experiments conducted at 1-MJ laser energy to confirm achieved ablator symmetry at 1.25 and 1.5 MJ. Average ablator P2 and P4 shapes measured in these experiments are within 5% of the simulated shape, which merits the platforms for further experimental studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Outer shell symmetry for double shell capsules with aluminum ablators

Double shell targets are a promising potential avenue to obtain robust neutron yield at current laser facilities. Similar to single shell designs, double shells require the symmetric implosion of an ablator in order to uniformly compress and heat a fuel volume, with the goal of achieving thermonuclear burn. Significant differences between double and single shells include the usage of an aluminum ablator as well as a reverse ramp laser pulse. In addition, double shells require a different convergence than single shells for fuel ignition. Numerical implosion studies at various energies with comparisons to experimental outcomes are required to gain confidence that simulations can capture the ablator shape from subscale to full scale. The current work builds on previous implosion experiments conducted at 1-MJ laser energy to con firm achieved ablator symmetry at 1.25 and 1.5 MJ. Average ablator P2 and P4 shapes measured in these experiments are within 5% of the simulated shape, which merits the platforms for further experimental studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Diluted axion star collisions with neutron stars

Diluted axion star, a self-gravitating object with the quantum pressure balancing gravity, has been predicted in many models with a QCD axion or axion-like particle. It can be formed in the early universe and composes a sizable fraction of dark matter. One could detect the transient radio signals when it passes by a magnetar with the axion particle converted into photon in the magnetic field. Using both numerical and semi-analytic approaches, we simulate the axion star's dynamic evolution and estimate the fraction of axion particles that can have a resonance conversion during such a collision event. We have found that both self-gravity and quantum pressure are not important after the diluted axion star enters the Roche radius. A free-fall approximate can capture individual particle trajectories very well. Finally, with some optimistic cosmological and astrophysical assumptions, the QCD axion parameter space can be probed from detecting such a collision event by radio telescopes.

79 ASTRONOMY AND ASTROPHYSICS↗

Part-scale evolution of fine-scale microstructural heterogeneity in solid-state additive manufacturing

Current solid-state additive manufacturing methods, refined through costly and time-consuming trial and error, have spurred interest in computational models that replicate material behavior under typical thermomechanical conditions (e.g., strain-rate ~ 102 s−1). These models, however, struggle to capture time-dependent microstructural evolution. In this work, Additive Friction-Stir Deposition (AFSD) is used as a representative case study for part-scale quantification of microstructure evolution at a fine spatial resolution (200 μm) by examining a liquid-nitrogen-cooled stop-action build via energy-dispersive X-ray diffraction coupled with a multi-channel detector. These results inform modeling efforts by linking process asymmetry to stored plastic strain, residual elastic strain, and texture development, and unlike current state-of-the-art characterization methods (e.g., EBSD or neutron diffraction), this approach provides both the spatial resolution and collection efficiency necessary to quantify fine-scale microstructural heterogeneity over large component volumes. As such, this technique provides essential validation data for computational models, e.g., crystal plasticity, enabling future prediction of heterogeneous behavior in AFSD and other additive manufacturing processes.

Franz, Cole [ORNL] (ORCID:0000000213465881)↗

Viper Science Operations: Science Traverse Planning Perspectives, Processes, and Tools.

Introduction: The NASA Volatiles Investigating Polar Exploration Rover (VIPER) launchesin late 2024 towards a landing site on Mons Mouton in the Nobile region of the Lunar South Pole (LSP). As described in other LPSC presentations [1,2,3], the primary objective of the VIPER mission is to study the composition and distribution of hydrogen-bearing and other volatiles by way of a complementary suite of payloads that the rover will carry to the Moon: three “prospecting” instruments which operate continuously while roving - the Neutron Spectrometer System (NSS), the Near InfraRed Volatiles Spectrometer System (NIRVSS), and the Mass Spectrometer observing lunar operations (MSolo). A 1-meter auguring/percussive drill called the The Regolith and Ice Drill for Exploration of New Terrains (TRIDENT) is used to bring subsurface cuttings to the surface in 10-cm increments where they are interrogated by NIRVSS and MSolo. The Visible Imaging System is comprised of eight cameras (the NavCam stereo pair mounted on the mast gimbal, the AftCam stereo pair mounted on the aft panel, and four HazCams mounted in the wheel wells) that capture grayscale visible wavelength images of the lunar environment and the rover’s upper deck. The VIPER mobility system is a four-wheel design that includes the following motorized modules: Suspension, Steering, and Drive/Propulsion. Wheel odometry and applied torque — combined with position data from rover imagery — can be used to compute assessments of ‘slip and sinkage’. Slope estimates can be computed from stereo rover imagery, as well as pitch and roll data from the IMU (Inertial Measurement Unit) and Star Tracker telemetry.

Darlene Sze Shien Lim↗

Evolution of dislocations during the rapid solidification in additive manufacturing

Materials processed by fusion-based additive manufacturing (AM) typically exhibit relatively high dislocation densities, along with cellular structures and elemental segregation. This representative structural feature significantly influences material performance; however, post-mortem microstructure characterizations of AM materials cannot capture the dynamic evolution of dislocations during the manufacturing process, thereby offering limited mechanism-based guidance for further advancing AM techniques and facilitating the qualification and certification of AM products. In this study, we conduct operando high-energy synchrotron X-ray diffraction experiments on wire-laser directed energy deposition of 316 L stainless steel. Through a unique configuration, our operando synchrotron experiments semi-quantitatively probe the dislocation density in solid phases and their dynamic changes during solidification and subsequent cooling. By integrating this advanced synchrotron technique with multi-physics simulation, in-situ neutron diffraction, and multi-scale electron microscopy characterization, our mechanistic study aims to elucidate the effects of rapid cooling and subsequent thermal cycling on the dislocation generation and evolution.

36 MATERIALS SCIENCE↗

Universal trend of charge radii of even-even Ca–Zn nuclei

Radii of nuclear charge distributions carry information about the strong and electromagnetic forces acting inside the atomic nucleus. Whereas the global behavior of nuclear charge radii is governed by the bulk properties of nuclear matter, their local trends are affected by quantum motion of proton and neutron nuclear constituents. The measured differential charge radii δ$\langle$$r^{2}_{c}$$\rangle$ between neutron numbers N = 28 and N = 40 exhibit a universal pattern as a function of n = N – 28 that is independent of the atomic number. In this work, we analyze this remarkable behavior in even-even nuclei from calcium to zinc using two state-of-the-art theories based on quantified nuclear interactions: the ab initio coupled cluster theory and nuclear density functional theory. Both theories reproduce the smooth rise of differential charge radii and their weak dependence on the atomic number. By considering a large set of isotopic chains, we show that this trend can be captured by just two parameters: the slope and curvature of δ$\langle$$r^{2}_{c}$$\rangle$(n). We demonstrate that these parameters show appreciable model dependence, and the statistical analysis indicates that they are not correlated with any single model property, i.e., they are impacted by both bulk nuclear properties as well as shell structure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Machine Learning to Select Experiments Driven by Fundamental Science and Applications for Targeted Nuclear Data Improvement

This work describes a blueprint for a process that accelerates progress in science by quantitatively answering the following question: What is the optimal combination of fundamental-science and application-driven experiments to maximally reduce pertinent data uncertainties? Answering this question entails solving a high-dimensional and complex optimization problem that is best solved with advanced statistic techniques often classified as machine learning. We apply this process within the framework of nuclear data with the aim to select an experiment combination that will reduce uncertainties in 239 Pu nuclear data for neutron energies between 1 and 600 keV. In this field, fundamental-physics driven data, called differential, look at one nuclear physics observable at a time. They are contrasted to application-driven, integral, data where one or few resulting values inform a broad set of nuclear data across several nuclides and energies. The candidates for integral experiments are criticality measurements that were refined by a genetic algorithm to be maximally sensitive to 239 Pu fission cross sections in the desired energy range. Twenty-three candidate differential experiments were investigated and span multiple nuclear physics observables (e.g., total, capture cross sections) for isotopes appearing in the integral experiments. The optimal combination among these candidate experiments was investigated via generalized least squares fitting, augmented with Gaussian processes to ameliorate statistical irregularities in data, and the D-optimality criterion. The latter evaluates for each pair of candidates the joint reduction in uncertainties of all 12200 nuclear data appearing in the integral experiments compared to the knowledge we have from 168 past experiments, theory, and nuclear data. We chose as differential measurements those that investigate 63 Cu and 239 Pu total cross sections, based on D-optimality rank and feasibility constraints. Two integral (criticality) experiments were selected: An experiment with Al 2 ⁢O 3 and graphite interleaved with Pu and a thick Cu reflector explores 1–30 keV, while we target the 30–600 keV range with an experiment that swaps boron in place of graphite with a different geometry.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Shielding Analysis of a Preclinical Bremsstrahlung X-ray FLASH Radiotherapy System within a Clinical Radiation Therapy Vault

A preclinical radiotherapy system producing FLASH dose rates with 12 MV bremsstrahlung x rays is being developed at Stanford University and SLAC National Accelerator Laboratory. Because of the high expected workload of 6,800 Gy w –1 at the isocenter, an efficient shielding methodology is needed to protect operators and the public while the preclinical system is operated in a radiation therapy vault designed for 6 MV x rays. Here, in this study, an analysis is performed to assess the shielding of the local treatment head and radiation vault using the Monte Carlo code FLUKA and the empirical methodology given in the National Council on Radiation Protection and Measurements Report 151. Two different treatment head shielding designs were created to compare single-layer and multilayer shielding methodologies using high-Z and low-Z materials. The multilayered shielding methodology produced designs with a 17% reduction in neutron fluence leaking from the treatment head compared to the single layered design of the same size, resulting in a decreased effective dose to operators and the public. The conservative assumptions used in the empirical methods can lead to over-shielding when treatment heads use polyethylene or multilayered shielding. High-Z/Low-Z multilayered shielding optimized via Monte Carlo is shown to be effective in the case of treatment head shielding and provide more effective shielding design for external beam radiotherapy systems that use 12 MV bremsstrahlung photons. Modifications to empirical methods used in the assessment of MV radiotherapy systems may be warranted to capture the effects of polyethylene in treatment head shielding.

61 RADIATION PROTECTION AND DOSIMETRY↗

Progress Towards NQA-1 for Cardinal in FY25

Cardinal is a wrapping of the GPU-oriented spectral element Computational Fluid Dynamics (CFD) code NekRS and the Monte Carlo particle transport code OpenMC within the Multiphysics Object-Oriented Simulation Environment (MOOSE). Cardinal provides high-resolution thermal-hydraulics and/or radiation transport feedback to MOOSE multiphysics simulations. Multiphysics feedback is implemented in a geometry-agnostic manner which eliminates the need for rigid one-to-one mappings. A generic data transfer implementation also allows NekRS and OpenMC to couple to any MOOSE application, enabling a broad set of multiphysics capabilities. Cardinal simulations can also leverage combinations of MPI, OpenMP, and GPU resources. Cardinal continuous development and improvement efforts have led to the software being considered as a high-fidelity design and licensing tool for key areas of nuclear reactor relevant physics, including neutron transport, fluid flow, heat transfer, and mechanical processes. The fast development and expansion of the software from a pure R&D framework towards its application in the nuclear industry and regulation require a focus on developing, enhancing,and maintaining Cardinal’s software quality through strict adherence to a Software Quality Assurance (SQA) framework and SQA program. To facilitate compliance with SQA standards, the Cardinal SQA Program was initiated during Fiscal Year 2023 (FY23). During the development of the Cardinal SQA Program, multiple gaps have been identified. These gaps are primarily related to model verification and code pedigree as they relate to the use of Cardinal as an analysis tool. These gaps were captured in a report published in 2023. A second report highlighted the progress made during Fiscal Year 2024 (FY24) and described Argonne’s effort to document and integrate software verification within Cardinal’s software development process. This report documents the progress made towards NQA-1 for Cardinal in the Fiscal Year 2025 (FY25). All cases in the expanded Continuous Integration (CI) suite of NekRS are included in this report which test the solvers and modules available in NekRS exhaustively. The NekRS tests are integrated with the Cardinal CI suite and made available in publicly accessible Github documentation. Following the CI practice permits integrating of source code changes frequently and ensuring that the integrated codebase clears the verification testing for the software. Also in this report is a brief overview of the development of the Cardinal Software Quality Assurance Plan (SQAP) that was done in FY25, though it should be noted that the rest of the documentation for the SQA program needs to be developed in a future step of this task.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Tunable chiral and nematic states in the triple-Q antiferromagnet Co 1/3 TaS 2

Complex spin configurations in magnetic materials, ranging from collinear single-Q to non-coplanar multi-Q states, exhibit rich symmetry and chiral properties. However, their detailed characterization is often hindered by the limited spatial resolution of neutron diffraction techniques. Here we employ magnetic circular dichroism and magnetic linear dichroism to investigate the triangular lattice antiferromagnet Co 1/3 TaS 2 , revealing three-state (Z 3 ) nematicity and also spin chirality across its multi-Q magnetic phases. At intermediate temperatures, the presence of linear dichroism identifies nematicity arising from a single-Q stripe phase, while at high magnetic fields and low temperatures, a phase characterized solely by circular dichroism emerges, signifying a purely chiral non-coplanar triple-Q state. Notably, at low temperatures and small fields, we discover a unique phase where both chirality and nematicity coexist. A theoretical analysis based on a continuous multi-Q manifold captures the emergence of these distinct magnetic phases, as a result of the interplay between four-spin interactions and weak magnetic anisotropy. Additionally, both circular and linear dichroism microscopy spatially resolves the chiral and nematic domains. Our findings establish Co 1/3 TaS 2 as a rare platform hosting diverse multi-Q states with distinct combinations of spin chirality and nematicity while demonstrating the effectiveness of polarized optical techniques in characterizing complex magnetic textures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Anisotropic magnetic excitations of a frustrated bilinear-biquadratic spin model: Implications for spin waves of detwinned iron pnictides

Elucidating the nature of spin excitations is important to understanding the mechanism of superconductivity in the iron pnictides. Motivated by recent inelastic neutron scattering measurements in the nearly 100% detwinned BaFe 2 As 2 , we study the spin dynamics of an $\textit{S}$ = 1 frustrated bilinear-biquadratic Heisenberg model in the antiferromagnetic phase with wave vector (π, 0). The biquadratic interactions are treated in a dynamical way using a flavor-wave theory in an $\textit{SU}$(3) representation. Besides the dipolar spin wave (magnon) excitations, the biquadratic interactions give rise to quadrupolar excitations at high energies. In this work, we find that the quadrupolar wave significantly influences, in an energy dependent way, the anisotropy between the spin excitation spectra along the (π, 0) and (0, π) directions in the wave vector space. Our theoretical results capture the essential behavior of the spin dynamics measured in the antiferromagnetic phase of the detwinned BaFe 2 As 2 . More generally, our results underscore the importance of electron correlation effects for the microscopic physics of the iron pnictides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Unraveling higher-order contributions to spin excitations probed using resonant inelastic x-ray scattering

Resonant inelastic x-ray scattering (RIXS) is an evolving tool for investigating the spin dynamics of strongly correlated materials, which complements inelastic neutron scattering. In isotropic spin-$\frac{1}{2}$ Heisenberg antiferromagnetic (HAFM) spin chains, both techniques have observed non-spin-conserving (NSC) excitations confined to the two-spinon phase space. However, a recent O K-edge RIXS study of the one-dimensional HAFM Sr 2 CuO 3 observed spin-conserving (SC) four-spinon excitations outside the two-spinon phase space. Here, we demonstrate that analogous four-spinon excitations can also be accessed at the Cu L 3 edge in the related material SrCuO 2 . Through detailed modeling, we establish that these excitations appear in both the SC and NSC channels of the Cu L 3 edge, and are only captured by higher-order terms in the ultrashort core-hole lifetime expansion. Finally, since these terms encode information about spin-spin correlations extending beyond nearest neighbors, our results offer different possibilities for studying nonlocal spin correlations in quantum magnets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Software Quality Assurance for the MOOSE-Based Open-Source Multiphysics Code Cardinal - An Expanded CI Testing Suite

Cardinal is a wrapping of the GPU-oriented spectral element Computational Fluid Dynamics (CFD) code NekRS and the Monte Carlo particle transport code OpenMC within the Multiphysics Object-Oriented Simulation Environment (MOOSE). Cardinal provides high-resolution thermal-hydraulics and/or radiation transport feedback to MOOSE multiphysics simulations. Multiphysics feedback is implemented in a geometry-agnostic manner which eliminates the need for rigid one-to-one mappings. A generic data transfer implementation also allows NekRS and OpenMC to couple to any MOOSE application, enabling a broad set of multiphysics capabilities. Cardinal simulations can also leverage combinations of MPI, OpenMP, and GPU resources. Cardinal continuous development and improvement efforts have led to the software being considered as a high-fidelity design and licensing tool for key areas of nuclear reactor relevant physics, including neutron transport, fluid flow, heat transfer, and mechanical processes. The fast development and expansion of the software from a pure R&D framework towards its application in the nuclear industry and regulation require a focus on developing, enhancing and, maintaining Cardinal’s software quality through strict adherence to a Software Quality Assurance (SQA) framework and SQA program. To facilitate compliance with SQA standards, the Cardinal SQA Program has been initiated during Fiscal Year 2023 (FY23). During the development of the Cardinal SQA Program, multiple gaps have been identified. These gaps are primarily related to model verification and code pedigree as they relate to the use of Cardinal as a safety analysis tool. These gaps have been captured in a report published in 2023. A second report highlighted the progress made during Fiscal Year 2024 (FY24) and described Argonne’s effort to document and integrate software verification within Cardinal’s software development process. This report documents a snapshot of the verification test cases currently available for Cardinal and NekRS in their assimilation into a Continuous Integration (CI) platform. Following the CI practice permits the integrating of source code changes frequently and ensuring that the integrated codebase clears the verification testing for the software. It should be noted that the SQA program itself, including the program plans, procedures, configuration management, and testing strategies, need to be developed in a future step of this task.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Characterization of a CMOS camera based film digitization platform for gated x-ray imaging diagnostics at the National Ignition Facility

Hardened gated x-ray detectors use photographic film as the data recording medium due to its low sensitivity to the high-yield neutron environments at the National Ignition Facility (NIF). The photographic film is digitized with a Photometric Data Systems (PDS) microdensitometer, which measures the film’s optical density. The PDS scanner is able to measure a dynamic range of 0–5 OD; however, raster scanning the film is time consuming and maintenance of the instrument is challenging due to legacy technology. Since film usage at NIF is expected to continue in the foreseeable future, a digitization platform that is faster and more maintainable would benefit the NIF’s current and future operations. Here, this work presents the characterization of the digital transitions (DT) atom, a CMOS camera-based digitization platform that records film data in a single image capture very quickly and has widely available user support. The preliminary results suggest that the DT atom is able to reconstruct exposures accurately enough to be a competitive alternative to the PDS Scanner.

47 OTHER INSTRUMENTATION↗

Chemical Framework to Design Linear-like Relaxors toward Capacitive Energy Storage

ABO 3 -type perovskite relaxor ferroelectrics (RFEs) have emerged as the preferred option for dielectric capacitive energy storage. However, the compositional design of RFEs with high energy density and efficiency poses significant challenges owing to the vast compositional space and the absence of general rules. Here, we present an atomic-level chemical framework that captures inherent characteristics in terms of radius and ferroelectric activity of ions. By categorizing A/B-site ions as host framework, rattling, ferroelectrically active, and blocking ions and assembling these four types of ions with specific criteria, linear-like relaxors with weak locally correlated and highly extendable unit-cell polarization vectors can be constructed. As example, we demonstrate two new compositions of Bi 0.5 K 0.5 TiO 3- based and BaTiO 3- based relaxors, showing extremely high recoverable energy densities of 17.3 and 12.1 J cm –3 , respectively, both with a high efficiency of about 90%. Further, the role of different types of ions in forming heterogeneous polar structures is identified through element-specific local structure analysis using neutron total scattering combined with reverse Monte Carlo modeling. Further, our work not only opens up new avenues toward rational compositional design of high energy storage performance lead-free RFEs but also sheds light on atomic-level manipulation of functional properties in compositionally complex ferroelectrics.

25 ENERGY STORAGE↗

Understanding asymmetries using integrated simulations of capsule implosions in low gas-fill hohlraums at the National Ignition Facility

Current capsule implosions at the National Ignition Facility (NIF) using high-density-carbon ablators and laser energies close to 2 MJ have shown neutron yields in excess of 50 kJ. Improving on this performance requires understanding of the different degradation mechanisms. For many NIF implosions, nuclear diagnostic signatures have inferred residual hot-spot velocities that correlate with fuel areal density variations consistent with a low-order mode-1 asymmetry. A current working hypothesis attributes these asymmetries to a combination of beam to beam variations in the laser delivery and possibly coupling to target features, such as the diagnostic holes needed for x-ray imaging. Recently, a new source has been identified, thickness variation in the ablator shell. To gain better understanding and eventually mitigate the causes of <ρR> asymmetries, 3D integrated simulations using the actual delivered laser powers are needed. To capture the effect of the diagnostic holes (DHs) using direct numerical simulation would require significantly large computational resources. Instead, our 3D simulations make use of a subgrid model developed using highly-resolved 2D simulations that include several details of the DH engineering complexity. Simulations of NIF shots using hohlraums without DHs, to isolate the effect of beam-to-beam variations, reproduce fairly well the observed nuclear diagnostic signatures. Similarly, reasonable agreement between data and simulations is also obtained in the presence of diagnostic holes. To account for the remaining discrepancies a sensitivity study of ablator thickness variation showed that 1% thickness asymmetries are comparable in effect to 1% peak drive mode-1 asymmetries. Furthermore, this study identified sensitivity to variations in the imbedded doped layer (needed to shield the DT ice from the high energy x-rays generated in the hohlraum) thickness even when the inner and outer surface of the ablator are perfectly spherical.

radiation hydrodynamics↗