Achievement of Target Gain Larger than Unity in an Inertial Fusion Experiment

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.

Observations and properties of the first laboratory fusion experiment to exceed a target gain of unity

An indirect-drive inertial fusion experiment on the National Ignition Facility was driven using 2.05 MJ of laser light at a wavelength of 351 nm and produced 3.1±0.16 MJ of total fusion yield, producing a target gain G=1.5±0.1 exceeding unity for the first time in a laboratory experiment [Phys. Rev. E 109, 025204 (2024)10.1103/PhysRevE.109.025204]. Herein we describe the experimental evidence for the increased drive on the capsule using additional laser energy and control over known degradation mechanisms, which are critical to achieving high performance. Improved fuel compression relative to previous megajoule-yield experiments is observed. Novel signatures of the ignition and burn propagation to high yield can now be studied in the laboratory for the first time.

Extended X-ray absorption fine structure of dynamically-compressed copper up to 1 terapascal

Large laser facilities have recently enabled material characterization at the pressures of Earth and Super-Earth cores. However, the temperature of the compressed materials has been largely unknown, or solely relied on models and simulations, due to lack of diagnostics under these challenging conditions. Here, we report on temperature, density, pressure, and local structure of copper determined from extended x-ray absorption fine structure and velocimetry up to 1 Terapascal. These results nearly double the highest pressure at which extended x-ray absorption fine structure has been reported in any material. In this work, the copper temperature is unexpectedly found to be much higher than predicted when adjacent to diamond layer(s), demonstrating the important influence of the sample environment on the thermal state of materials; this effect may introduce additional temperature uncertainties in some previous experiments using diamond and provides new guidance for future experimental design.

X-ray continuum spectroscopy of inertial confinement fusion implosions at the National Ignition Facility

A methodology for measuring x-ray continuum spectra of inertial confinement fusion (ICF) implosions is described. The method relies on the use of ConSpec, a high-throughput spectrometer using a highly annealed pyrolytic graphite crystal [MacDonald et al., J. Instrum. 14, P12009 (2019)], which measures the spectra in the ≃20-30 keV range. Due to its conical shape, the crystal is sagittally focusing a Bragg-reflected x-ray spectrum into a line, which enhances the recorded x-ray emission signal above the high neutron-induced background accompanying ICF implosions at the National Ignition Facility. To improve the overall measurement accuracy, the sensitivity of the spectrometer measured in an off-line x-ray laboratory setting was revised. The error analysis was expanded to include the accuracy of the off-line measurements, the effect of the neutron-induced background, as well as the influence of possible errors in alignment of the instrument to the ICF target. We demonstrate how the improved methodology is applied in the analysis of ConSpec data with examples of a relatively low-neutron-yield implosion using a tritium-hydrogen-deuterium mix as a fuel and a high-yield deuterium-tritium (DT) implosion producing high level of the background. In both cases, the shape of the measured spectrum agrees with the exponentially decaying spectral shape of bremsstrahlung emission to within ±10%. In the case of the high-yield DT experiment, non-monotonic deviations slightly exceeding the measurement uncertainties are observed and discussed.

Design and simulation of multilayer coatings for a multi-channel Wolter-like x-ray imager with large field of view and high resolution

X-ray diagnostics are key instruments for understanding the physics behind inertial confinement fusion experiments. We report on the multilayer design optimization for the Toroidal X-ray Imager (TXI), a hard x-rays microscope instrument designed by Commissariat à l'énergie atomique (CEA) and Laboratoire Charles Fabry (LCF) to be installed on the National Ignition Facility. TXI includes six channels designed for three different energy bands centered on 8.7, 13, and 17.5 keV. Each channel is made up of two toroidal mirrors arranged in a Wolter-like configuration. The required field of view is 800 × 400 µm2, and the resolution should be better than 5 µm. In addition, we seek to estimate the spatial distribution of the temperature, which requires no spectral overlap of the different energy bands and a good spectral homogeneity of the image produced. The development of the multilayer coatings was performed in a two-step method. First, the coatings were optimized to obtain proper energy bands. Then, an x-ray tracing code was used to calculate the integrated optical response of each channel and adjust the response of the mirror to fulfill the requirements. To fulfill all the specifications, we propose an original design using a combination of two aperiodic coatings, one with a narrow bandwidth and the other one with a larger bandwidth.

Dynamics and Power Balance of Near Unity Target Gain Inertial Confinement Fusion Implosions

The change in the power balance, temporal dynamics, emission weighted size, temperature, mass, and areal density of inertially confined fusion plasmas have been quantified for experiments that reach target gains up to 0.72. It is observed that as the target gain rises, increased rates of self-heating initially overcome expansion power losses. This leads to reacting plasmas that reach peak fusion production at later times with increased size, temperature, mass and with lower emission weighted areal densities. Analytic models are consistent with the observations and inferences for how these quantities evolve as the rate of fusion self-heating, fusion yield, and target gain increase. At peak fusion production, it is found that as temperatures and target gains rise, the expansion power loss increases to a near constant ratio of the fusion self-heating power. This is consistent with models that indicate that the expansion losses dominate the dynamics in this regime.

Measurement of Dark Ice-Ablator Mix in Inertial Confinement Fusion

We present measurements of ice-ablator mix at stagnation of inertially confined, cryogenically layered capsule implosions. An ice layer thickness scan with layers significantly thinner than used in ignition experiments enables us to investigate mix near the inner ablator interface. Our experiments reveal for the first time that the majority of atomically mixed ablator material is "dark" mix. It is seeded by the ice-ablator interface instability and located in the relatively cooler, denser region of the fuel assembly surrounding the fusion hot spot. The amount of dark mix is an important quantity as it is thought to affect both fusion fuel compression and burn propagation when it turns into hot mix as the burn wave propagates through the initially colder fuel region surrounding an igniting hot spot. We demonstrate a significant reduction in ice-ablator mix in the hot-spot boundary region when we increase the initial ice layer thickness.

Increased Ion Temperature and Neutron Yield Observed in Magnetized Indirectly Driven D_{2}-Filled Capsule Implosions on the National Ignition Facility

The application of an external 26 Tesla axial magnetic field to a D_{2} gas-filled capsule indirectly driven on the National Ignition Facility is observed to increase the ion temperature by 40% and the neutron yield by a factor of 3.2 in a hot spot with areal density and temperature approaching what is required for fusion ignition [1]. The improvements are determined from energy spectral measurements of the 2.45 MeV neutrons from the D(d,n)^{3}He reaction, and the compressed central core B field is estimated to be ∼4.9  kT using the 14.1 MeV secondary neutrons from the D(T,n)^{4}He reactions. The experiments use a 30 kV pulsed-power system to deliver a ∼3  μs current pulse to a solenoidal coil wrapped around a novel high-electrical-resistivity AuTa_{4} hohlraum. Radiation magnetohydrodynamic simulations are consistent with the experiment.

A new class of variable-radii diffraction optics for high-resolution x-ray spectroscopy at the National Ignition Facility (invited)

A new class of crystal shapes has been developed for x-ray spectroscopy of point-like or small (a few mm) emission sources. These optics allow for dramatic improvement in both achievable energy resolution and total throughput of the spectrometer as compared with traditional designs. This class of crystal shapes, collectively referred to as the Variable-Radii Spiral (VR-Spiral), utilize crystal shapes in which both the major and minor radii are variable. A crystal using this novel VR-Spiral shape has now been fabricated for high-resolution Extended X-ray Absorption Fine Structure (EXAFS) experiments targeting the Pb-L₃ (13.0 keV) absorption edge at the National Ignition Facility. The performance of this crystal has been characterized in the laboratory using a microfocus x-ray source, showing that high-resolution high-throughput EXAFS spectra can be acquired using this geometry. Importantly, these successful tests show that the complex three-dimensional crystal shape is manufacturable with the required precision needed to realize the expected performance of better than 5 eV energy resolution while using a 30 mm high crystal. An improved generalized mathematical form for VR-Spiral shapes is also presented allowing improved optimization as compared to the first sinusoidal-spiral based design. This new formulation allows VR-Spiral spectrometers to be designed at any magnification with optimized energy resolution at all energies within the spectrometer bandwidth.

Lawson Criterion for Ignition Exceeded in an Inertial Fusion Experiment

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. 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 (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion.

Absolute calibration of the conical crystal configuration of the zinc spectrometer (ZSPEC) at the OMEGA laser facility

In this study, we present the absolute calibration of the conical crystal for the zinc spectrometer (ZSPEC), an x-ray spectrometer at the OMEGA laser facility at the Laboratory for Laser Energetics. The ZSPEC was originally designed to measure x-ray Thomson scattering using flat or cylindrically curved highly oriented pyrolytic graphite crystals centered around Zn He-alpha emission at 9 keV. To improve the useful spectral range and collection efficiency of the ZSPEC, a conical highly annealed pyrolytic graphite crystal was fabricated for the ZSPEC. The conically bent crystal in the Hall geometry produces a line focus perpendicular to the spectrometer axis, corresponding to the detector plane of electronic detectors at large scale laser facilities such as OMEGA, extending the useful range of the spectrometer to 7-11 keV. Using data collected using a microfocus Mo x-ray source, we determine important characteristics of ZSPEC such as the dispersion, spatial resolution, and absolute sensitivity of the instrument. A ray-trace model of ZSPEC provides another point of agreement in calculations of the ZSPEC dispersion and crystal response.

The multi-optics high-resolution absorption x-ray spectrometer (HiRAXS) for studies of materials under extreme conditions

We report the development of a high-resolution spectrometer for extended x-ray absorption fine structure (EXAFS) studies of materials under extreme conditions. A curved crystal and detector in the spectrometer are replaceable such that a single body is employed to perform EXAFS measurements at different x-ray energy intervals of interest. Two configurations have been implemented using toroidal crystals with Ge 311 reflection set to provide EXAFS at the Cu K-edge (energy range 8.9-9.8 keV) and Ge 400 reflection set to provide EXAFS at the Ta L3-edge (9.8-10.7 keV). Key performance characteristics of the spectrometer were found to be consistent with design parameters. The data generated at the National Ignition Facility have shown an ≃3 eV spectral resolution for the Cu K-edge configuration and ≃6 eV for the Ta L3-edge configuration.

Design of multilayer-based diagnostics for measurement of high energy x rays and gamma rays

We investigate several possible multilayer-based optic designs for future hard x-ray and gamma ray diagnostics, including the detection and measurement of the positron annihilation radiation at 511 keV. The focus is set on increasing the photon efficiency and signal-to-noise ratio, compared to a previous multilayer-based system that was successfully employed to measure spectra in the 55 keV-100 keV range. Several possible designs using multilayer coatings are discussed, including mirror-based optics and multilayer Laue lenses.

Erratum: Delayed Onset of Nonthermal Melting in Single-Crystal Silicon Pumped with Hard X Rays [Phys. Rev. Lett. 120, 265701 (2018)]

This corrects the article DOI: 10.1103/PhysRevLett.120.265701.

Design and raytrace simulations of a multilayer-coated Wolter x-ray optic for the Z machine at Sandia National Laboratories

Recent breakthroughs in the fabrication of small-radii Wolter optics for astrophysics allow high energy density facilities to consider such optics as novel x-ray diagnostics at photon energies of 15-50 keV. Recently, the Lawrence Livermore National Laboratory, Sandia National Laboratories (SNL), the Smithsonian Astrophysical Observatory, and the NASA Marshall Space Flight Center jointly developed and fabricated the first custom Wolter microscope for implementation in SNL's Z machine with optimized sensitivity at 17.5 keV. To achieve spatial resolution of order 100-200 microns over a field of view of 5 × 5 × 5 mm³ with high throughput and narrow energy bandpass, the geometry of the optic and its multilayer required careful design and optimization. While the geometry mainly influences resolution and the field of view of the diagnostic, the mirror coating determines the spectral response and throughput. Here we outline the details of the design and fabrication process for the first multilayer-coated Wolter I optic for SNL's Z machine (Z Wolter), including its W/Si multilayer, and present results of raytrace simulations completed to predict and verify the performance of the optic.

Characterization and calibration of a multilayer coated Wolter optic for an imager on the Z-machine at Sandia National Laboratories

The need for a time-resolved monochromatic x-ray imaging diagnostic at photon energies >15 keV has motivated the development of a Wolter optic to study x-ray sources on the Z-machine at Sandia National Laboratories. The work is performed in both the LLNL's x-ray calibration facility and SNL's micro-focus x-ray lab. Characterizations and calibrations include alignment, measurement of throughput within the field of view (FOV), the point-spread function within the FOV both in and out of focus, and bandpass in the FOV. These results are compared with ray tracing models, showing reasonable agreement.

A Wolter imager on the Z machine to diagnose warm x-ray sources

A new Wolter x-ray imager has been developed for the Z machine to study the emission of warm (>15 keV) x-ray sources. A Wolter optic has been adapted from observational astronomy and medical imaging, which uses curved x-ray mirrors to form a 2D image of a source with 5 × 5 × 5 mm³ field-of-view and measured 60-300-μm resolution on-axis. The mirrors consist of a multilayer that create a narrow bandpass around the Mo Kα lines at 17.5 keV. We provide an overview of the instrument design and measured imaging performance. In addition, we present the first data from the instrument of a Mo wire array z-pinch on the Z machine, demonstrating improvements in spatial resolution and a 350-4100× increase in the signal over previous pinhole imaging techniques.

Delayed Onset of Nonthermal Melting in Single-Crystal Silicon Pumped with Hard X Rays

In this work, we monitor the onset of nonthermal melting in single-crystal silicon by implementing an x-ray pump-x-ray probe scheme. Using the ultrashort pulses provided by the Linac Coherent Light Source (SLAC) and a custom-built split-and-delay line for hard x rays, we achieve the temporal resolution needed to detect the onset of the transition. Our data show no loss of long-range order up to 150±40  fs from photoabsorption, which we interpret as the time needed for the electronic system to equilibrate at or above the critical nonthermal melting temperature. Once such equilibration is reached, the loss of long-range atomic order proceeds inertially and is completed within 315±40  fs from photoabsorption.

First high-convergence cryogenic implosion in a near-vacuum hohlraum

Recent experiments on the National Ignition Facility [M. J. Edwards et al., Phys. Plasmas 20, 070501 (2013)] demonstrate that utilizing a near-vacuum hohlraum (low pressure gas-filled) is a viable option for high convergence cryogenic deuterium-tritium (DT) layered capsule implosions. This is made possible by using a dense ablator (high-density carbon), which shortens the drive duration needed to achieve high convergence: a measured 40% higher hohlraum efficiency than typical gas-filled hohlraums, which requires less laser energy going into the hohlraum, and an observed better symmetry control than anticipated by standard hydrodynamics simulations. The first series of near-vacuum hohlraum experiments culminated in a 6.8 ns, 1.2 MJ laser pulse driving a 2-shock, high adiabat (α∼3.5) cryogenic DT layered high density carbon capsule. This resulted in one of the best performances so far on the NIF relative to laser energy, with a measured primary neutron yield of 1.8×10(15) neutrons, with 20% calculated alpha heating at convergence ∼27×.

Thin shell, high velocity inertial confinement fusion implosions on the national ignition facility

Experiments have recently been conducted at the National Ignition Facility utilizing inertial confinement fusion capsule ablators that are 175 and 165  μm in thickness, 10% and 15% thinner, respectively, than the nominal thickness capsule used throughout the high foot and most of the National Ignition Campaign. These three-shock, high-adiabat, high-foot implosions have demonstrated good performance, with higher velocity and better symmetry control at lower laser powers and energies than their nominal thickness ablator counterparts. Little to no hydrodynamic mix into the DT hot spot has been observed despite the higher velocities and reduced depth for possible instability feedthrough. Early results have shown good repeatability, with up to 1/2 the neutron yield coming from α-particle self-heating.