Design of the first fusion experiment to achieve target energy gain G>1.

In this work we present the design of the first controlled fusion laboratory experiment to reach target gain G>1 N221204 (5 December 2022) [Phys. Rev. Lett. 132, 065102 (2024)10.1103/PhysRevLett.132.065102], performed at the National Ignition Facility, where the fusion energy produced (3.15 MJ) exceeded the amount of laser energy required to drive the target (2.05 MJ). Following the demonstration of ignition according to the Lawson criterion N210808, experiments were impacted by nonideal experimental fielding conditions, such as increased (known) target defects that seeded hydrodynamic instabilities or unintentional low-mode asymmetries from nonuniformities in the target or laser delivery, which led to reduced fusion yields less than 1 MJ. This Letter details design changes, including using an extended higher-energy laser pulse to drive a thicker high-density carbon (also known as diamond) capsule, that led to increased fusion energy output compared to N210808 as well as improved robustness for achieving high fusion energies (greater than 1 MJ) in the presence of significant low-mode asymmetries. For this design, the burnup fraction of the deuterium and tritium (DT) fuel was increased (approximately 4% fuel burnup and a target gain of approximately 1.5 compared to approximately 2% fuel burnup and target gain approximately 0.7 for N210808) as a result of increased total (DT plus capsule) areal density at maximum compression compared to N210808. Radiation-hydrodynamic simulations of this design predicted achieving target gain greater than 1 and also the magnitude of increase in fusion energy produced compared to N210808. The plasma conditions and hotspot power balance (fusion power produced vs input power and power losses) using these simulations are presented. Since the drafting of this manuscript, the results of this paper have been replicated and exceeded (N230729) in this design, together with a higher-quality diamond capsule, setting a new record of approximately 3.88MJ of fusion energy and fusion energy target gain of approximately 1.9.

Smoothing tool design and performance during subaperture glass polishing.

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).

Understanding the tool influence function during sub-aperture belt-on-wheel glass polishing.

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.

Understanding and reducing mid-spatial frequency ripples during hemispherical sub-aperture tool glass polishing.

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.

Effect of workpiece curvature on the tool influence function during hemispherical sub-aperture tool glass polishing.

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.

Mechanisms influencing and prediction of tool influence function spots during hemispherical sub-aperture tool polishing on fused silica.

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.

Sapphire advanced mitigation process: wet etch to expose sub-surface damage and increase laser damage resistance and mechanical strength.

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.

Particle damage sources for fused silica optics and their mitigation on high energy laser systems.

High energy laser systems are ultimately limited by laser-induced damage to their critical components. This is especially true of damage to critical fused silica optics, which grows rapidly upon exposure to additional laser pulses. Much progress has been made in eliminating damage precursors in as-processed fused silica optics (the advanced mitigation process, AMP3), and very high damage resistance has been demonstrated in laboratory studies. However, the full potential of these improvements has not yet been realized in actual laser systems. In this work, we explore the importance of additional damage sources-in particular, particle contamination-for fused silica optics fielded in a high-performance laser environment, the National Ignition Facility (NIF) laser system. We demonstrate that the most dangerous sources of particle contamination in a system-level environment are laser-driven particle sources. In the specific case of the NIF laser, we have identified the two important particle sources which account for nearly all the damage observed on AMP3 optics during full laser operation and present mitigations for these particle sources. Finally, with the elimination of these laser-driven particle sources, we demonstrate essentially damage free operation of AMP3 fused silica for ten large optics (a total of 12,000 cm2 of beam area) for shots from 8.6 J/cm2 to 9.5 J/cm2 of 351 nm light (3 ns Gaussian pulse shapes). Potentially many other pulsed high energy laser systems have similar particle sources, and given the insight provided by this study, their identification and elimination should be possible. The mitigations demonstrated here are currently being employed for all large UV silica optics on the National Ignition Facility.

High fluence laser damage precursors and their mitigation in fused silica.

The use of any optical material is limited at high fluences by laser-induced damage to optical surfaces. In many optical materials, the damage results from a series of sources which initiate at a large range of fluences and intensities. Much progress has been made recently eliminating silica surface damage due to fracture-related precursors at relatively low fluences (i.e., less than 10 J/cm(2), when damaged by 355 nm, 5 ns pulses). At higher fluence, most materials are limited by other classes of damage precursors which exhibit a strong threshold behavior and high areal density (>10(5) cm(-2)); we refer to these collectively as high fluence precursors. Here, we show that a variety of nominally transparent materials in trace quantities can act as surface damage precursors. We show that by minimizing the presence of precipitates during chemical processing, we can reduce damage density in silica at high fluence by more than 100 times while shifting the fluence onset of observable damage by about 7 J/cm(2). A better understanding of the complex chemistry and physics of cleaning, rinsing, and drying will likely lead to even further improvements in the damage performance of silica and potentially other optical materials.

Fracture-induced subbandgap absorption as a precursor to optical damage on fused silica surfaces.

The optical damage threshold of indentation-induced flaws on fused silica surfaces was explored. Mechanical flaws were characterized by laser damage testing, as well as by optical, secondary electron, and photoluminescence microscopy. Localized polishing, chemical leaching, and the control of indentation morphology were used to isolate the structural features that limit optical damage. A thin defect layer on fracture surfaces, including those smaller than the wavelength of visible light, was found to be the dominant source of laser damage initiation during illumination with 355 nm, 3 ns laser pulses. Little evidence was found that either displaced or densified material or fluence intensification plays a significant role in optical damage at fluences >35 J/cm(2). Elimination of the defect layer was shown to increase the overall damage performance of fused silica optics.