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 goal of the Xflows experimental campaign is to study the radiation flow on the National Ignition Facility (NIF) reproducing the sensitivity of the temperature (±8 eV, ±23 μm) and density (±11 mg/cc) measurements of the COAX platform [Johns et al., High Energy Density Phys. 39, 100939 (2021); Fryer et al., High Energy Density Phys. 35, 100738 (2020); and Coffing et al., Phys. Plasmas 29, 083302 (2022)]. This new platform will enable future astrophysical experiments involving supernova shock breakout, such as Radishock (Johns et al., Laboratory for Laser Energetics Annual Report 338, 2020) on OMEGA-60 [Boehly et al., Rev. Sci. Instrum. 66, 508 (1995)], and stochastic media (such as XFOL on OMEGA). Greater energy and larger physical scale on NIF [Moses et al., Eur. Phys. J. D 44, 215 (2007)] will enable a greater travel distance of radiation flow, higher density, and more manufacturable foams and enable exploration of a greater range of radiation behavior than achievable in the prior OMEGA experiments. This publication will describe the baseline configuration for the Xflows experimental campaign and the roadmap to achieve its primary objectives.

beam with annular radial profile and a second beam with the uniform radial profile. It is found that the first beam causes some additional fuel compression and confinement that decrease the total beam energy required for the ignition to 6 kJ, which is 40% smaller than in the case of a single beam with uniform radial profile.

The Opacity Platform on the National Ignition Facility (NIF) has been developed to measure opacities at varying densities and temperatures relevant to the solar interior and thermal cooling rates in white dwarf stars. The typical temperatures reached at NIF range between 150 and 210 eV, which allow these measurements to be performed experimentally. The captured opacities are crucial to validating radiation-hydrodynamic models that are used in astrophysics. The NIF opacity platform has a unique new capability that allows in situ measurement of the sample expansion. The sample expansion data are used to better understand the plasma conditions in our experiments by inferring the sample density throughout the duration of the laser drive. We present the details of the density measurement technique, data analysis, and recent results for Fe and MgO.

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.

new analysis of the anchor 1 data and compared the results to a series of calculations using the LANL ATOMIC code. Figures 1 and 2 compare the data with the best-fit to calculations. This result is significantly improved over the result published in Atoms. The differences are small for the iron quasi-continuum between 8-9.5 Å and for the Mg Heα and Lyα lines. The opacities near the centers of the iron bound-bound features also match fairly well in the 9.5-12.5 Å range. However, the opacity windows between the large iron bound-bound features are deeper in the Atomic predictions than the measurement. Furthermore, large discrepancies exist for the Mg He β, γ, and δ lines and for the short-wavelength quasicontinuum. The experiment and analysis refinements described below have set the stage for unraveling these discrepancies. Specifically, we can repeat the Anchor 1 experiments using improved backlighter, hohlraum, and spectrometers to obtain reduced backgrounds and better spectral resolution. Exploiting the AlMg calibration experiments and repeating the Anchor 1 measurements multiple times will enable formal and rigorous uncertainty determination. This well-defined path gives us confidence that high quality opacity data can be obtained on NIF.

The Opacity Platform on the National Ignition Facility (NIF) has been developed to measure iron opacities at varying densities and temperatures relevant to the solar interior and to verify recent experimental results obtained at the Sandia Z-machine, that diverge from theory. The first set of NIF experiments collected iron opacity data at ∼150 eV to 160 eV and an electron density of ∼7 × 1021 cm-3, with a goal to study temperatures up to ∼210 eV, with electron densities of up to ∼3 × 1022 cm-3. Among several techniques used to infer the temperature of the heated Fe sample, the absolutely calibrated DANTE-2 filtered diode array routinely provides measurements of the hohlraum conditions near the sample. However, the DANTE-2 temperatures are consistently low compared to pre-shot LASNEX simulations for a range of laser drive energies. We have re-evaluated the estimated uncertainty in the reported DANTE-2 temperatures and also the error generated by varying channel participation in the data analysis. An uncertainty of ±5% or better can be achieved with appropriate spectral coverage, channel participation, and metrology of the viewing slot.

We present the results of a study where we use machine learning to enhance hohlraum design for opacity measurement experiments. Opacity experiments on laser facilities use hohlraums, which, when their interior walls are illuminated by the National Ignition Facility (NIF) lasers, produce a high radiation flux that heats a central sample to a temperature that is constant over a measurement time window. Given a baseline hohlraum design and a computational model, we train a deep neural network to predict the time evolution of the radiation temperature as measured by the Dante diagnostic. This enables us to rapidly explore design space and determine the effect of adjusting design parameters. We also construct an “inverse” machine learning model that predicts the design parameters given a desired time history of radiation temperature. Calculations using the machine learning model demonstrate that improved performance over the baseline hohlraum could reduce sensitivities and uncertainties in experimental opacity measurements.

Several approaches to Inertial Confinement Fusion (ICF), including double-shell, pushered-single-shell, and the Revolver designs, have fuel surrounded by pushers made from high-Z materials. An advantage of these designs is that radiation emitted by the hot fuel will be absorbed and re-radiated into the fuel to reduce cooling. This process is referred to as radiation-trapping, and it lowers the fuel temperature required for ignition. To elucidate the physics of radiation trapping, a simplified model comprising a set of coupled differential equations has been developed to model the arbitrary time-dependent wall temperature from the Hammer and Rosen solution [J. H. Hammer and M. D. Rosen, Phys. Plasmas 10, 1829 (2003)] to a Marshak wave. The derivation of the model and a set of analytical power-law solutions will be presented. A discussion on numerical implementation of the differential equations into a model for burn in ICF capsules is also included.

In FY2020 we fulfilled the exit criteria of milestone 7118. We fielded iron opacity experiments at higher densities and temperatures approaching anchor 2 conditions and made good progress on overcoming the problems that we found. This report describes in detail the progress that has been made. We presented the results in a LANL seminar on August 10 and we gave two talks on our results to the National Opacity Workshop Series, one on July 9 and the other on September 14. Before discussing the anchor 2 measurements, we present an update of the NIF anchor 1 data. We did a new analysis of the anchor 1 data and compared the results to a series of calculations using the LANL ATOMIC code. Figures 1 and 2 compare the data with the best-fit to calculations. This result is significantly improved over the result published in Atoms. The differences are small for the iron quasi-continuum between 8-9.5 Å and for the Mg Heα and Lyα lines. The opacities near the centers of the iron bound-bound features also match fairly well in the 9.5-12.5 Å range. However, the opacity windows between the large iron bound-bound features are deeper in the Atomic predictions than the measurement. Furthermore, large discrepancies exist for the Mg He β, γ, and δ lines and for the short-wavelength quasicontinuum. The experiment and analysis refinements described below have set the stage for unraveling these discrepancies. Specifically, we can repeat the Anchor 1 experiments using improved backlighter, hohlraum, and spectrometers to obtain reduced backgrounds and better spectral resolution. Exploiting the AlMg calibration experiments and repeating the Anchor 1 measurements multiple times will enable formal and rigorous uncertainty determination. This well-defined path gives us confidence that high quality opacity data can be obtained on NIF.

The opacities of iron and other mid-Z elements help to regulate the transport of energy in the sun. Recent experiments on the Sandia National Laboratories Z machine have shown large discrepancies between the measured and calculated opacities of iron at certain solar conditions. To replicate these opacity measurements a platform is being developed on the National Ignition Facility to measure the opacities of iron and other elements at the same conditions as in the Z experiments. The NIF platform consists of a hohlraum to heat the opacity sample to the desired conditions, a separate backlighter to radiograph the sample, and a spectrometer to give the spectrally resolved opacity. Not only must the opacity be measured but the temperature and density of the sample must also be accurately determined. This platform has now produced its first iron transmission measurements. These measurements will be presented along with plans for future measurements and details on how the measurements will be improved.

Advances in target fabrication have made double shell capsule implosions a viable platform to study burning fusion plasmas. Central to the double shell capsule is a high-Z (e.g., Au) metal pusher that accesses the volume-burn regime by reducing radiative losses through radiation trapping and compressing a uniform fuel volume at reduced velocities. A double shell implosion relies on a series of energy transfer processes starting from x-ray absorption by the outer shell, followed by transfer of kinetic energy to an inner shell, and finally conversion of kinetic energy to fuel internal energy. We present simulation and experimental results on momentum transfer to different layers in a double shell. We also present the details of the development of the NIF cylindrical hohlraum double shell platform including an imaging shell design with a mid-Z inner shell necessary for imaging the inner shell shape and the trajectory with the current 2DConA platform capability. We examine 1D energy transfer between shell layers using trajectory measurements from a series of surrogate targets; the series builds to a complete double shell layer by layer, isolating the physics of each step of the energy transfer process. The measured energy transfer to the foam cushion and the inner shell suggests that our radiation-hydrodynamics simulations capture most of the relevant collision physics. With a 1 MJ laser drive, the experimental data indicate that 22% ± 3% of the ablator kinetic energy couples into inner shell KE, compared to a 27% ± 2% coupling in our xRAGE simulations. Thus, our xRAGE simulations match experimental energy transfer to ∼5%, without inclusion of higher order 2D and 3D effects.

Double shell targets1 on the National Ignition Facility (NIF) provide for an alternative path to a high yield experiment compared to the single shells. The concept of the design is that through kinetic energy transfer between an outer ablator and inner pusher, conditions needed for robust burn can be achieved with a lower convergence ratio and internal temperature compared to a single shell. Due to the multilayer construction of the target, features that can perturb any of the multiple layers of the capsule and degrade target performance are a concern. Understanding the mechanics of these degradations and ways to prevent them is extremely important for a successful design.

Discrepancies exist between theoretical and experimental opacity data for iron, at temperatures 180–195 eV and electron densities near 3 × 1022/cm3, relevant to the solar radiative-convective boundary. Another discrepancy, between theory and helioseismic measurements of the boundary’s location, would be ameliorated if the experimental opacity is correct. To address these issues, this paper details the first results from new experiments under development at the National Ignition Facility (NIF), using a different method to replicate the prior experimental conditions. In the NIF experiments, 64 laser beams indirectly heat a plastic-tamped rectangular iron-magnesium sample inside a gold cavity. Another 64 beams implode a spherical plastic shell to produce a continuum X-ray flash which backlights the hot sample. An X-ray spectrometer records the transmitted X-rays, the unattenuated X-rays passing around the sample, and the sample’s self-emission. From these data, X-ray transmission spectra are inferred, showing Mg K-shell and Fe L-shell X-ray transitions from plasma at a temperature of ~150 eV and electron density of ~8 × 1021/cm3. These conditions are similar to prior Z measurements which agree better with theory. The NIF transmission data show statistical uncertainties of 2–10%, but various systematic uncertainties must be addressed before pursuing quantitative comparisons. The paths to reduction of the largest uncertainties are discussed. Once the uncertainty is reduced, future NIF experiments will probe higher temperatures (170–200 eV) to address the ongoing disagreement between theory and Z data.

A point-projection soft X-ray Opacity Spectrometer (OpSpec) has been implemented to measure X-ray spectra from ∼1 to 2 keV on the National Ignition Facility (NIF). Measurement of such soft X-rays with open-aperture point-projection detectors is challenging because only very thin filters may be used to shield the detector from the hostile environment. OpSpec diffracts X-rays from 540 to 2100 eV off a potassium (or rubidium) acid phthalate (KAP or RbAP) crystal onto either image plates or, most recently, X-ray films. A "sacrificial front filter" strategy is used to prevent crystal damage, while 2 or 3 rear filters protect the data. Since May 2017, OpSpec has been recording X-ray transmission data for iron-magnesium plasmas on the NIF, at "Anchor 1" plasma conditions (temperature ∼150 eV, density ∼7 × 1021 e -/cm3). Upgrades improved OpSpec's performance on 6 NIF shots in August and December 2017, with reduced backgrounds and 100% data return using filter stacks as thin as 2.9 μm (total). Photometric noise is beginning to meet requirements, and further work will reduce systematic errors.