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.

At the National Ignition Facility, inertial confinement fusion experiments aim to burn and ignite a hydrogen plasma to generate a net source of energy through the fusion of deuterium and tritium ions. The energy deposited by α-particles released from the deuterium–tritium fusion reaction plays the central role in heating the fuel to achieve a sustained thermonuclear burn. In the hydrodynamic picture, α-heating increases the temperature of the plasma, leading to increased reactivity because the mean ion kinetic energy increases. Therefore, the ion temperature is related to the mean ion kinetic energy. Here we use the moments of the neutron spectrum to study the relationship between the ion temperature (measured by the variance in the neutron kinetic energy spectrum) and the ion mean kinetic energy (measured by the shift in the mean neutron energy). We observe a departure from the relationship expected for plasmas where the ion relative kinetic energy distribution is Maxwell–Boltzmann, when the plasma begins to burn. Understanding the cause of this departure from hydrodynamic behaviour could be important for achieving robust and reproducible ignition. Inertial confinement fusion experiments reveal a departure from the expected hydrodynamic behaviour of a plasma when the fusion reactions become the primary source of plasma heating.

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. As recently reported, a burning plasma state, where the alpha-heating in the plasma is the primary source of heating, was achieved in laboratory experiments. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin ``burn propagation'' into surrounding cold fuel, enabling the possibility of high energy gain. While ``scientific breakeven'' (i.e. unity target gain) has not yet been achieved, this talk reports the first controlled fusion experiment on the National Ignition Facility to produce capsule gain greater than unity (here 5.8) and reach ignition by many different formulations of the Lawson criterion. In the talk, we will discuss some key basic physics inertial confinement fusion (ICF) principles behind the burning plasma and ignition results as well as discuss future challenges.

Nuclear diagnostics provide measurements of inertial confinement fusion implosions used as metrics of performance for the shot. The interpretation of these measurements for shots with low mode asymmetries requires a way of combining the data to produce a “sky map” where the individual line-of-sight values are used to interpolate to other positions in the sky. These interpolations can provide information regarding the orientation of the low mode asymmetries. We describe the interpolation method, associated uncertainties, and correlations between different metrics, e.g., Tion, down scatter ratio, and hot-spot velocity direction. This work is also related to recently reported studies [H. G. Rinderknecht et al., Phys. Rev. Lett. 124, 145002 (2020) and K. M. Woo et al., Phys. Plasmas 27, 062702 (2020)] of low mode asymmetries. We report an analysis that makes use of a newly commissioned line of sight, a scheme for incorporating multiple neutron spectrum measurement types, and recent work on the sources of implosion asymmetry to provide a more complete picture of implosion performance.

The measurement of plasma hotspot velocity provides an important diagnostic of implosion performance for inertial confinement fusion experiments at the National Ignition Facility. The shift of the fusion product neutron mean kinetic energy as measured along multiple line-of-sight time-of-flight spectrometers provides velocity vector components from which the hotspot velocity is inferred. Multiple measurements improve the hotspot velocity inference; however, practical considerations of available space, operational overhead, and instrumentation costs limit the number of possible line-of-sight measurements. We propose a solution to this classical “experiment design” problem that optimizes the precision of the velocity inference for a limited number of measurements.

Inertial confinement fusion implosions designed to have minimal fluid motion at peak compression often show significant linear flows in the laboratory, attributable per simulations to percent-level imbalances in the laser drive illumination symmetry. We present experimental results which intentionally varied the mode 1 drive imbalance by up to 4% to test hydrodynamic predictions of flows and the resultant imploded core asymmetries and performance, as measured by a combination of DT neutron spectroscopy and high-resolution x-ray core imaging. Neutron yields decrease by up to 50%, and anisotropic neutron Doppler broadening increases by 20%, in agreement with simulations. Furthermore, a tracer jet from the capsule fill-tube perturbation that is entrained by the hot-spot flow confirms the average flow speeds deduced from neutron spectroscopy.

To achieve hotspot ignition, an inertial confinement fusion implosion must achieve high hotspot pressure that is inertially confined by a dense shell of DT fuel. This requires a symmetric implosion having high in-flight shell velocity and high areal density at stagnation. The size of the driver and scale of the capsule required can be minimized by maintaining a high efficiency of energy coupling from the imploding shell to the hotspot. Significant 3D low mode asymmetries, however, are commonly observed in indirect-drive implosions and reduce the coupling of shell kinetic energy to the hotspot. To better quantify the magnitudes and impacts of shell density asymmetries, we have developed new analysis techniques and analytic models [Hurricane et al., Phys. Plasmas 27(6), 062704 (2020)]. To build confidence in the underlying data, we have also developed an analytic neutron transport model to cross-compare two independent measurements of asymmetry, which shows excellent agreement across shots for mode-1 (ℓ = 1). This work also demonstrates that asymmetry can introduce potential sampling bias into down-scattered ratio measurements causing the solid-angle-average and uncertainty-weighted-average down-scattered ratios to differ significantly. Diagnosing asymmetries beyond mode-1 (ℓ > 1) presents significant challenges. Using new diagnostic instruments and analysis techniques, however, evidence of significant Legendre mode P2 (ℓ = 2, m = 0) and additional 3D asymmetries (ℓ > 1, m ≠ 0) are beginning to emerge from the high precision activation diagnostic data (real-time nuclear activation detectors) and down-scattered neutron imaging data.

A simple 3D dynamic model for inertial confinement fusion (ICF) implosions has been developed and used to assess the impacts of low-mode asymmetry, aneurysms and mix-induced radiative loss on capsule performance across ICF platforms. The model, while benchmarked against radiation hydrodynamics simulations, benefits from simplicity and speed to allow rapid assessment of possible sources of degradation as well as to help build intuition about the relative importance of different effects. Degradations in the model result from 3D areal density perturbations that grow under deceleration from a radial stagnation flow, resulting in reduced convergence, stagnation pressure and temperature. When available, experimental data are used as input to seed 3D perturbations in the model so that the actual observed hotspot and shell areal density asymmetry at stagnation, as well as the radiation loss increase from mix impurities, are accurately reproduced. This model is applied to a broad set of implosion data from the NIF and Omega, including examples from both indirect drive and direct drive. The model matches most experimental observables and explains major performance degradation mechanisms which can result in 30–100-fold reductions in yield. We examine a modified ignition criterion that accounts for the increase in expansion work, due to the presence of 3D perturbations and loss-of-confinement in thin regions of the shell.

The goal of an inertially confined, igniting plasma on the National Ignition Facility (NIF) [M. L. Spaeth, Fusion Sci. Technol. 69, 25 (2016)] remains elusive. However, there is a growing understanding of the factors that appear to be limiting current implosion performance. And with this understanding, the question naturally arises: What conditions will ultimately be required to achieve ignition, either by continuing to improve the quality of current implosions, or by hydrodynamically scaling those implosions to larger driver energies on some future facility? Given the complexity of NIF implosions, answering this question must rely heavily on sophisticated numerical simulations. In particular, those simulations must respect the three-dimensionality of real NIF implosions and also resolve the wide range of scales for the many perturbation sources that degrade them. This prospectus article reviews the current state of detailed modeling of NIF implosions, the scaling to ignition from recent experiments that that modeling implies, and areas for future improvements in modeling technique that could increase understanding and further enhance predictive capabilities. Given the uncertainties inherent in any extrapolation, particularly for a process as nonlinear as ignition, there will be no definitive answer on the requirements for ignition until it is actually demonstrated experimentally. However, with continuing improvements in modeling technique and a growing experience base from NIF, the requirements for ignition are becoming clearer.

Doppler broadening of the 14 MeV DT and 2.45 MeV DD fusion neutron lines has long been our best measure of temperature in a burning plasma. At the National Ignition Facility (NIF), yields are high enough and our neutron spectrometers accurate enough that we see finer details of the peak shape. For example, we can measure the shift of the peak due to the bulk motion of the plasma, and we see indications of non-thermal broadening, skew, and kurtosis of the peak caused by the variations of temperature and fluid velocity during burn. We can also distinguish spectral differences among several lines of sight. This paper will review the theory of fusion neutron line shape, show examples of non-Gaussian line shapes and directional variations in NIF data, and describe detailed spectral shapes we see in radiation-hydrodynamics simulations of implosions.

In recent high-foot-implosion experiments at the National Ignition Facility (NIF), directional measurements of the Inertial Confinement Fusion (ICF) neutron spectrum illustrate the existence of substantial bulk-fluid motion and low-mode areal-density (ρR) asymmetries near peak convergence, which significantly degrade the implosion performance. Measured energy shifts of the primary neutron spectrum, beyond iontemperature-induced shifts, indicate bulk-fluid motions up to about 50 km/s. The measured width of the primary neutron spectrum, which is broadened by the variance of the bulk-fluid motion and thermal ion temperature in the burning region, is also indicative of substantial bulk-fluid motion. The reason for this is that the measured apparent DT ion temperature (DT-“Ti“) is consistently higher than the DD-“Ti”, a discrepancy that increases with increasing implosion velocity, which cannot be explained by profiles and reactivity differences. Three-dimensional (3D) asymmetries and bulk-fluid motion must be invoked in the modelling of the measured apparent ion temperatures. Directional yield measurements of scattered neutrons and un-scattered neutrons also indicate ρR asymmetries up to about ±500 mg/cm2 in the layer of cold and dense fuel surrounding the hot spot. The hypothesis is that these observations are mainly driven by radiation drive asymmetries and instabilities seeded by the fill tube and thin tent holding the capsule in the Hohlraum, which are currently being addressed by new engineering solutions, more refined implosion modeling and implementation of new diagnostics.

An accurate understanding of burn dynamics in implosions of cryogenically layered deuterium (D) and tritium (T) filled capsules, obtained partly through precision diagnosis of these experiments, is essential for assessing the impediments to achieving ignition at the National Ignition Facility. We present measurements of neutrons from such implosions. The apparent ion temperatures T_{ion} are inferred from the variance of the primary neutron spectrum. Consistently higher DT than DD T_{ion} are observed and the difference is seen to increase with increasing apparent DT T_{ion}. The line-of-sight rms variations of both DD and DT T_{ion} are small, ∼150eV, indicating an isotropic source. The DD neutron yields are consistently high relative to the DT neutron yields given the observed T_{ion}. Spatial and temporal variations of the DT temperature and density, DD-DT differential attenuation in the surrounding DT fuel, and fluid motion variations contribute to a DT T_{ion} greater than the DD T_{ion}, but are in a one-dimensional model insufficient to explain the data. We hypothesize that in a three-dimensional interpretation, these effects combined could explain the results.

A burning laser fusion plasma produces a neutron spectrum first described by Brysk (1973 Plasma Phys. Control. Fusion 15 611). This and more recent work deals with the spectrum produced by a single fluid element. The distribution of temperatures and velocities in multiple fluid elements combine in any real spectrum; we derive formulas for how the neutron spectrum averages these contributions. The single element momentum spectrum is accurately Gaussian, but the multi-element spectrum exhibits higher moments. In particular, the skew and kurtosis are likely to be large enough to measure. Even the single fluid element spectrum may exhibit measurable directional anisotropy, so that instruments with different lines of sight should see different yields, mean velocities, mean temperatures, and higher moments. Finally, we briefly discuss how scattering in the imploded core modifies the neutron spectrum by changing the relative weighting of fuel regions with different temperatures and velocities.

A common analysis procedure minimizes the ln-likelihood that a set of experimental observables matches a parameterized model of the observation. The model includes a description of the underlying physical process as well as the instrument response function (IRF). In the case investigated here, the National Ignition Facility (NIF) neutron time-of-flight (nTOF) spectrometers, the IRF is constructed from measurements and models. IRF measurements have a finite precision that can make significant contributions to determine the uncertainty estimate of the physical model’s parameters. We apply a Bayesian analysis to properly account for IRF uncertainties in calculating the ln-likelihood function used to find the optimum physical parameters.

The Neutron Imaging System at the National Ignition Facility is used to observe the primary ∼14 MeV neutrons from the hotspot and down-scattered neutrons (6-12 MeV) from the assembled shell. Due to the strong spatial dependence of the primary neutron fluence through the dense shell, the down-scattered image is convolved with the primary-neutron fluence much like a backlighter profile. Using a characteristic scattering angle assumption, we estimate the primary neutron fluence and compensate the down-scattered image, which reveals information about asymmetry that is otherwise difficult to extract without invoking complicated models.