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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.

Hot electrons generated by laser-plasma instabilities degrade the performance of laser-fusion implosions by preheating the DT fuel and reducing core compression. The hot-electron energy deposition in the DT fuel has been directly measured for the first time by comparing the hard x-ray signals between DT-layered and mass-equivalent ablator-only implosions. The electron energy deposition profile in the fuel is inferred through dedicated experiments using Cu-doped payloads of varying thickness. The measured preheat energy accurately explains the areal-density degradation observed in many OMEGA implosions. This technique can be used to assess the viability of the direct-drive approach to laser fusion with respect to the scaling of hot-electron preheat with laser energy.

Focusing laser light onto a very small target can produce the conditions for laboratory-scale nuclear fusion of hydrogen isotopes. The lack of accurate predictive models, which are essential for the design of high-performance laser-fusion experiments, is a major obstacle to achieving thermonuclear ignition. Here we report a statistical approach that was used to design and quantitatively predict the results of implosions of solid deuterium-tritium targets carried out with the 30-kilojoule OMEGA laser system, leading to tripling of the fusion yield to its highest value so far for direct-drive laser fusion. When scaled to the laser energies of the National Ignition Facility (1.9 megajoules), these targets are predicted to produce a fusion energy output of about 500 kilojoules-several times larger than the fusion yields currently achieved at that facility. This approach could guide the exploration of the vast parameter space of thermonuclear ignition conditions and enhance our understanding of laser-fusion physics.

This corrects the article DOI: 10.1103/PhysRevLett.119.175702.

Nanosecond in situ x-ray diffraction and simultaneous velocimetry measurements were used to determine the crystal structure and pressure, respectively, of ramp-compressed aluminum at stress states between 111 and 475 GPa. The solid-solid Al phase transformations, fcc-hcp and hcp-bcc, are observed at 216±9 and 321±12  GPa, respectively, with the bcc phase persisting to 475 GPa. The high-pressure crystallographic texture of the hcp and bcc phases suggests close-packed or nearly close-packed lattice planes remain parallel through both transformations.

Collective Thomson scattering is a technique for measuring the plasma conditions in laser-plasma experiments. Simultaneous measurements of ion-acoustic and electron plasma-wave spectra were obtained using a 263.25-nm Thomson-scattering probe beam. A fully reflective collection system was used to record light scattered from electron plasma waves at electron densities greater than 10 21 cm -3 , which produced scattering peaks near 200 nm. An accurate analysis of the experimental Thomson-scattering spectra required accounting for plasma gradients, instrument sensitivity, optical effects, and background radiation. Practical techniques for including these effects when fitting Thomson-scattering spectra are presented and applied to the measured spectra to show the improvements in plasma characterization.

A record fuel hot-spot pressure P_{hs}=56±7  Gbar was inferred from x-ray and nuclear diagnostics for direct-drive inertial confinement fusion cryogenic, layered deuterium-tritium implosions on the 60-beam, 30-kJ, 351-nm OMEGA Laser System. When hydrodynamically scaled to the energy of the National Ignition Facility, these implosions achieved a Lawson parameter ∼60% of the value required for ignition [A. Bose et al., Phys. Rev. E 93, 011201(R) (2016)], similar to indirect-drive implosions [R. Betti et al., Phys. Rev. Lett. 114, 255003 (2015)], and nearly half of the direct-drive ignition-threshold pressure. Relative to symmetric, one-dimensional simulations, the inferred hot-spot pressure is approximately 40% lower. Three-dimensional simulations suggest that low-mode distortion of the hot spot seeded by laser-drive nonuniformity and target-positioning error reduces target performance.

Multilayer direct-drive inertial-confinement-fusion targets are shown to significantly reduce two-plasmon decay (TPD) driven hot-electron production while maintaining high hydrodynamic efficiency. Implosion experiments on the OMEGA laser used targets with silicon layered between an inner beryllium and outer silicon-doped plastic ablator. A factor-of-5 reduction in hot-electron generation (>50  keV) was observed in the multilayer targets relative to pure CH targets. Three-dimensional simulations of the TPD-driven hot-electron production using a laser-plasma interaction code (lpse) that includes nonlinear and kinetic effects show good agreement with the measurements. The simulations suggest that the reduction in hot-electron production observed in the multilayer targets is primarily caused by increased electron-ion collisional damping.

Clear evidence of the transition from hydrodynamiclike to strongly kinetic shock-driven implosions is, for the first time, revealed and quantitatively assessed. Implosions with a range of initial equimolar D3He gas densities show that as the density is decreased, hydrodynamic simulations strongly diverge from and increasingly overpredict the observed nuclear yields, from a factor of ∼2 at 3.1  mg/cm3 to a factor of 100 at 0.14  mg/cm3. (The corresponding Knudsen number, the ratio of ion mean-free path to minimum shell radius, varied from 0.3 to 9; similarly, the ratio of fusion burn duration to ion diffusion time, another figure of merit of kinetic effects, varied from 0.3 to 14.) This result is shown to be unrelated to the effects of hydrodynamic mix. As a first step to garner insight into this transition, a reduced ion kinetic (RIK) model that includes gradient-diffusion and loss-term approximations to several transport processes was implemented within the framework of a one-dimensional radiation-transport code. After empirical calibration, the RIK simulations reproduce the observed yield trends, largely as a result of ion diffusion and the depletion of the reacting tail ions.

Using a spherically bent quartz crystal for the Si He(α) line at ~1.865 keV, a narrowband x-ray imager has been deployed at the Omega Laser Facility to record backlit images of direct-drive laser implosions. The crystal was cut along the 1011 planes for a 2d spacing of 0.687 nm, resulting in a Bragg angle of 83.9°. Apertures in front of the crystal were used to control the astigmatism of the imaging system. The backlit images show a high signal-to-background ratio of >10:1 with backlighter laser energies ≥1.5 kJ at a 10-ps pulse duration and a spatial resolution of better than 20 μm.

Measurements of the D(d,p)T (dd) and T(t,2n)(4)He (tt) reaction yields have been compared with those of the D(t,n)(4)He (dt) reaction yield, using deuterium-tritium gas-filled inertial confinement fusion capsule implosions. In these experiments, carried out on the OMEGA laser, absolute spectral measurements of dd protons and tt neutrons were obtained. From these measurements, it was concluded that the dd yield is anomalously low and the tt yield is anomalously high relative to the dt yield, an observation that we conjecture to be caused by a stratification of the fuel in the implosion core. This effect may be present in ignition experiments planned on the National Ignition Facility.

A spectroscopic method is discussed to measure core and compressed-shell conditions in thick-wall plastic-shell implosions filled with deuterium and a tracer amount of argon. Simultaneous observation over a broad photon energy range of the argon line emission and the attenuation and self-emission effects of the compressed shell confining the core yields enough information to extract average temperature and density conditions in both core and compressed shell. The spectroscopic analysis also provides an estimate of the target areal density which is an important characteristic of inertial confinement fusion implosions.

Thin-foil targets were irradiated with high-power (1 ≤ P(L) ≤ 210 TW), 10-ps pulses focused to intensities of I>10(18) W/cm(2) and studied with K-photon spectroscopy. Comparing the energy emitted in K photons to target-heating calculations shows a laser-energy-coupling efficiency to hot electrons of η(L-e) = 20 ± 10%. Time-resolved x-ray emission measurements suggest that laser energy is coupled to hot electrons over the entire duration of the incident laser drive. Comparison of the K-photon emission data to previous data at similar laser intensities shows that η(L-e) is independent of laser-pulse duration from 1 ≤ τ(p) ≤ 10 ps.

We present results from the spectral postprocessing of a one-dimensional hydrodynamic simulation of an argon-doped, warm-shell shock-ignition implosion with a detailed atomic and radiation physics model. The argon tracer is added to the deuterium filling in the core for diagnostic purposes. Spectral features in the emergent intensity distribution in the photon energy range of the argon K-shell spectrum that have potential for diagnostic application are discussed.

Direct-drive implosions with 20-microm-thick glass shells were conducted on the Omega Laser Facility to test the performance of high-Z glass ablators for direct-drive, inertial confinement fusion. The x-ray signal caused by hot electrons generated by two-plasmon-decay instability was reduced by more than approximately 40x and hot-electron temperature by approximately 2x in the glass compared to plastic ablators at ignition-relevant drive intensities of approximately 1x10(15) W/cm2, suggesting reduced target preheat. The measured absorption and compression were close to 1D predictions. The measured soft x-ray production in the spectral range of approximately 2 to 4 keV was approximately 2x to 3x lower than 1D predictions, indicating that the shell preheat caused by soft x-rays is less than predicted. A direct-drive-ignition design based on glass ablators is introduced.

The Rayleigh-Taylor (RT) growth of 3D broadband nonuniformities was measured using x-ray radiography in spherical plastic shells accelerated by laser light at an intensity of approximately 2 x 10(14) W/cm(2). The 20- and 24-microm-thick spherical shells were imploded with 54 beams on the OMEGA laser system. The shells contained diagnostic openings for backlighter x rays used to image shell modulations. The measured shell trajectories and modulation RT growth were in fair agreement with 2D hydro simulations during the acceleration phase of the implosions with convergence ratios of up to approximately 2.2. Since the ignition designs rely on these simulations, improvements in the numerical codes will be implemented to achieve better agreement with experiments.

Expressions for the yield of electron-positron pairs, their energy spectra, and production rates have been obtained in the interaction of multi-kJ pulses of high-intensity laser light interacting with solid targets. The Bethe-Heitler conversion of hard x-ray bremsstrahlung [D. A. Gryaznykh, Y. Z. Kandiev, and V. A. Lykov, JETP Lett. 67, 257 (1998); K. Nakashima and H. Takabe, Phys. Plasmas 9, 1505 (2002)] is shown to dominate over direct production (trident process) [E. P. Liang, S. C. Wilks, and M. Tabak, Phys. Rev. Lett. 81, 4887 (1998)]. The yields and production rates have been optimized as a function of incident laser intensity by the choice of target material and dimensions, indicating that up to 5 x 10 (11) pairs can be produced on the OMEGA EP laser system [L. J. Waxer, Opt. Photonics News 16, 30 (2005)]. The corresponding production rates are high enough to make possible the creation of a pair plasma.

The fuel layer density of an imploding laser-driven spherical shell is inferred from framed x-ray radiographs. The density distribution is determined by using Abel inversion to compute the radial distribution of the opacity kappa from the observed optical depth tau. With the additional assumption of the mass of the remaining fuel, the absolute density distribution is determined. This is demonstrated on the OMEGA laser system with two x-ray backlighters of different mean energies that lead to the same inferred density distribution independent of backlighter energy.

Detailed analysis of x-ray narrow-band images from argon-doped deuterium-filled inertial confinement fusion implosion experiments yields information about the temperature spatial structure in the core at the collapse of the implosion. We discuss the analysis of direct-drive implosion experiments at OMEGA, in which multiple narrow-band images were recorded with a multimonochromatic x-ray imaging instrument. The temperature spatial structure is investigated by using the sensitivity of the Ly beta/He beta line emissivity ratio to the temperature. Three analysis methods that consider the argon He beta and Ly beta image data are discussed and the results compared. The methods are based on a ratio of image intensities, ratio of Abel-inverted emissivities, and a search and reconstruction technique driven by a Pareto genetic algorithm.

We discuss the observation and data analysis of argon K-shell line spectra from argon-doped deuterium-filled OMEGA direct-drive implosion cores based on data recorded with two streaked crystal spectrometers. The targets were 870 microm in diameter, 27 microm wall thickness plastic shells filled with 20 atm of deuterium gas, and a tracer amount of argon for diagnostic purposes. The argon K-shell line spectrum is primarily emitted at the collapse of the implosion and its analysis provides a spectroscopic diagnostic of the core implosion conditions. The observed spectra includes the He alpha, Ly alpha, He beta, He gamma, Ly beta, and Ly gamma line emissions and their associated He- and Li-like satellites thus covering a broad photon energy range from 3100 to 4200 eV with a spectral resolution power of approximately 500. The data analysis relies on detailed atomic and spectral models that take into account nonequilibrium collisional-radiative atomic kinetics, Stark-broadened line shapes, and radiation transport calculations.

The first observation of ignition-relevant areal-density deuterium from implosions of capsules with cryogenic fuel layers at ignition-relevant adiabats is reported. The experiments were performed on the 60-beam, 30-kJUV OMEGA Laser System [T. R. Boehly, Opt. Commun. 133, 495 (1997)10.1016/S0030-4018(96)00325-2]. Neutron-averaged areal densities of 202+/-7 mg/cm2 and 182+/-7 mg/cm2 (corresponding to estimated peak fuel densities in excess of 100 g/cm3) were inferred using an 18-kJ direct-drive pulse designed to put the converging fuel on an adiabat of 2.5. These areal densities are in good agreement with the predictions of hydrodynamic simulations indicating that the fuel adiabat can be accurately controlled under ignition-relevant conditions.

The compression of direct-drive, spherical implosions is studied using cryogenic D2 targets on the 60-beam, 351-nm OMEGA laser with intensities ranging from approximately 3x10(14) to approximately 1x10(15) W/cm2. The hard-x-ray signal from hot electrons generated by laser-plasma instabilities increases with laser intensity, while the areal density decreases. Mitigating hot-electron production, by reducing the laser intensity to approximately 3x10(14) W/cm2, results in areal density of the order of approximately 140 mg/cm2, in good agreement with 1D simulations. These results will be considered in future direct-drive-ignition designs.

A distinctive way of quantitatively imaging inertial fusion implosions has resulted in the characterization of two different types of electromagnetic configurations and in the measurement of the temporal evolution of capsule size and areal density. Radiography with a pulsed, monoenergetic, isotropic proton source reveals field structures through deflection of proton trajectories, and areal densities are quantified through the energy lost by protons while traversing the plasma. The two field structures consist of (i) many radial filaments with complex striations and bifurcations, permeating the entire field of view, of magnetic field magnitude 60 tesla and (ii) a coherent, centrally directed electric field of order 10(9) volts per meter, seen in proximity to the capsule surface. Although the mechanism for generating these fields is unclear, their effect on implosion dynamics is potentially consequential.

In the field of inertial confinement fusion (ICF), work has been consistently progressing in the past decade toward a more fundamental understanding of the plasma conditions in ICF implosion cores. The research presented here represents a substantial evolution in the ability to diagnose plasma temperatures and densities, along with characteristics of mixing between fuel and shell materials. Mixing is a vital property to study and quantify, since it can significantly affect implosion quality. We employ a number of new spectroscopic techniques that allow us to probe these important quantities. The first technique developed is an emissivity analysis, which uses the emissivity ratio of the optically thin Lybeta and Hebeta lines to spectroscopically extract temperature profiles, followed by the solution of emissivity equations to infer density profiles. The second technique, an intensity analysis, models the radiation transport through the implosion core. The nature of the intensity analysis allows us to use an optically thick line, the Lyalpha, to extract information on mixing near the core edge. With this work, it is now possible to extract directly from experimental data not only detailed temperature and density maps of the core, but also spatial mixing profiles.

The Rayleigh-Taylor unstable growth of laser-seeded, 3D broadband perturbations was experimentally measured in the laser-accelerated, planar plastic foils. The first experimental observation showing the self-similar behavior of the bubble size and amplitude distributions under ablative conditions is presented. In the nonlinear regime, the modulation sigma(rms) grows as alpha(sigma)gt(2), where g is the foil acceleration, t is the time, and alpha(sigma) is constant. The number of bubbles evolves as N(t) alpha(omegat sq.rt(9) + C)(-4) and the average size evolves as (t) alpha omega(2)gt(2), where C is a constant and omega = 0.83 +/- 0.1 is the measured scaled bubble-merging rate.

Nonlinear growth of 3D broadband nonuniformities was measured near saturation levels using x-ray radiography in planar foils accelerated by laser light. The initial target modulations were seeded by laser nonuniformities and later amplified during acceleration by Rayleigh-Taylor instability. The nonlinear saturation velocities are measured for the first time and are found to be in excellent agreement with Haan predictions. The measured growth of long-wavelength modes is consistent with enhanced, nonlinear, long-wavelength generation in ablatively driven targets.

Target areal density (rhoR) asymmetries in OMEGA direct-drive spherical implosions are studied. The rms variation / for low-mode-number structure is approximately proportional to the rms variation of on-target laser intensity / with an amplification factor of approximately 1/2(C(r)-1), where C(r) is the capsule convergence ratio. This result has critical implications for future work on the National Ignition Facility as well as OMEGA.