Reliable, secure access to energy is a major focus for national security efforts. One potential route to such energy is through fusion reactions in inertial confinement fusion (ICF) experiments. Such experiments are carried out at facilities such as the National Ignition Facility (NIF) in Livermore, California, where high powered lasers are used to compress a DT fuel-containing target to the necessary high temperature, high pressure conditions. These experiments are limited in number, which creates a heavy dependence on high fidelity predictive physics simulations and analysis performed “pre shot,” or before the experiment occurs. Many of these simulations in higher dimensions (2D and 3D) are computationally expensive, so finding optimal simulation-based designs presents its own challenges. In this work, we present our multi-fidelity Bayesian optimization with Gaussian processes (GPs) for ICF double shell targets, where a 1D surrogate model is used to help find a 2D surrogate model, enabling us to find optimal targets in the higher fidelity (2D), while saving computational cost.

Double shell targets are an alternative ignition platform for inertial confinement fusion. One design consideration for double shell targets is the choice of inner shell material to help trap radiation emitted by the hot fuel to aid ignition. Materials such as molybdenum and tungsten are of interest for the inner shell layer of the targets. While molybdenum has a lower density that could inhibit instability growth and allow for radiography and code benchmarking, tungsten has a higher density that could provide more compression and confinement. These tradeoffs have been explored using optimized designs for each material. Our previous work [Vazirani et al., “Coupling 1D xRAGE simulations with machine learning for graded inner shell design optimization in double shell capsules,” Phys. Plasmas 28, 122709 (2021); Vazirani et al., “Coupling multi-fidelity xRAGE with machine learning for graded inner shell design optimization in double shell capsules,” Phys. Plasmas 30, 062704 (2023); and Vazirani et al., “Bayesian batch optimization for molybdenum versus tungsten inertial confinement fusion double shell target design,” Stat. Anal. Data Min. 17, e11698 (2024)] resulted in a multi-fidelity Bayesian optimization framework to find yield-optimized double shell target geometries. By leveraging simulations of varying fidelities (one-dimensional and two-dimensional) to inform one another, the multi-fidelity optimization was able to optimize a design in the highest fidelity with significantly fewer simulations than would be used in a systematic parameter scan. In this work, we apply the multi-fidelity Bayesian optimization to explore the optimized designs of double shell targets with molybdenum and tungsten inner shells as well as the physics producing the high performing implosions. A physics exploration of all the simulations used in this study shows trends in designs that contribute to high yields, ion temperatures, and fuel areal densities. Comparison of molybdenum and tungsten simulations shows that they can produce similar implosion conditions with different geometries, which would be important to study in experiments. Graded density layers produce varying performances with the two materials but continue to be of interest for future studies along with studies of doped inner shell materials and applied surface roughness.

This work provides a numerical study of how double shell capsule deformations caused by drive asymmetries and fabrication imperfections affect implosion symmetry and neutron yield. Hydrodynamics simulations are performed in two dimensions and focus on low-mode deformations that are caused by corresponding asymmetries in the Hohlraum drive, component offsets, and ablator joint gaps. By providing a parameter study of these features, our goal is to understand the dominant sources for inner shell deformation and yield degradation. The discussed capsules are composed of an aluminum ablator with a chromium inner shell. The latter encloses a carbon-deuterium foam ball that serves as fuel. We find that for clean capsules, even-numbered low-mode asymmetries in the drive are imprinted on the ablator and smoothly transferred to the inner shell during shell collision. The resulting deformation of the inner shell is more pronounced with larger fuel radius, while the yield is inversely proportional to the amplitude of the drive asymmetry and varies by factors ≤4 in comparison with clean simulations. Capsule component offsets in the vertical direction and ablator thickness nonuniformity result in p1-type deformations of the imploding inner shell. Finally, joint gaps have the largest effect in deforming the ablator and inner shell and degrading yield. While small gap widths (1 μm) result in prolate inner shells, larger gap widths (4 μm) cause an oblate deformation. More importantly, capsules with a small outer gap (1 μm) experience a dramatic drop in yield, typically <3% of a clean simulation.

Access to reliable, clean energy sources is a major concern for national security. Much research is focused on the “grand challenge” of producing energy via controlled fusion reactions in a laboratory setting. For fusion experiments, specifically inertial confinement fusion (ICF), to produce sufficient energy, the fusion reactions in the ICF fuel need to become self‐sustaining and burn deuterium‐tritium (DT) fuel efficiently. The recent record‐breaking NIF ignition shot was able to achieve this goal as well as produce more energy than used to drive the experiment. This achievement brings self‐sustaining fusion‐based power systems closer than ever before, capable of providing humans with access to secure, renewable energy. In order to further progress toward the actualization of such power systems, more ICF experiments need to be conducted at large laser facilities such as the United States's National Ignition Facility (NIF) or France's Laser Mega‐Joule. The high cost per shot and limited number of shots that are possible per year make it prohibitive to perform large numbers of experiments. As such, experimental design relies heavily on complex predictive physics simulations for high‐fidelity “preshot” analysis. These multidimensional, multi‐physics, high‐fidelity simulations have to account for a variety of input parameters as well as modeling the extreme conditions (pressures and densities) present at ignition. Such simulations (especially in 3D) can become computationally prohibitive to turn around for each ICF experiment. In this work, we explore using Bayesian optimization with Gaussian processes (GPs) to find optimal designs for ICF double shell targets, while keeping computational costs to manageable levels. These double shell targets have an inner shell that grades from beryllium on the outer surface to the higher Z material molybdenum, as opposed to the nominally used tungsten, on the inside in order to trade off between the high performance associated with high density inner shells and capsule stability. We describe our results for “capsule‐only” xRAGE simulations to study the physics between different capsule designs, inner shell materials, and potential for future experiments.

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 outer surface of the high-Z inner shell in the double shell configuration of inertial confinement fusion experiments experiences Rayleigh-Taylor instability growth during the implosion process due to inverted density and pressure gradients between a highly compressed foam interstitial layer and the accelerating dense inner shell. Graded density layers have long been known to reduce instability growth rates. In this study, we employ high-fidelity radiation hydrodynamic simulations to demonstrate this improved stability when grading beryllium into tungsten. We first characterize the response to L-band preheat of these layers using a newly calibrated radiation drive. While graded layer capsules suffer reduced performance (here, measured as DD neutron yield from a CD foam fuel) in 1D simulations due to reduced kinetic energy coupling and reduced fuel compression, they suffer less of a performance drop when 2D instabilities are accounted for. With the improved stability of graded layers, we explore the performance of capsules with larger fuel radii and thinner shells as a preliminary study to find new designs in which graded layers produce the highest yields.

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.

tests. Using the Firing point TA-39-88 capacitor bank, 3.5 MA was delivered to the FCG for the initial magnetic field, and 36.4 MA were delivered to the load having an initial inductance of 2.5 nH. Implosion speeds over 1.1 cm/us were recorded, which exceeds previous LANL solid liner experimental results. The test was diagnosed with 18 PDV channels, 12 of which recorded liner implosion data, and the other 6 of which tracked the FCG armature during flux compression. These armature expansion data recorded during flux compression are the first of their kind, and it was previously unknown, due to unknown effects of the SF6 in the flux compression volume, whether or not the expansion could be recorded using the PDV technique. Post shot 2D MHD calculations employed a complete external circuit model, and an improved flux diffusion model not available prior to the test. Results from these simulations show very good agreement with the experimental result. Four PDV channels recorded the liner implosion viewed radially outward from the center of the liner. All four of these probes recorded implosion velocities greater that 1 cm/µs, with the cylindrical center displaced by ~2 mm from actual center. Four PDV channels looked at +10° angles from the CMU wall, and four looked at -10° angles. A glide plane interaction is shown moving toward the center of the liner in MHD calculations, and PDV probes provide confirmation. The high explosive (HE) in the LA-R43S6-L1 test was PBX 9501 which had to be glued together in many pieces, and the test was preceded by a camera test to verify that the PBX 9501 could be assembled with acceptable tolerance in glue joints to prevent severing the armature during expansion. The camera test verified an acceptable armature performance, and results are given in complete detail in a post shot report LA-UR-19-20124, and summarized here. This report provides complete detail of the considerable body of data obtained on the test and in the post shot calculations. It is prepared in Power Point for ease of preparation and future review. Shot documentation available in the LANL on-line library are included as references, and non-referenceable documents will be cited and stored in an LA- R43S6-L1 post shot folder stored on an M-6 shared drive. Fabrication drawings are also maintained in an M-6 shared drive and paper files are available from M-6 personnel. This report will be maintained as a PowerPoint document on the shared drive, as well, since included movies will play and graphs from Excel files retain information in the PowerPoint versions. PDF versions are required for clearance and are not to large to send by e-mail.

Inertial confinement fusion (ICF) and high-energy density (HED) physics experiments experience complicated forcing for instability growth and mix due to the ubiquitous presence of multiple shocks interacting with perturbations on multiple material interfaces. One common driver of instability growth is successive shocks from the same direction. However, there is a severe lack of analytic work and modeling validation for same-sided successive shocks since they are extremely difficult to achieve with conventional (non-HED) drivers. Successive shocks access a large instability parameter space; idealized fluid theory [K. O. Mikaelian, Phys. Rev. A 31, 410 (1985)] predicts 15 different interface evolution scenarios for a sinusoidal perturbation. Growth becomes more complex for multi-mode, compressible HED systems. The Mshock campaign is the first experiment in any fluid regime to probe a wide portion of successive shock parameter space. This is enabled by our development of a hybrid direct/indirect drive platform capable of creating independently controllable successive shocks on the National Ignition Facility. These experiments have delivered the first data capable of rigorously challenging our models and their ability to accurately capture Richtmyer–Meshkov growth under successive shocks. Single-mode and two-mode experiments have successfully demonstrated the ability to access and control the various growth scenarios of the shocked interface, including re-inversion, freeze out, and continued growth. Simulations and theoretical modeling are shown to accurately capture the experimental observations in the linear growth phase, giving us confidence in our ICF/HED design codes.

lead shock can affect the accuracy of inferring shock locus points used for the shock pressure of Pop plot data points and for Hugoniot data to calibrate the reactants EOS.

the shock tube occurred when the pre-pulse mimicked a direct drive, achieved by re-pointing the inner beam cones, and when a liner was used to ensure that the free-electron number density was below the critical density for NIF. Additional simulations (presented in the Appendix) that used the two-component laser source but focused on specific choices in laser-pulse design space, as proposed by Kirk Flippo for use in the first MShock experiments at NIF, also demonstrated the presence of two shocks.

2. Perform validation assessments using small-scale experiments. 3. Evaluate sensitivities and quantify uncertainties due to model form variations and mesh dependencies.

the form of summary analytical tables were provided to the project in advance of this final report to enable early estimation of evaporator operational parameters, using the Predict modeling program. Analyses were performed at the 222-S Laboratory as defined and specified in the TSAP and the Laboratory's Quality Assurance P1an, References 6 and 7. Any deviations from the instructions documented in the TSAP are discussed in this narrative and are supported with additional documentation.

Double shell capsule implosions are an alternative approach to achieving alpha heating on the National Ignition Facility. Current machining techniques construct the outer shell as two hemispheres that are glued together, and the deuterium and tritium (DT) liquid inside the inner shell will be injected by a fill tube. These features introduce asymmetries and jetting that may disrupt the confinement of the DT fuel if not carefully controlled. Simulations indicate that in order to achieve high yields in the laboratory, these features as well as susceptibility to the Rayleigh–Taylor instability (RTI) must be mitigated. Due to uncertainties in computational models and the expense of using the best physics models at adequate resolution in three dimensions, our computational modeling must be constrained by experiments. We report on the results of recent hydrogrowth radiography and dual-axis keyhole experiments with double shell targets that have been used to evaluate our modeling of the outer shell joint as well as the impacts of high-energy x-ray preheat that strongly impacts RTI growth. Our simulations show good agreement with the experimental data and inform several important modeling choices.

Double shell capsules are an attractive alternative in inertial confinement fusion experiments due to their potential for achieving a low-convergence, robust burn 1 . However, symmetry degradation and accompanying reduced fuel confinement plagues these systems due to the joint between the two hemispheres of the outer shell. The gap widens during irradiation and this perturbation grows and imprints onto the inner shell during the collision. xRAGE Eulerian radiation-hydrodynamic simulations predict significant reductions in deuterium–tritium fusion yields compared to joint-less simulations when the depth of the outer joint is increased. We demonstrate that the technique of plating the insides of the outer gap with gold can mitigate the impact of this feature. Gold-plating in quantities comparable to or exceeding the "missing" outer shell mass shows promise toward restoring both implosion symmetry and yield closer to the joint-less levels 2 . The shape and symmetry retention in the outer and inner shells is captured in high-energy x-ray synthetic radiographs.

Converting and using the National Ignition Facility (NIF) to deliver 527 nm light instead of its current 351 nm would allow the laser to deliver more energy and power to ignition targets. We update previous 527 nm target design work to reflect more contemporary target designs using high-density carbon capsules and low density helium gas filled Hohlraums. We extend single shell capsule designs based on current experimental results to higher energy and power and also explore double shell capsules, both driven by green light. These studies were completed using detailed pulse shapes found for targets that converged with acceptable 2D implosion symmetries and then used the Lava Lamp II code to confirm their feasibility at NIF. A 1.2× dimensional scaleup of one tuned NIF target at the limit of its current 351 nm capabilities and shot 170827 uses 3.3 MJ, at the limit of the current NIF's 527 nm capability. With the less-structured pulse of a double shell target, 3.7 MJ could be delivered by the laser. Our LPI calculations do not preclude operation at 527 nm, particularly for low fill Hohlraums, and suggest that the stimulated Raman backscatter may be no worse than the small quantities seen in 170827; stimulated forward Raman scattering may be present. If Stimulated Brillouin Scattering is too great, the much greater laser bandwidth available at 527 nm could be used to decrease backscatter. These larger targets with higher energy and power may offer a better chance of achieving ignition with only modest changes to the NIF laser.

fielded double shell keyhole target, but the tungsten inner shell is replaced with molybdenum to allow imaging with X-rays from a zirconium backlighter (16.3 keV). Eulerian radiation-hydrodynamics simulations with adaptive mesh refinement are used to predict joint feature evolution for several different joint designs. Synthetic radiographs produced from ablator-only calculations demonstrate that the evolution of different joint morphologies can be radiographed and distinguished. Feedthrough of the joint perturbation to a molybdenum inner shell is predicted to be measurable at a convergence ratio of 2.

Double shell capsules provide an attractive option in inertial confinement fusion experiments due to their potential for achieving a low-convergence, robust burn. However, these designs suffer from symmetry degradation and accompanying reduced fuel confinement due to the currently necessary joint between the two hemispheres of the outer shell. The gap widens as a result of the excess ablation pressure produced by x rays that penetrate the joint during the drive phase, and this perturbation grows and imprints onto the inner shell during the collision. xRAGE Eulerian radiation-hydrodynamic simulations predict significant reductions in deuterium–tritium fusion yields compared to joint-less simulations when the depth of the outer joint is increased, whereas the performance is less sensitive to the depth of the inner gap. Here we examine the technique of plating the insides of the outer gap with a high-Z material to mitigate the impact of this feature. Gold-plating in quantities comparable to or exceeding the “missing” outer shell mass shows promise toward restoring both implosion symmetry and yield closer to the joint-less levels, and synthetic diagnostics suggest that high-energy x-ray radiographs can capture this shape retention of the inner and outer shells in experiments.