Considerable progress has been made in deuterium-tritium-layered implosion experiments on the OMEGA Laser System, bringing the prospects for thermonuclear ignition in direct-drive configurations with megajoule-class lasers closer to reality. Doing so has required navigating the balance between improved 1D performance and multidimensional stability. Using statistical modeling based on over 350 cryogenic implosions to identify various degradation mechanisms, and combined with multidimensional simulations and experimental techniques such as target offsets to combat residual flows, core conditions have repeatably been achieved that extrapolate to the burning-plasma state when scaled to 2.15 MJ of symmetric laser illumination. Using high implosion velocities (>450 km/s) and moderately high adiabats (∼5), these experiments produced record-high scaled Lawson parameters in direct drive equal to 89±2% of that required for ignition with expected yields of up to 1.5±0.2 MJ. To improve these results still further, focused physics studies are performed to improve physics understanding and identify routes to even greater performance. Recent studies include investigations into the impact of mounting features, laser imprint, reduced fuel temperatures, and greater on-target intensities through subscale experiments. This manuscript gives a summary of the cryogenic direct-drive program on the OMEGA laser, including routes taken to achieve the current best performance, the status of recent focused physics investigations, and future designs—such as target solutions to laser imprint and reducing vapor density to increase convergence—that are expected lead to the demonstration of hydro-equivalent ignition on OMEGA.

Multidimensional effects degrade the neutron yield and the compressed areal density of laser-direct-drive inertial confinement fusion implosions of layered deuterium–tritium cryogenic targets on the OMEGA Laser System with respect to 1D radiation-hydrodynamic simulation predictions. A comprehensive physics-informed 3D reconstruction effort is under way to infer hot-spot and shell conditions at stagnation from four x-ray and seven neutron detectors distributed around the OMEGA target chamber. Neutron diagnostics, providing measurements of the neutron yield, hot-spot flow velocity, and apparent ion-temperature distribution, are used to infer the mode-1 perturbation at stagnation. The x-ray imagers record the shape of the hot-spot plasma to diagnose mode-1 and mode-2 perturbations. A deep-learning convolutional neural network trained on an extensive set of 3D radiation-hydrodynamic simulations is used to interpret the x-ray and nuclear measurements to infer the 3D profiles of the hot-spot plasma conditions and the amount of laser energy coupled to the hot-spot plasma. A 3D simulation database shows that larger mode-1 asymmetries are correlated with higher hot-spot flow velocities and reduced laser-energy coupling and neutron yield. Three-dimensional hot-spot reconstructions from x-ray measurements indicate that higher amounts of residual kinetic energy are correlated with higher measured hot-spot flow velocities, consistent with 3D simulations.

A multi-laboratory collaborative effort is currently exploring the feasibility of laser direct drive liquid deuterium–tritium (DT) wetted foam inertial confinement fusion concepts being considered for novel neutron sources on the National Ignition Facility (NIF) laser. In contrast to the laser indirect drive approach that recently demonstrated ignition in the laboratory, these concepts also offer the potential of multi-MJ yields but with less damaging laser drives, improved robustness to target and drive imperfections, and enhanced facility fielding flexibility and orders-of-magnitude less target debris: favorable aspects for neutron exposure environments and inertial fusion energy concepts, alike. We present the current status of the experimental platform and radiation-hydrodynamics modeling development efforts to better understand the potential risks and benefits associated with these designs for the envisioned implementation on the NIF laser encompassing (i) novel two-photon-polymerization additively manufactured capsules, (ii) cryogenic target cooling through a large conductive fill tube, (iii) polar direct drive, and (iv) direct laser ablation of the liquid DT wetted foam layer.

This paper presents a simple physics-based model for the interpretation of key metrics in laser direct drive. The only input parameters required are target scale, in-flight aspect ratio, and beam-to-target radius, and the importance of each has been quantified with a tailored set of cryogenic implosion experiments. These analyses lead to compact and accurate predictions of the fusion yield and areal density as a function of hydrodynamic stability, and they suggest new ways to take advantage of direct drive. To provide examples, we discuss how the inferred mix width behaves relative to theory and then show how it could be exploited to perform a direct drive implosion with a Lawson metric or χ_{noα} of 0.24±0.02-using a novel parameter space at high velocities and beam radii on the OMEGA laser-that projects to ignition at a laser energy of ≤2.0 MJ.

Focussing laser light onto the surface of a small target filled with deuterium and tritium implodes it and leads to the creation of a hot and dense plasma, in which thermonuclear fusion reactions occur. In order for the plasma to become self-sustaining, the heating of the plasma must be dominated by the energy provided by the fusion reactions—a condition known as a burning plasma. A metric for this is the generalized Lawson parameter, where values above around 0.8 imply a burning plasma. Here, we report on hydro-equivalent scaling of experimental results on the OMEGA laser system and show that these have achieved core conditions that reach a burning plasma when the central part of the plasma, the hotspot, is scaled in size by at least a factor of 3.9 ± 0.10, which would require a driver laser energy of at least 1.7 ± 0.13 MJ. In addition, we hydro-equivalently scale the results to the 2.15 MJ of laser energy available at the National Ignition Facility and find that these implosions reach 86% of the Lawson parameter required for ignition. Our results support direct-drive inertial confinement fusion as a credible approach for achieving thermonuclear ignition and net energy in laser fusion.

Indirect Drive Inertial Confinement Fusion Experiments on the National Ignition Facility (NIF) have achieved a burning plasma state with neutron yields exceeding 170 kJ, roughly 3 times the prior record and a necessary stage for igniting plasmas. The results are achieved despite multiple sources of degradations that lead to high variability in performance. Results shown here, for the first time, include an empirical correction factor for mode-2 asymmetry in the burning plasma regime in addition to previously determined corrections for radiative mix and mode-1. Analysis shows that including these three corrections alone accounts for the measured fusion performance variability in the two highest performing experimental campaigns on the NIF to within error. Here we quantify the performance sensitivity to mode-2 symmetry in the burning plasma regime and apply the results, in the form of an empirical correction to a 1D performance model. Furthermore, we find the sensitivity to mode-2 determined through a series of integrated 2D radiation hydrodynamic simulations to be consistent with the experimentally determined sensitivity only when including alpha-heating. Recent improvements in the indirect-drive inertial confinement fusion experiments include the achievement of burning plasma state. Here the authors report the scaling of neutron yield in a burning plasma of Deuterium-Tritium fusion reaction by including the mode-2 asymmetry.

Low convergence ratio implosions (where wetted-foam layers are used to limit capsule convergence, achieving improved robustness to instability growth) and auxiliary heating (where electron beams are used to provide collisionless heating of a hotspot) are two promising techniques that are being explored for inertial fusion energy applications. In this paper, a new analytic study is presented to understand and predict the performance of these implosions. Firstly, conventional gain models are adapted to produce gain curves for fixed convergence ratios, which are shown to well-describe previously simulated results. Secondly, auxiliary heating is demonstrated to be well understood and interpreted through the burn-up fraction of the deuterium-tritium fuel, with the gradient of burn-up with respect to burn-averaged temperature shown to provide good qualitative predictions of the effectiveness of this technique for a given implosion. Simulations of auxiliary heating for a range of implosions are presented in support of this and demonstrate that this heating can have significant benefit for high gain implosions, being most effective when the burn-averaged temperature is between 5 and 20 keV.

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.

Irradiating a small capsule containing deuterium and tritium fuel directly with intense laser light causes it to implode, which creates a plasma hot enough to initiate fusion reactions between the fuel nuclei. Here we report on such laser direct-drive experiments and observe that the fusion reactions produce more energy than the amount of energy in the central so-called hot-spot plasma. This condition is identified as having a hot-spot fuel gain greater than unity. A hot-spot fuel gain of around four was previously accomplished at the National Ignition Facility in indirect-drive inertial confinement fusion experiments where the capsule is irradiated by X-rays. In that case, up to 1.9 MJ of laser energy was used, but in contrast, our experiments on the OMEGA laser system require as little as 28 kJ. As the hot-spot fuel gain is predicted to grow with laser energy and target size, our work establishes the direct-drive approach to inertial fusion as a promising path towards burning and ignited plasmas in the laboratory. Additionally, we report a record (direct-drive) fusion yield of 0.9 kJ on OMEGA, which we achieved with thin-ice deuterium–tritium liner targets.

This paper presents a “hybrid” approach to direct drive inertial confinement fusion that can exploit a high-energy gas laser with two opposed beams. The target and driver are asymmetric, much like experiments performed on the National Ignition Facility, but have been designed to benefit from scale and their particular compatibility with a fusion power plant. The imploded masses (and areal densities) are increased by a factor of 12 (3) relative to findings by Abu-Shawareb et al. [Phys. Rev. Lett. 129, 075001 (2022)] and provide a path to high-gain implosions that robustly ignite. The design also mitigates common concerns such as laser imprint and cross-beam energy transfer. We discuss the rationales for a hybrid target, the methods used to control implosion symmetry, and the implication(s) for inertial fusion energy.

Multidimensional effects on hot-spot formation must be considered to better understand the current limits on the performance of direct-drive inertial confinement fusion experiments on OMEGA with cryogenically layered solid deuterium–tritium targets. A comprehensive reconstruction effort has been established at the Laboratory for Laser Energetics to infer hot-spot and shell conditions at stagnation from a large collection of x-ray, neutron, and particle detectors along multiple lines of sight. Several time-gated and time-integrated x-ray imagers are being used to record the shape of the hot-spot plasma. A 3D hot-spot x-ray emission tomography technique has been developed to infer low-mode drive asymmetries from the hot-spot shape. A suite of neutron diagnostics is used to provide measurements of hot-spot flow velocity, ion temperature, and areal density. The information obtained from the x-ray and neutron detectors will be combined into a coherent model of the shape of the hot spot and shell assembly.

We show that an x-ray emission signature associated with acceleration phase mass injection [R. C. Shah et al., Phys. Rev. E 103, 023201 (2021)] correlates with poor experimental hot-spot convergence and a reduced neutron production relative to expectations. It is shown that with increased target mass as well as with higher-design adiabats, this signature is reduced, whereas with increased debris on the target, the signature is increased. We estimate that the vapor region in typical best designs may have up to 2x the assumed hydrogen mass at the start of deceleration.

A deep-learning convolutional neural network (CNN) is used to infer, from x-ray images along multiple lines of sight, the low-mode shape of the hot-spot emission of deuterium-tritium (DT) laser-direct-drive cryogenic implosions on OMEGA. The motivation of this approach is to develop a physics-informed 3-D reconstruction technique that can be performed within minutes to facilitate the use of the results to inform changes to the initial target and laser conditions for the subsequent implosion. The CNN is trained on a 3D radiation-hydrodynamic simulation database to relate 2D x-ray images to 3D emissivity at stagnation. The CNN accounts for the lack of an absolute spatial reference and the different bands of photon energies in the x-ray images. While previous work [O. M. Mannion et al., Phys. Plasmas 28, 042701 (2021) and A. Lees et al., Phys. Rev. Lett. 127, 105001 (2021)] studied the effect of mode-1 asymmetries on implosion performance using nuclear diagnostics, this work focuses on the effect of mode 2 inferred from x-ray diagnostics on implosion performance. A current analysis of 19 DT cryogenic implosions indicates there is an upper limit of similar to 20% reduction in the neutron yield caused by an & ell; = 2 amplitude for & ell;(2)/& ell;(0 )<= 0.32. These conclusions are supported by 2D simulations.

In indirect-drive implosions, the final core hot spot energy and pressure and, hence, neutron yield attainable in 1D increase with increasing laser peak power and, hence, radiation drive temperature at the fixed capsule and Hohlraum size. We present simple analytic scalings validated by 1D simulations that quantify the improvement in performance and use this to explain existing data and simulation trends. Extrapolating to the 500 TW National Ignition Facility peak power limit in a low gas-fill 5.4 mm diameter Hohlraum based on existing high adiabat implosion data at 400 TW, 1.3 MJ and 1 × 1016 yield, we find that a 2–3 × 1017 yield (0.5–0.7 MJ) is plausible using only 1.8 MJ of laser energy. Based on existing data varying deuterium–tritium (DT) fuel thickness and dopant areal density, further improvements should be possible by increasing DT fuel areal density, and hence confinement time and yield amplification.

In order to understand how close current layered implosions in indirect-drive inertial confinement fusion are to ignition, it is necessary to measure the level of alpha heating present. To this end, pairs of experiments were performed that consisted of a low-yield tritium-hydrogen-deuterium (THD) layered implosion and a high yield deuterium-tritium (DT) layered implosion to validate experimentally current simulation-based methods of determining yield amplification. The THD capsules were designed to reduce simultaneously DT neutron yield (alpha heating) and maintain hydrodynamic similarity with the higher yield DT capsules. The ratio of the yields measured in these experiments then allowed the alpha heating level of the DT layered implosions to be determined. The level of alpha heating inferred is consistent with fits to simulations expressed in terms of experimentally measurable quantities and enables us to infer the level of alpha heating in recent high-performing implosions.

Improving the performance of inertial confinement fusion implosions requires physics models that can accurately predict the response to changes in the experimental inputs. Good predictive capability has been demonstrated for the fusion yield using a statistical mapping of simulated outcomes to experimental data [Gopalaswamy et al., Nature 565(771), 581–586 (2019)]. In this paper, a physics-based statistical mapping approach is used to extract and quantify all the major sources of degradation of fusion yield for direct-drive implosions on the OMEGA laser. The yield is found to be dependent on the age of the deuterium tritium fill, the ℓ=1 asymmetry in the implosion core, the laser beam-to-target size ratio, and parameters related to the hydrodynamic stability. A controlled set of experiments were carried out where only the target fill age was varied while keeping all other parameters constant. The measurements were found to be in excellent agreement with the fill age dependency inferred using the mapping model. In addition, a new implosion design was created, guided by the statistical mapping model by optimizing the trade-offs between increased laser energy coupling at larger target size and the degradations caused by the laser beam-to-target size ratio and hydrodynamic instabilities. When experimentally performed, an increased fusion yield was demonstrated in targets with larger diameters.

Following indirect-drive experiments which demonstrated promising performance for low convergence ratios (below 17), previous direct-drive simulations identified a fusion-relevant regime which is expected to be robust to hydrodynamic instability growth. This paper expands these results with simulated implosions at lower energies of 100 and 270 kJ, and 'hydrodynamic equivalent' capsules which demonstrate comparable convergence ratio, implosion velocity and in-flight aspect ratio without the need for cryogenic cooling, which would allow the assumptions of one-dimensional-like performance to be tested on current facilities. A range of techniques to improve performance within this regime are then investigated, including the use of two-colour and deep ultraviolet laser pulses. Finally, further simulations demonstrate that the deposition of electron energy into the hotspot of a low convergence ratio implosion through auxiliary heating also leads to significant increases in yield. Results include break even for 1.1 MJ of total energy input (including an estimated 370 kJ of short-pulse laser energy to produce electron beams for the auxiliary heating), but are found to be highly dependent upon the efficiency with which electron beams can be created and transported to the hotspot to drive the heating mechanism.

Three-dimensional effects play a crucial role during the hot-spot formation in inertial confinement fusion (ICF) implosions. A data analysis technique for 3D hot-spot reconstruction from experimental observables has been developed to characterize the effects of low modes on 3D hot-spot formations. In nuclear measurements, the effective flow direction, governed by the maximum eigenvalue in the velocity variance of apparent ion temperatures, has been found to agree with the measured hot-spot flows for implosions dominated by mode ℓ=1. Asymmetries in areal-density (ρR) measurements were found to be characterized by a unique cosine variation along the hot-spot flow axis. In x-ray images, a 3D hot-spot x-ray emission tomography method was developed to reconstruct the 3D hot-spot plasma emissivity using a generalized spherical-harmonic Gaussian function. The gradient-descent algorithm was used to optimize the mapping between the projections from the 3D hot-spot emission model and the measured x-ray images along multiple views. This work establishes a platform to analyze 3D low-mode core asymmetries in ICF.