The configurations of instruments fielded on an experiment affect the amount of information captured and the quality of subsequent inference. We investigate the problem of optimizing plasma x-ray radiation detectors in a magneto-inertial fusion experiment at Sandia National Laboratories. It is impossible to directly measure properties such as the temperature of the thermonuclear fusion plasma produced in these experiments because of the extreme environment and destructive nature of the experiment. Among other diagnostics, several detectors are placed with significant standoff from the fusion target to capture the x-rays emitted by the fusion plasma, which can be used to infer some of its properties. To optimize the configuration of these detectors, a high-fidelity model (HFM) is used for simulating outputs and a low-fidelity model (LFM) is used for inference. We develop methods based on A- and L-optimality criteria that are efficient to compute while explicitly accounting for the discrepancy between the HFM and the LFM. The method allows us to find detector configurations that perform similarly to or better than the configuration obtained using an existing sampling-based optimization method while decreasing computational time by a factor of 50. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

We report two magnetized liner inertial fusion (MagLIF) experiments that produced record thermonuclear D-D neutron yields of 2.11 & times;10(13 )and 2.33 & times;10(13). These yields are about a factor of two higher than previous MagLIF results. The experiments achieved ion temperatures of 3.0 and 3.3 keV and stagnation pressures of 1.6 and 1.3 Gbar. The inferred Lawson parameters were chi=0.2 and 0.1, which are the largest reported for MagLIF. The performance increase used a high-aspect-ratio beryllium liner with a dielectric coating and modest increases in preheat energy ( similar to 2.2 kJ), peak current (18.5 MA), and axial magnetic field (15 T). Three-dimensional HYDRA simulations are consistent with the measured liner dynamics and fusion outputs. These results indicate a pathway to higher-yield MagLIF designs using coated, high-aspect-ratio liners and improved input parameters. Simulations further suggest that adding an ice fuel layer could increase yield by up to a factor of 2.5 by reducing liner convergence, instability feedthrough, and mix.

Magnetically driven implosions such as in magnetized liner inertial fusion (MagLIF) on the Z accelerator suffer from magneto-Rayleigh–Taylor instabilities (MRTI) that dynamically redistribute liner mass during implosion, limiting fusion fuel compression and confinement, which ultimately degrades performance. Driving the implosion with an initially helical drive field that dynamically shifts the direction of the magnetic field surrounding the liner (i.e., a dynamic screw pinch, DSP) is a method proposed to mitigate MRTI in-flight and improve target performance. In DSPs, the axial drive magnetic field component implodes the liner and diffuses through the shocked, melted liner material into the fuel throughout the implosion. Liners can be designed to enable enough axial magnetic flux to diffuse through the liner material to effectively magnetize the fuel region without the need of an initial axial magnetic field (i.e., from external field coils). We present results from three-dimensional radiation-magnetohydrodynamic simulations of MagLIF implosions employing drive magnetic fields composed of axial and azimuthal components (a helical drive field). These simulated DSP-driven MagLIF targets demonstrate improved fuel conditions and thermonuclear yield compared to a traditional MagLIF target implosion. Synthetic x-ray radiography of the imploding liner material and x-ray emission images of the fuel region at the time of peak neutron yield rate indicate superior implosion morphology for DSP-MagLIF implosions.

Magnetized liner inertial fusion (MagLIF) implosions on the Z accelerator require magnetization of the fuel to reduce thermal conduction losses of energy from the laser-preheated deuterium fusion fuel to the surrounding liner material. While external field coils traditionally used to axially magnetize MagLIF targets are limited to 10–20 T (or perhaps ∼ 30 T with technological development), calculations suggest that higher axial magnetic fields would improve thermal insulation of the fuel and improve MagLIF target performance. We present results from three-dimensional radiation-magnetohydrodynamic simulations of MagLIF implosions employing auto-magnetizing helical liners composed of discrete metallic helical conduction paths separated by electrically insulating material. These simulated auto-magnetizing (AutoMag) liners produce axial magnetic fields >30 T inside the fusion fuel prior to implosion. Simulations indicate that higher thermonuclear yields and burn-averaged fuel ion temperatures are attained for implosions using AutoMag liners compared to standard MagLIF implosions. Comparable implosion morphology is evident in synthetic x-ray images of AutoMag–MagLIF and standard MagLIF implosions.

The Magnetized Liner Inertial Fusion (MagLIF) experimental platform at Sandia National Laboratories has realized a number of recent improvements in electrical current and laser preheat coupling but fusion yields are below expectations, based on modeling with clean (that is, simulations with no interfacial instabilities and no mix) two-dimensional (2D) magneto-hydrodynamics (MHD) simulations, by a factor of 5 or more. However, magnetized liner implosions are known to produce helical magneto-Rayleigh–Taylor (MRT) modes and complex stagnation structures that cannot be directly modeled in 2D. This paper presents the results of 3D HYDRA MHD simulations, including helical MRT, showing that degradation from these instabilities can readily reproduce experimental yields, but it is difficult to simultaneously match the yield along with inferred fuel temperature, pressure, and burn history (assessed with x-rays), which are larger in the experiments considered here. Additional analysis methods and future experiments are proposed to help address the discrepancies. The 3D simulations also show, without substantive improvements to stability, changing the applied Bz or preheat is unlikely to increase performance of MagLIF to the same degree as clean 2D simulations. Finally, the first 3D HYDRA simulations with the Hall term show the ab initio production of helical MRT and produce a clear change in stagnation morphology compared to pre-seeded simulations without Hall. In spite of the differences, the simulations still produce comparable fusion performance but with longer, lower power, neutron yield history.

Magnetized liner inertial fusion (MagLIF) experiments have demonstrated fusion-relevant ion temperatures up to 3.1 keV and thermonuclear production of up to 1.1 × 1013 deuterium–deuterium neutrons. This performance was enabled through platform development that provided increases in applied magnetic field, coupled preheat energy, and drive current. Advanced coil designs with internal reinforcement enabled an increase from 10 to 20 T. An improved laser pulse shape, beam smoothing, and thinner laser entrance foils increased preheat energy coupling from less than 1 to 2.3 kJ. A redesign of the final transmission line and load region increased peak load current from 16 to 20 MA. The wider range of input parameters was leveraged to study target performance trends with preheat energy, applied magnetic field, and peak load current. Ion temperature and neutron yield generally followed trends in two-dimensional clean Lasnex calculations. Stagnation performance improved with peak load current when other input parameters were also increased such that convergence was maintained. This dataset suggests that reducing convergence to less than 30 would improve predictability of target performance. Lasnex was used to identify a simulation-optimized scaling path, which suggests 10+ kJ of fusion yield is possible on the Z facility with achievable input parameters. This path also indicates >10 MJ could be generated through volume burn on a future facility with a path to high yield (>200 MJ) using cryogenic dense fuel layers. The newly developed MagLIF platform enables exploration of both this simulation optimized scaling path and a recently developed similarity-scaling path.

The ability to visualize x-ray and neutron emission from fusion plasmas in 3D is critical to understand the origin of the complex shapes of the plasmas in experiments. Unfortunately, this remains challenging in experiments that study a fusion concept known as Magnetized Liner Inertial Fusion (MagLIF) due to a small number of available diagnostic views. Here, we present a basis function-expansion approach to reconstruct MagLIF stagnation plasmas from a sparse set of x-ray emission images. A set of natural basis functions is “learned” from training volumes containing quasi-helical structures whose projections are qualitatively similar to those observed in experimental images. Tests on several known volumes demonstrate that the learned basis outperforms both a cylindrical harmonic basis and a simple voxel basis with additional regularization, according to several metrics. Two-view reconstructions with the learned basis can estimate emission volumes to within 11% and those with three views recover morphology to a high degree of accuracy. The technique is applied to experimental data, producing the first 3D reconstruction of a MagLIF stagnation column from multiple views, providing additional indications of liner instabilities imprinting onto the emitting plasma.

This article aims at discovering the unknown variables in the system through data analysis. The main idea is to use the time of data collection as a surrogate variable and try to identify the unknown variables by modeling gradual and sudden changes in the data. We use Gaussian process modeling and a sparse representation of the sudden changes to efficiently estimate the large number of parameters in the proposed statistical model. The method is tested on a realistic dataset generated using a one-dimensional implementation of a Magnetized Liner Inertial Fusion (MagLIF) simulation model and encouraging results are obtained.

X-ray imaging indicates magnetized liner inertial fusion (MagLIF) stagnation columns have a complicated quasi-helical structure with significant variations in x-ray brightness along the column. In this work, we describe MagLIF experiments aimed at controlling these stagnation structures by varying the initial liner geometry and composition. First, by varying the initial aspect ratio of the liner, we demonstrate a change in the stagnation structures that is consistent with helical magneto Rayleigh–Taylor (MRT) instabilities feedthrough from the outer-to-inner surfaces of the liner. Second, to minimize the seed for such instabilities, we incorporate a dielectric coating on the outer surface of the beryllium liner, which has previously been shown to reduce the growth of the electrothermal instability, a likely seed for MRT growth. Using this coating, we achieve a stagnation column with significantly reduced helical structure and axial variation in x-ray brightness. We discuss how this coating changes the evolution of structures through stagnation along with the spatial uniformity of neutron production. Finally, we show that these more uniform stagnations also result in improved reproducibility in stagnation temperatures and primary DD neutron yield.

Magnetized Liner Inertial Fusion experiments have been performed at the Z facility at Sandia National Laboratories. These experiments use deuterium fuel, which produces 2.45 MeV neutrons on reaching thermonuclear conditions. To study the spatial structure of neutron production, the one-dimensional imager of neutrons diagnostic was fielded to record axial resolved neutron images. In this diagnostic, neutrons passing through a rolled edge aperture form an image on a CR-39-based solid state nuclear track detector. Here, we present a modified generalized expectation–maximization algorithm to reconstruct an axial neutron emission profile of the stagnated fusion plasma. We validate the approach by comparing the reconstructed neutron emission profile to an x-ray emission profile provided by a time-integrated pinhole camera.

In magnetized liner inertial fusion (MagLIF), a cylindrical liner filled with fusion fuel is imploded with the goal of producing a one-dimensional plasma column at thermonuclear conditions. However, structures attributed to three-dimensional effects are observed in self-emission x-ray images. Despite this, the impact of many experimental inputs on the column morphology has not been characterized. We demonstrate the use of a linear regression analysis to explore correlations between morphology and a wide variety of experimental inputs across 57 MagLIF experiments. Results indicate the possibility of several unexplored effects. For example, we demonstrate that increasing the initial magnetic field correlates with improved stability. Although intuitively expected, this has never been quantitatively assessed in integrated MagLIF experiments. We also demonstrate that azimuthal drive asymmetries resulting from the geometry of the “current return can” appear to measurably impact the morphology. In conjunction with several counterintuitive null results, we expect the observed correlations will encourage further experimental, theoretical, and simulation-based studies. Finally, we note that the method used in this work is general and may be applied to explore not only correlations between input conditions and morphology but also with other experimentally measured quantities.

Accurate constitutive data, such as equations of state and plasma transport coefficients, are necessary for reliable hydrodynamic simulations of plasma systems such as fusion targets, planets, and stars. Here, we develop a framework for automatically generating transport-coefficient tables using a parameterized model that incorporates data from both high-fidelity sources (e.g., density functional theory calculations and reference experiments) and lower-fidelity sources (e.g., average-atom and analytic models). The framework incorporates uncertainties from these multi-fidelity sources, generating ensembles of optimally diverse tables that are suitable for uncertainty quantification of hydrodynamic simulations. We illustrate the utility of the framework with magnetohydrodynamic simulations of magnetically launched flyer plates, which are used to measure material properties in pulsed-power experiments. We explore how changes in the uncertainties assigned to the multi-fidelity data sources propagate to changes in simulation outputs and find that our simulations are most sensitive to uncertainties near the melting transition. The presented framework enables computationally efficient uncertainty quantification that readily incorporates new high-fidelity measurements or calculations and identifies plasma regimes where additional data will have high impact.

We report on a series of Magnetized Liner Inertial Fusion (MagLIF) experiments conducted on the Z pulsed power facility that utilized high aspect ratio (ratio of outer radius to wall thickness) liners with dielectric coatings and low-mix laser preheat configurations. The liners consisted of an aspect ratio of 10.6 beryllium tube coated with 75 μm of epoxy on the outside that have been shown to maintain a better implosion stability than uncoated beryllium and have demonstrated consistent stagnation performances in previous experiments [Ampleford et al., Phys. Plasmas 31, 022703 (2024)]. Two-dimensional HYDRA simulations were used to design three different “co-injection” laser configurations, whereby a second laser is used to provide an early prepulse before the main pulse, to reduce LEH foil mix while increasing the fuel density and coupled energy. The laser preheat energy for each configuration was constrained using dedicated laser experiments before being applied to the integrated MagLIF experiments on Z. The DD neutron yield for experiments using co-injection preheat configurations is found to increase with the specific preheat energy in line with simulations. The highest neutron yield achieved in this study of 1.1 × 1013 matches the highest reported in a MagLIF experiment to date and is a factor 3.5 times higher than similar experiments using preheat with no phase plate smoothing. We attempt to assess the effects of mix and morphology to explain the improved performance; however, neither factor is found to be conclusive within the uncertainty of the measurements.

Bayesian analysis enables flexible and rigorous definition of statistical model assumptions with well-characterized propagation of uncertainties and resulting inferences for single-shot, repeated, or even cross-platform data. This approach has a strong history of application to a variety of problems in physical sciences ranging from inference of particle mass from multi-source high-energy particle data to analysis of black-hole characteristics from gravitational wave observations. The recent adoption of Bayesian statistics for analysis and design of high-energy density physics (HEDP) and inertial confinement fusion (ICF) experiments has provided invaluable gains in expert understanding and experiment performance. In this Review, we discuss the basic theory and practical application of the Bayesian statistics framework. We highlight a variety of studies from the HEDP and ICF literature, demonstrating the power of this technique. Due to the computational complexity of multi-physics models needed to analyze HEDP and ICF experiments, Bayesian inference is often not computationally tractable. Two sections are devoted to a review of statistical approximations, efficient inference algorithms, and data-driven methods, such as deep-learning and dimensionality reduction, which play a significant role in enabling use of the Bayesian framework. We provide additional discussion of various applications of Bayesian and machine learning methods that appear to be sparse in the HEDP and ICF literature constituting possible next steps for the community. We conclude by highlighting community needs, the resolution of which will improve trust in data-driven methods that have proven critical for accelerating the design and discovery cycle in many application areas.

A variety of spherical crystal x-ray imager (SCXI) diagnostics have been developed and fielded on Magnetized Liner Inertial Fusion (MagLIF) experiments at the Sandia National Laboratories Z-facility. These different imaging modalities provide detailed insight into different physical phenomena such as mix of liner material into the hot fuel, cold liner emission, or reduce impact of liner opacity. However, several practical considerations ranging from the lack of a consistent spatial fiducial for registration to different point-spread-functions and tuning crystals or using filters to highlight specific spectral regions make it difficult to develop broadly applicable metrics to compare experiments across our stagnation image database without making significant unverified assumptions. We leverage experimental data for a model-free assessment of sensitivities to instrumentation-based features for any specified image metric. In particular, we utilize a database of historical and recent MagLIF data including $N_{\text{scans}} = 139$ image plate scans gathered across $N_{\text{exp}} = 67$ different experiments to assess the impact of a variety of features in the experimental observations arising from uncertainties in registration as well as discrepancies in signal-to-noise ratio and instrument resolution. We choose a wavelet-based image metric known as the Mallat Scattering Transform for the study and highlight how alternate metric choices could also be studied. In particular, we demonstrate a capability to understand and mitigate the impact of signal-to-noise, image registration, and resolution difference between images. This is achieved by utilizing multiple scans of the same image plate, sampling random translations and rotations, and applying instrument specific point-spread-functions found by ray tracing to high-resolution datasets, augmenting our data in an effectively model-free fashion.

Computational simulation allows scientists to explore, observe, and test physical regimes thought to be unattainable. Validation and uncertainty quantification play crucial roles in extrapolating the use of physics-based models. Bayesian analysis provides a natural framework for incorporating the uncertainties that undeniably exist in computational modeling. However, the ability to perform quality Bayesian and uncertainty analyses is often limited by the computational expense of first-principles physics models. In the absence of a reliable low-fidelity physics model, phenomenological surrogate or machine learned models can be used to mitigate this expense; however, these data-driven models may not adhere to known physics or properties. Furthermore, the interactions of complex physics in high-fidelity codes lead to dependencies between quantities of interest (QoIs) that are difficult to quantify and capture when individual surrogates are used for each observable. Although this is not always problematic, predicting multiple QoIs with a single surrogate preserves valuable insights regarding the correlated behavior of the target observables and maximizes the information gained from available data. A method of constructing a Gaussian Process (GP) that emulates multiple QoIs simultaneously is presented. As an exemplar, we consider Magnetized Liner Inertial Fusion, a fusion concept that relies on the direct compression of magnetized, laser-heated fuel by a metal liner to achieve thermonuclear ignition. Magneto-hydrodynamics (MHD) codes calculate diagnostics to infer the state of the fuel during experiments, which cannot be measured directly. The calibration of these diagnostic metrics is complicated by sparse experimental data and the expense of high-fidelity neutron transport models. The development of an appropriate surrogate raises long-standing issues in modeling and simulation, including calibration, validation, and uncertainty quantification. The performance of the proposed multi-output GP surrogate model, which preserves correlations between QoIs, is compared to the standard single-output GP for a 1D realization of the MagLIF experiment.