Shapes of objects in images are often complex, high-dimensional, and vary in ways not captured by standard Euclidean geometry and statistics. Statistical shape analysis encompasses methods for flexible and interpretable measurement of intrinsic shape and shape variability in geometric objects. Elastic Shape Analysis (ESA) is one such method that measures shape differences between objects, represented by contours, in a way that is invariant to rotation, scale, translation, and parameterization. Although ESA is useful for quantifying shape of objects in many image applications, formal methods for statistical inference in image-based ESA remain limited. This work introduces a hypothesis test procedure based on empirical confidence intervals for the elastic shape distance (ESD) between a proposed underlying true shape and an estimated shape. The confidence intervals are created using a bootstrap procedure for non-smooth functionals, which accounts for the non-differentiability of the ESD. The effectiveness of the method is illustrated through both numerical studies and real world image examples from inertial confinement fusion (ICF).

The Nuclear Imaging System at the National Ignition Facility (NIF) collects primary and downscattered neutron, x-ray, and gamma-ray images of inertial confinement fusion implosions. Penumbral and pinhole-projection images are recorded using scintillators coupled to fast-gated intensified cameras. Successful reconstruction relies on accurate characterization of the imaging system sensitivity, which can vary by up to a factor of 2 across the field of view. Historically, this has been accomplished by using NIF shots without the aperture to uniformly illuminate the detector, or to project onto it a grid pattern from a fiducial plate to correct for detector sensitivity and optical system aberrations, respectively. However, frequent changes to the imaging system due to equipment failures or vibrations within the building have increased the need for calibrations, which are limited in availability to approximately once per year because they require sacrificing imaging data on a neutron-producing shot. We present development work on an optical calibration system that will enable the collection of this data without that requirement promptly, easily, and at regular intervals.

the remaining ablator and potential contamination of the hot spot—a powerful diagnostic window into the capsule assembly during burn.

Neutron time-of-flight (nTOF) detectors are crucial in diagnosing the performance of inertial confinement fusion (ICF) experiments, which implode targets of deuterium–tritium fuel to achieve thermonuclear conditions. These detectors utilize the fusion neutron energy spectrum to extract key measurements, including the hotspot ion temperature and fuel areal density. Previous work [Danly et al., Rev. Sci. Instrum. 94, 043502 (2023)] has demonstrated adding 1D spatial resolution to an nTOF-like detector using a neutron aperture and streak camera to measure the ion temperature profile of an ICF implosion. By contrast, the study presented herein explores modifying the 1D detector to use a fast photomultiplier tube (PMT) to validate the design of a 2D spatially resolved instrument based on reconstruction from 1D profiles. The modification would collect time-of-flight traces from separate scintillators in an imaging array with one PMT using optical fibers of varying lengths to time-multiplex the signals. This technique has been demonstrated in ride-along experiments on the OMEGA laser with 20 fiber-coupled scintillator channels connected to a Photek PMT210. Results provide constraints on the fiber lengths and PMT gating requirements to promote pulse fidelity throughout all channels. Calibration of the detector to fixed nTOFs can provide a preliminary estimate of the instrument response function (IRF), although measurement of the IRF is currently under way. These results suggest that nTOF signals can potentially be time-multiplexed with fibers so long as the design is strategic to mitigate signal-to-noise reduction, modal dispersion, and charge build-up in the PMT, which has implications beyond ion temperature imaging.

An indirect -drive inertial fusion experiment on the National Ignition Facility was driven using 2.05 MJ of laser light at a wavelength of 351 nm and produced 3.1 +/- 0.16 MJ of total fusion yield, producing a target gain G = 1.5 +/- 0.1 exceeding unity for the first time in a laboratory experiment [Phys. Rev. E 109, 025204 (2024)]. Herein we describe the experimental evidence for the increased drive on the capsule using additional laser energy and control over known degradation mechanisms, which are critical to achieving high performance. Improved fuel compression relative to previous megajoule-yield experiments is observed. Novel signatures of the ignition and burn propagation to high yield can now be studied in the laboratory for the first time.

Neutron imaging systems are important diagnostic tools for characterizing the physics of inertial confinement fusion reactions at the National Ignition Facility (NIF). In particular, neutron images give diagnostic information on the size, symmetry, and shape of the fusion hot spot and surrounding cold fuel. Images are formed via collection of neutron flux from the source using a system of aperture arrays and scintillator-based detectors. Currently, reconstruction of fusion source geometry from the collected neutron images is accomplished by solving a computationally intensive maximum likelihood estimation problem via expectation maximization. In contrast, it is often useful to have simple representations of the overall source geometry that can be computed quickly. In this work, we develop convolutional neural networks (CNNs) to reconstruct the outer contours of simple source geometries. We compare the performance of the CNN for penumbral and pinhole data and provide experimental demonstrations of our methods on both non-noisy and noisy data.

On December 5, 2022, an indirect drive fusion implosion on the National Ignition Facility (NIF) achieved a target gain G_{target} of 1.5. This is the first laboratory demonstration of exceeding "scientific breakeven" (or G_{target}>1) where 2.05 MJ of 351 nm laser light produced 3.1 MJ of total fusion yield, a result which significantly exceeds the Lawson criterion for fusion ignition as reported in a previous NIF implosion [H. Abu-Shawareb et al. (Indirect Drive ICF Collaboration), Phys. Rev. Lett. 129, 075001 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.075001]. This achievement is the culmination of more than five decades of research and gives proof that laboratory fusion, based on fundamental physics principles, is possible. This Letter reports on the target, laser, design, and experimental advancements that led to this result.

The nuclear imaging system has been capturing neutron images of inertial confinement fusion (ICF) driven implosions for over a decade at the National Ignition Facility. This imaging system has evolved from one to three nearly orthogonal lines-of-sight, allowing for the study of three-dimensional shape characteristics of ignition shots. Limited-view tomography algorithms help visualize the burning hotspot in 3D and assess neutron source geometry using Legendre mode parameters. With its neutron, gamma-ray, and x-ray image reconstruction capabilities, NIS has provided critical insight into mechanisms that have limited implosion performance, such as fill tube diameter for ignition-type targets. This comprehensive diagnostic suite opens a window into the shape characteristics of ignition shots and how symmetry affects ICF implosion performance. In more recent ignition shots, neutron yields have visibly increased. Analyzing the shape and size of the reconstructed neutron source has shown an expansion of the burn volume, which is indicative of more efficient alpha heating during the implosion process.

The nuclear imaging system at the National Ignition Facility (NIF) is a crucial diagnostic for determining the geometry of inertial confinement fusion implosions. The geometry is reconstructed from a neutron aperture image via a set of reconstruction algorithms using an iterative Bayesian inference approach. An important step in these reconstruction algorithms is finding the fusion source location within the camera field-of-view. Currently, source localization is achieved via an iterative optimization algorithm. In this paper, we introduce a machine learning approach for source localization. Specifically, we train a convolutional neural network to predict source locations given a neutron aperture image. We show that this approach decreases computation time by several orders of magnitude compared to the current optimization-based source localization while achieving similar accuracy on both synthetic data and a collection of recent NIF deuterium-tritium shots.

We have recently demonstrated significant improvements to the resolution and sensitivity of the NIF gamma imaging system by replacing the existing EJ262 plastic scintillator with the Ce-doped gadolinium garnet transparent ceramic scintillator GYGAG. Penumbral imaging of inelastic gammas emitted during inertial confinement fusion (ICF) experiments at NIF can be used to recover the time integrated spatial distribution of the remaining shell during the fusion burn, the technique is therefore a critical diagnostic for understanding the failure modes and quality of NIF implosions. In this work we discuss GEANT4 calculations of the relative sensitivities of GYGAG and EJ262 as well as rolled edge measurements made on NIF shot N221204 in December 2022, for the purpose of directly comparing the spatial resolution of each scintillator in-situ.

While nuclear fusion ignition has been achieved at the National Ignition Facility in inertial confinement fusion (ICF) experiments, obtaining higher gain and more efficient burn is still desired. In that regard, increasing the compression of the fuel is an important factor. In recent indirect-drive capsule implosions, the SQ-n campaign is testing the hypothesis that reducing the hydrodynamic growth of perturbations is key to achieving higher compression of high-density carbon based-ablators for ICF. SQ-n uses a design at lower adiabat with a ramped foot laser pulse shape to minimize early-time hydrodynamic instability growth, predicted to be reduced by a factor of 10, and an optimized ablator dopant distribution. Subsets of experiments were conducted within the SQ-n campaign to study the implosion symmetry, laser backscatter, stability, and compression. Only the latter two will be reviewed here. Shock timing experiments using the velocity interferometer system for any reflector diagnostic enabled the development of a gently accelerating shock velocity. The ice–ablator interface acceleration, important for managing the Richtmyer–Meshkov phase growth, was observed with refraction enhanced radiography and the ablation front growth was measured using radiography of pre-imposed modulations. Finally, layered tritium-hydrogen-deuterium (∼75% H, ∼25% T, ∼2–10% D) and deuterium–tritium implosions demonstrate that between 15% ± 3% and 30% ± 6% improved compression has been achieved.

and testing of the model, a discussion of the test results, recommendations for future field programs, a discussion of the model's limitations, and a recommended procedure to be followed in subsequent ELSTAR applications. A companion report, User's Guide to the ELSTAR Photochemical Air Quality Simulation Model, is available to provide user instruction for running the ELSTAR computer program.

This manuscript examines the correlations between the hot-spot velocity (an observable signature of residual kinetic energy), low-mode implosion asymmetries, and burn amplification in inertial confinement fusion implosions on the National Ignition Facility (NIF). Using a combination of two-dimensional axis-symmetric and three-dimensional radiation-hydrodynamic simulations coupled to neutronics, we find that for typical NIF implosions, the stagnation asymmetry multiplies the observed hot-spot velocity anywhere from 80% to 120%, while burn amplification always increases it. Additionally, we find stagnation asymmetry typically deflects the observed hot-spot flow. The two mechanisms (low-mode implosion asymmetries and burn amplification) can be decoupled, and application of a simple model to a database of cryogenic implosions on the NIF infers the total hot-spot velocity amplification. This finding modifies the interpretation of data collected from inertial confinement fusion experiments and impacts the magnitude and origin of low-mode asymmetries.

Modern experiments in laser-driven inertial confinement fusion (ICF) are susceptible to contamination of the central hotspot by high-Z material during compression that impedes thermonuclear burn. Hotspot mix can be quantified using the ion temperature distribution of the implosion given the predicted deviation between the plasma and contaminant1. but current neutron time-of-flight (nToF) diagnostics can only measure the spatially integrated temperature. This project probes the feasibility of using time multiplexed optical fibers to record nToF spectra from segmented thin scintillators, which could be used to collect a spatially resolved temperature measurement on a single photomultiplier tube (PMT). A prototype detector was constructed in which 20 optical fibers of increasing length were coupled to an EJ-262 plastic scintillator at one end and a Photek PMT210 at the other. The detector was tested on the OMEGA laser and an nToF pulse was successfully measured through all 20 channels at the expected time separations, though direct interactions of fusion products with the PMT interfered with the first 5 channels. Design methodology, material selection, experimental results, and preliminary data analysis are discussed. Next steps will be aimed at applying this technique to previous work demonstrating a 1D spatially resolved ion temperature imager on OMEGA 2 ,3 to evaluate the feasibility of 2D ion temperature imaging at NIF with a cost-efficient detector.

The performance of modern laser-driven inertial confinement fusion (ICF) experiments is degraded by contamination of the deuterium-tritium (DT) fuel with high-Z material during compression. Simulations suggest that this mix can be described by the ion temperature distribution of the implosion, given that such contaminants deviate in temperature from the surrounding DT plasma. However, existing neutron time-of-flight (nTOF) diagnostics only measure the spatially integrated ion temperature. This paper describes the techniques and forward modeling used to develop a novel diagnostic imaging system to measure the spatially resolved ion temperature of an ICF implosion for the first time. The technique combines methods in neutron imaging and nTOF diagnostics to measure the ion temperature along one spatial dimension at yields currently achievable on the OMEGA laser. A detailed forward model of the source and imaging system was developed to guide instrument design. The model leverages neutron imaging reconstruction algorithms, radiation hydrodynamics and Monte Carlo simulations, optical ray tracing, and more. The results of the forward model agree with the data collected on OMEGA using the completed diagnostic. The analysis of the experimental data is still ongoing and will be discussed in a separate publication.

challenging due to the complex environment of the NIF target chamber. The collector surface is first exposed to a large photon flux, followed by the debris wind that is produced. The material used in the catcher must be mechanically strong in order to withstand the large amount of energy it is exposed to, as well as be chemically compatible with the form and composition of the debris. In addition, the location of the catcher is equally important. If it is positioned too close to the center of the target chamber, it will be significantly ablated, which could interfere with the ability of the debris to reach the surface and stick. If it is too far away, the fraction of the debris cloud collected will be too small to result in a statistically significant measurement. Material, geometric configuration, and location must all be tested in order to design the optimal debris collection system for NIF. One of the first ideas regarding solid debris collection at NIF was to use the disposable debris shields (DDS), which are fielded over the final optics assemblies (FOA) 7 m away from the center of the target chamber. The DDS are meant to be replaced after a certain number of shots, and if the shields could be subsequently analyzed after removal, it would serve as a mechanism for fielding a relatively large collection area through the use of a part meant to be replaced regularly. The solid angle covered by one of the shields is roughly 10{sup -4} of 4{pi}. If several shields were analyzed at once, it would increase the solid angle of the collection area accordingly. The glass shields consist of ammonia hardened silica with a sol gel coating and kapton tape around the edge. The square sheets are 14-inch on each side. The original shields were 1 mm thick, but it was determined that a thicker shield (3.3 mm) was more effective in preventing debris from reaching the FOA. The Solid Radchem group received two sets of DDS as part of our evaluation of the potential use of the DDS as solid debris collectors. The first set consisted of two 3.3 mm shields, one each from the top and bottom of the chamber (the '3mm set'). The second set consisted of four 1mm shields, one from the top of the chamber and the other three from the bottom (the 'IFSA set'). For each set, the shields were cut into smaller subsamples, which were then imaged using scanning electron microscopy (SEM) followed by chemical leaching and mass spectrometry. The purpose was to evaluate both the quantity and identity of the debris that was present on the DDS surfaces, and to determine if any of the capsule debris was reaching the chamber walls. In addition, potential enhancement due to gravity in the chamber was evaluated by directly comparing shields fielded in the top and bottom of the chamber. Based on the results, the use of the DDS as debris collectors would be evaluated. The results from both sets were presented to the DDS Working Group. The slides are attached to this document. The 3mm set results are presented first, followed by the results from the IFSA set. In both cases it was determined that a small fraction of the overall debris field was collected on the DDS. This means that the debris that is formed during a NIF shot is condensing out of the plasma and depositing on surfaces closer to the target chamber center, or else it is simply falling to the bottom of the chamber. In either case, it was determined that using the DDS, or fielding a debris collector at the chamber wall, was not feasible for solid debris collection at NIF due to the small amount of debris that had been collected. In addition, since the glass shields suffered quite a bit of damage from particles impacting the surface, glass was ruled out as a collection medium.