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 tool influence function (TIF) during sub-aperture belt-on-wheel polishing has been evaluated as a function of various process conditions (belt use/wear, dwell time, displacement, belt velocity, and wheel modulus and diameter) on fused silica glass workpieces using C e O 2 polishing media. TIF spots are circular or elliptical in shape with a largely flat bottom character. The volumetric removal rate varies significantly with belt use (or wear), stabilizing after ∼15m i n of use. A modified Preston model, where the pressure dependence is adjusted using a different scaling of the wheel modulus (E w0.5), largely predicts the volumetric removal rate over the range of process conditions evaluated. The relatively high volumetric removal rate of 30-60m m 3/h using a fixed C e O 2-in-resin-host belt offers a rapid, and hence, more economical, initial polish of aspheric and freeform optics.

During subaperture tool grinding and polishing, overlaps of the tool influence function can result in undesirable mid-spatial frequency (MSF) errors in the form of surface ripples, which are often corrected using a smoothing polishing step. In this study, flat multi-layer smoothing polishing tools are designed and tested to simultaneously (1) reduce or remove MSF errors, (2) minimize surface figure degradation, and (3) maximize the material removal rate. A time-dependent convergence model in which spatial material removal varies with a workpiece-tool height mismatch, combined with a finite element mechanical analysis to determine the interface contact pressure distribution, was developed to evaluate various smoothing tool designs as a function of tool material properties, thicknesses, pad textures, and displacements. An improvement in smoothing tool performance is achieved when the gap pressure constant, h¯ (which describes the inverse rate at which the pressure drops with a workpiece-tool height mismatch), is minimized for smaller spatial scale length surface features (namely, MSF errors) and maximized for large spatial scale length features (i.e., surface figure). Five specific smoothing tool designs were experimentally evaluated. A two-layer smoothing tool using a thin, grooved IC1000 polyurethane pad (with a high elastic modulus, E p a d =360M P a), thicker blue foam (with an intermediate modulus, E f o a m =5.3M P a) underlayer, and an optimized displacement (d t=1m m) provided the best overall performance (namely, high MSF error convergence, minimal surface figure degradation, and high material removal rate).

During sub-aperture tool polishing of glass optics, mid-spatial surface ripples are generated because of material removal non-uniformities during tool linear translation (resulting in feed ripples) and tool pathway step overlaps (resulting in pitch ripples). A variety of tool influence function (TIF) spots, trenches, and patches were created to understand and minimize such ripples on fused silica workpieces after polishing with cerium oxide slurry using a rotating hemispherical pad-foam tool. The feed ripple amplitude can be decreased by reducing the non-uniformities in the pad texture and/or by minimizing a derived feed ripple metric (rf=Vmax0.5Vf/Rt) via adjustments in processing parameters. Pitch ripples can be minimized by reducing relative step distance to spot radius ratio (xs/at) and by achieving a flat bottom trench shape cross section or by reducing the material removal per pass. Using the combined methods, an overall ripple error of ∼1.2nm rms has been achieved.

The influence of workpiece curvature on the tool influence function spot during polishing of fused silica glass with cerium oxide slurry, while using a rotating hemispherical pad-foam tool for a wide variety of process conditions (tool displacement, inclination angle, and rotation rate), has been investigated. (Workpiece curvature ranged from 500 mm radius concave to 43 mm radius convex.) The TIF spot decreases in diameter and increases in the peak removal rate on more convex workpieces. In contrast, the TIF spot increases both in diameter and peak removal rate on more concave workpieces. For the range of workpiece curvatures investigated, both the spot size and the peak removal rate changed significantly, as much as 2 times. An elastic sphere-sphere contact mechanics model, which utilizes both a modified displacement (that leads to a change in the applied load) as well as a mismatch factor (that influences the pressure distribution shape), has been developed. The model was validated using both offline load-displacement measurements and finite-element analysis simulations. The model quantitatively describes the measured change in the relative contact diameter and relative pressure distribution, as well as semiquantitively describes the change in the relative volumetric removal rate on a large variety of TIF spots. The change in the volumetric removal rate for convex workpieces is a result of the balance between a decreasing spot size (reducing removal) and an increasing peak pressure (increasing removal), which usually results in relatively small changes in volumetric removal. In the case of concave workpieces, the volumetric removal rate change is also governed by a similar balance, but the spot size increase contribution dominates, resulting in a significant increase in volumetric removal rate. Understanding these trends can enable methods to add greater determinism during the fabrication of freeform optics by adjusting polishing parameters (such as dwell time) while the tool translates along a workpiece surface with different local curvatures.

Sub-aperture tool polishing of precision optics requires a detailed understanding of the local material removal [tool influence function (TIF)] at the contact spot between the workpiece and tool to achieve high removal determinism and hence precision of the optic relative to the desired/design surface figure. In this study, the mechanisms influencing and the quantitative prediction of the removal rate and shape of TIF spots during polishing of fused silica glass with cerium oxide slurry using a rotating hemispherical pad-foam tool for a wide variety of process conditions (including tool properties, kinematics, and applied displacements) are investigated. The TIF volumetric removal rate can be estimated utilizing the average relative velocity and contact area using a simple analytical model. In addition, stability of the volumetric removal rate for fixed process conditions is shown to be greatly dependent on the pad preparation and amount of tool use (affecting both pad topography and slurry buildup), whose general behavior shows an increase in removal rate followed by stabilization with polishing time. The determination of the TIF removal shape is more complex. An extended version of the Preston removal model is developed to explain a comprehensive set of measured TIF removal shapes to within ∼22%. This model incorporates a number of phenomena impacting the TIF removal shape including: (a) temporal and spatial dependent relative velocity between the workpiece and tool; (b) an elastic mechanics based, as well as hydrodynamic, pressure distribution; (c) a spatially dependent friction coefficient possibly caused by both reduced slurry replenishment in low velocity regions and pad slurry islands (100 µm scale) and porosity (millimeter scale); and (d) a shear-based removal mechanism on the periphery of the contact spot.

A novel, to the best of our knowledge, method of wet chemical etching of sapphire workpieces (such as optics, wafers, windows, and cones), called the sapphire advanced mitigation process (or sapphire AMP), has been developed that exposes sub-surface mechanical damage created during the optical fabrication process and significantly enhances the surface laser damage resistance ($ \gt {2{\times}}$>2×) and mechanical strength (up to $\sim{2.6{\times}}$∼2.6×). Sapphire AMP involves first treating the workpiece with a mixture of sulfuric and phosphoric acid $([{\rm H_{2}{\rm SO_{4}}}]:[{\rm H_{3}{\rm PO_{4}}}]=1:3)$([H2SO4]:[H3PO4]=1:3) at 220°C, followed with phosphoric acid at 160°C, then with sodium hydroxide base (NaOH) and surfactant at 40°C, and finally with a high-pressure deionized water spray rinse. Sapphire AMP has been demonstrated on both A- and C-plane sapphire workpieces. The mechanism of this etch process involves the reaction of the sapphire $({\rm Al_{2}}{\rm O_{3}})$(Al2O3) surface with sulfuric acid $({\rm H_{2}}{\rm SO_{4}})$(H2SO4) forming aluminum sulfate $[{{\rm Al}_2}{({{\rm SO}_4})_3}]$[Al2(SO4)3], which has low solubility. The high phosphoric acid content in the first and second steps of sapphire AMP results in the efficient conversion of ${{\rm Al}_2}{({{\rm SO}_4})_3}$Al2(SO4)3 to aluminum phosphate $({\rm AlPO_{4}})$(AlPO4), which is very soluble, greatly reducing reaction product redeposition on the workpiece surface. Sapphire AMP is shown to expose sub-surface mechanical damage on the sapphire surface created during the grinding and polishing processes, whose etched morphology has either isotropic or anisotropic evolution depending on the nature of the initial surface damage. Sapphire AMP was also designed to remove the key known surface, laser absorbing precursors (namely, foreign chemical impurities, the fracture surface layer of preexisting sub-surface damage, and reaction product or foreign species redeposition or precipitation). Static and sliding indention induced surface microfractures on sapphire are shown after sapphire AMP to have a significant decrease in the fast photoluminescence intensity (a known metric for measuring the degree of laser damaging absorbing precursors). In addition, the onset of laser damage (at 351 nm 3 ns) on sapphire AMP treated workpieces was shown to increase in fluence from $\sim{4}$∼4 to $ \gt {9}.{5}\;{{\rm J/cm}^2}$>9.5J/cm2. Finally, biaxial ball-on-ring mechanical tests on sapphire disks showed an increase in the failure stress from 340 MPa (with pre-existing 28 µm flaws) to $\sim{900}\;{\rm MPa}$∼900MPa after sapphire AMP, which is attributed to the blunting of the surface microfractures.

We have demonstrated the world's highest average power, fully diode-pumped, petawatt-class peak power laser, the High-repetition-rate Advanced Petawatt Laser System (HAPLS) [1-3]. These first commissioning results at 16J (stretched) at 3%Hz fully validate projected performance of 30J/30fs (>1PW) at 10Hz. The laser has been operated at this intermediate level at Lawrence Livermore National Laboratory to demonstrate integrated performance of all subsystems and provide benchmarking data to laser performance models before further increasing energy and peak power. Data was obtained during multiple campaigns, exceeding several hours of run time, and a snapshot of 60min of data is shown in Fig. 1. The average pump laser 1ω (1053nm) energy was 97J with an rms stability of 0.7%, 2ω (527nm) energy at the Ti:sapphire power amplifier was 62J, and the average stretched short pulse energy was 16J. A full-aperture diagnostic suite allows simultaneous, single-shot measurement of energy, spectrum, beam quality, and pulse duration at full repetition rate. Single-shot SPIDER retrieved pulse shapes (Fig. 1 inset) with an average pulse duration over 12000 consecutive shots of 28.6fs (rms=1.4fs). The mean pulse duration is consistent with the measured spectral bandwidth and is ∼1.2× the transform limit. All results shown are raw data without filtering or averaging, demonstrating the exceptional pulse characteristics, repeatability, and stability of the entire laser system.

Large laser systems that deliver optical pulses with peak powers exceeding one Petawatt (PW) have been constructed at dozens of research facilities worldwide and have fostered research in High-Energy-Density (HED) Science, High-Field and nonlinear physics [1]. Furthermore, the high intensities exceeding 1018W/cm2 allow for efficiently driving secondary sources that inherit some of the properties of the laser pulse, e.g. pulse duration, spatial and/or divergence characteristics. In the intervening decades since that first PW laser, single-shot proof-of-principle experiments have been successful in demonstrating new high-intensity laser-matter interactions and subsequent secondary particle and photon sources. These secondary sources include generation and acceleration of charged-particle (electron, proton, ion) and neutron beams, and x-ray and gamma-ray sources, generation of radioisotopes for positron emission tomography (PET), targeted cancer therapy, medical imaging, and the transmutation of radioactive waste [2, 3]. Each of these promising applications requires lasers with peak power of hundreds of terawatt (TW) to petawatt (PW) and with average power of tens to hundreds of kW to achieve the required secondary source flux.

The HAPLS laser system has been commissioned to its first integrated performance milestone, delivering laser pulses with 16J sub-30fs duration at a 3⅓Hz repetition rate. This first all-diode-pumped petawatt-class laser offers the average powers required for secondary source applications.

A novel finishing process, called Convergent Polishing, is described where the workpiece regardless of its initial shape will converge to final surface figure under a fixed, unchanging set of polishing parameters in a single iteration.

The effects of HF/NH4F, wet chemical etching on the morphology of individual surface fractures (indentations, scratches) and of an ensemble of surface fractures (ground surfaces) on fused silica glass has been characterized. For the individual surface fractures, a series of static or dynamic (sliding) Vickers and Brinnell indenters were used to create radial, lateral, Hertzian cone and trailing indentation fractures on a set of polished fused silica substrates which were subsequently etched. After short etch times, the visibility of both surface and subsurface cracks is significantly enhanced when observed by optical microscopy. This is attributed to the increased width of the cracks following etching, allowing for greater optical scatter at the fracture interface. The removal of material during etching was found to be isotropic except in areas where the etchant has difficulty penetrating or in areas that exhibit significant plastic deformation/densification. Isolated fractures continue to etch, but will never be completely removed since the bottom and top of the crack both etch at the same rate. The etching behavior of ensembles of closely spaced cracks, such as those produced during grinding, has also been characterized. This was done using a second set of fused silica samples that were ground using either fixed or loose abrasives. The resulting samples were etched and both the etch rate and the morphology of the surfaces were monitored as a function of time. Etching results in the formation of a series of open cracks or cusps, each corresponding to the individual fractures originally on the surface of the substrate. During extended etching, the individual cusps coalesce with one another, providing a means of reducing the depth of subsurface damage and the peak-to-valley roughness. In addition, the material removal rate of the ground surfaces was found to scale with the surface area of the cracks as a function of etch time. The initial removal rate for the ground surface was typically 3.5× the bulk etch rate. The evolving morphology of ground surfaces during etching was simulated using an isotropic finite difference model. This model illustrates the importance that the initial distributions of fracture sizes and spatial locations have on the evolution of roughness and the rate at which material is removed during the etching process. The etching of ground surfaces can be used during optical fabrication to convert subsurface damage into surface roughness thereby reducing the time required to produce polished surfaces that are free of subsurface damage.

The effects of kinematics and lap viscoelastic properties have been quantitatively correlated to a revised Preston Model by monitoring the surface figure and material removal rate during fused silica polishing (ceria on pad or pitch).

The distribution and characteristics of surface cracks (i.e., sub-surface damage or scratching) on fused silica formed during grinding/polishing resulting from the addition of rogue particles in the base slurry has been investigated. Fused silica samples (10 cm diameter × 1 cm thick) were: (1) ground by loose abrasive grinding (alumina particles 9–30 μm) on a glass lap with the addition of larger alumina particles at various concentrations with mean sizes ranging from 15 to 30 μm, or (2) polished (using 0.5 μm cerium oxide slurry) on various laps (polyurethane pads or pitch) with the addition of larger rogue particles (diamond (4–45 μm), pitch, dust, or dried Ceria slurry agglomerates) at various concentrations. For the resulting ground samples, the crack distributions of the as-prepared surfaces were determined using a polished taper technique. The crack depth was observed to: (1) increase at small concentrations (>10−4 fraction) of rogue particles; and (2) increase with rogue particle concentration to crack depths consistent with that observed when grinding with particles the size of the rogue particles alone. For the polished samples, which were subsequently etched in HF:NH4F to expose the surface damage, the resulting scratch properties (type, number density, width, and length) were characterized. The number density of scratches increased exponentially with the size of the rogue diamond at a fixed rogue diamond concentration suggesting that larger particles are more likely to lead to scratching. The length of the scratch was found to increase with rogue particle size, increase with lap viscosity, and decrease with applied load. At high diamond concentrations, the type of scratch transitioned from brittle to ductile and the length of the scratches dramatically increased and extended to the edge of the optic. The observed trends can be explained semi-quantitatively in terms of the time needed for a rogue particle to penetrate into a viscoelastic lap. The results of this study provide useful insights and ‘rules-of-thumb’ relating scratch characteristics observed on surfaces during optical glass fabrication to the characteristics of the rogue particles causing them and their possible source.

The distribution and characteristics of surface cracking (i.e., sub-surface damage or SSD) formed during standard grinding processes have been measured on fused silica glass using a surface taper polishing technique. The measured SSD depth distributions are described by a single exponential followed by an asymptotic cutoff in depth. The observed surface cracks are characterized as near-surface lateral and deeper trailing indent type fractures (i.e., chatter marks). The length of the trailing indent is strongly correlated with a given grinding process. It is shown that only a small fraction of the abrasive particles are being mechanically loaded and causing fracture, and most likely it is the larger particles in the abrasive particle size distribution that bear the higher loads. The SSD depth increased with load and with a small amount of larger contaminant particles. Using a simple brittle fracture model for grinding, the SSD depth distribution has been related to the SSD length distribution to gain insight into ‘effective’ size distribution of particles participating in the fracture. Both the average crack length and the surface roughness were found to scale linearly with the maximum SSD depth. These relationships can serve as useful rules-of-thumb for non-destructively estimating SSD depth and for identifying the process that caused the SSD.