Burning plasma achieved in inertial fusion.

Obtaining a burning plasma is a critical step towards self-sustaining fusion energy1. A burning plasma is one in which the fusion reactions themselves are the primary source of heating in the plasma, which is necessary to sustain and propagate the burn, enabling high energy gain. After decades of fusion research, here we achieve a burning-plasma state in the laboratory. These experiments were conducted at the US National Ignition Facility, a laser facility delivering up to 1.9 megajoules of energy in pulses with peak powers up to 500 terawatts. We use the lasers to generate X-rays in a radiation cavity to indirectly drive a fuel-containing capsule via the X-ray ablation pressure, which results in the implosion process compressing and heating the fuel via mechanical work. The burning-plasma state was created using a strategy to increase the spatial scale of the capsule2,3 through two different implosion concepts4-7. These experiments show fusion self-heating in excess of the mechanical work injected into the implosions, satisfying several burning-plasma metrics3,8. Additionally, we describe a subset of experiments that appear to have crossed the static self-heating boundary, where fusion heating surpasses the energy losses from radiation and conduction. These results provide an opportunity to study α-particle-dominated plasmas and burning-plasma physics in the laboratory.

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.

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.

The impact of low-mode symmetry on inertial fusion energy output in the burning plasma state.

Indirect Drive Inertial Confinement Fusion Experiments on the National Ignition Facility (NIF) have achieved a burning plasma state with neutron yields exceeding 170 kJ, roughly 3 times the prior record and a necessary stage for igniting plasmas. The results are achieved despite multiple sources of degradations that lead to high variability in performance. Results shown here, for the first time, include an empirical correction factor for mode-2 asymmetry in the burning plasma regime in addition to previously determined corrections for radiative mix and mode-1. Analysis shows that including these three corrections alone accounts for the measured fusion performance variability in the two highest performing experimental campaigns on the NIF to within error. Here we quantify the performance sensitivity to mode-2 symmetry in the burning plasma regime and apply the results, in the form of an empirical correction to a 1D performance model. Furthermore, we find the sensitivity to mode-2 determined through a series of integrated 2D radiation hydrodynamic simulations to be consistent with the experimentally determined sensitivity only when including alpha-heating.

Measurement of high-pressure shock waves in cryogenic deuterium-tritium ice layered capsule implosions on NIF.

The first measurements of multiple, high-pressure shock waves in cryogenic deuterium-tritium (DT) ice layered capsule implosions on the National Ignition Facility have been performed. The strength and relative timing of these shocks must be adjusted to very high precision in order to keep the DT fuel entropy low and compressibility high. All previous measurements of shock timing in inertial confinement fusion implosions [T. R. Boehly et al., Phys. Rev. Lett. 106, 195005 (2011), H. F. Robey et al., Phys. Rev. Lett. 108, 215004 (2012)] have been performed in surrogate targets, where the solid DT ice shell and central DT gas regions were replaced with a continuous liquid deuterium (D2) fill. This report presents the first experimental validation of the assumptions underlying this surrogate technique.

Onset of hydrodynamic mix in high-velocity, highly compressed inertial confinement fusion implosions.

Deuterium-tritium inertial confinement fusion implosion experiments on the National Ignition Facility have demonstrated yields ranging from 0.8 to 7×10(14), and record fuel areal densities of 0.7 to 1.3 g/cm2. These implosions use hohlraums irradiated with shaped laser pulses of 1.5-1.9 MJ energy. The laser peak power and duration at peak power were varied, as were the capsule ablator dopant concentrations and shell thicknesses. We quantify the level of hydrodynamic instability mix of the ablator into the hot spot from the measured elevated absolute x-ray emission of the hot spot. We observe that DT neutron yield and ion temperature decrease abruptly as the hot spot mix mass increases above several hundred ng. The comparison with radiation-hydrodynamic modeling indicates that low mode asymmetries and increased ablator surface perturbations may be responsible for the current performance.

Early-time symmetry tuning in the presence of cross-beam energy transfer in ICF experiments on the National Ignition Facility.

On the National Ignition Facility, the hohlraum-driven implosion symmetry is tuned using cross-beam energy transfer (CBET) during peak power, which is controlled by applying a wavelength separation between cones of laser beams. In this Letter, we present early-time measurements of the instantaneous soft x-ray drive at the capsule using reemission spheres, which show that this wavelength separation also leads to significant CBET during the first shock, even though the laser intensities are 30× smaller than during the peak. We demonstrate that the resulting early drive P2/P0 asymmetry can be minimized and tuned to <1% accuracy (well within the ±7.5% requirement for ignition) by varying the relative input powers between different cones of beams. These experiments also provide time-resolved measurements of CBET during the first 2 ns of the laser drive, which are in good agreement with radiation-hydrodynamics calculations including a linear CBET model.

Performance of high-convergence, layered DT implosions with extended-duration pulses at the National Ignition Facility.

Radiation-driven, low-adiabat, cryogenic DT layered plastic capsule implosions were carried out on the National Ignition Facility (NIF) to study the sensitivity of performance to peak power and drive duration. An implosion with extended drive and at reduced peak power of 350 TW achieved the highest compression with fuel areal density of ~1.3±0.1 g/cm2, representing a significant step from previously measured ~1.0 g/cm2 toward a goal of 1.5 g/cm2. Future experiments will focus on understanding and mitigating hydrodynamic instabilities and mix, and improving symmetry required to reach the threshold for thermonuclear ignition on NIF.

Direct measurement of energetic electrons coupling to an imploding low-adiabat inertial confinement fusion capsule.

We have imaged hard x-ray (>100 keV) bremsstrahlung emission from energetic electrons slowing in a plastic ablator shell during indirectly driven implosions at the National Ignition Facility. We measure 570 J in electrons with E>100 keV impinging on the fusion capsule under ignition drive conditions. This translates into an acceptable increase in the adiabat α, defined as the ratio of total deuterium-tritium fuel pressure to Fermi pressure, of 3.5%. The hard x-ray observables are consistent with detailed radiative-hydrodynamics simulations, including the sourcing and transport of these high energy electrons.

Lead (Pb) hohlraum: target for inertial fusion energy.

Recent progress towards demonstrating inertial confinement fusion (ICF) ignition at the National Ignition Facility (NIF) has sparked wide interest in Laser Inertial Fusion Energy (LIFE) for carbon-free large-scale power generation. A LIFE-based fleet of power plants promises clean energy generation with no greenhouse gas emissions and a virtually limitless, widely available thermonuclear fuel source. For the LIFE concept to be viable, target costs must be minimized while the target material efficiency or x-ray albedo is optimized. Current ICF targets on the NIF utilize a gold or depleted uranium cylindrical radiation cavity (hohlraum) with a plastic capsule at the center that contains the deuterium and tritium fuel. Here we show a direct comparison of gold and lead hohlraums in efficiently ablating deuterium-filled plastic capsules with soft x rays. We report on lead hohlraum performance that is indistinguishable from gold, yet costing only a small fraction.

Symmetric inertial confinement fusion implosions at ultra-high laser energies.

Indirect-drive hohlraum experiments at the National Ignition Facility have demonstrated symmetric capsule implosions at unprecedented laser drive energies of 0.7 megajoule. One hundred and ninety-two simultaneously fired laser beams heat ignition-emulate hohlraums to radiation temperatures of 3.3 million kelvin, compressing 1.8-millimeter-diameter capsules by the soft x-rays produced by the hohlraum. Self-generated plasma optics gratings on either end of the hohlraum tune the laser power distribution in the hohlraum, which produces a symmetric x-ray drive as inferred from the shape of the capsule self-emission. These experiments indicate that the conditions are suitable for compressing deuterium-tritium-filled capsules, with the goal of achieving burning fusion plasmas and energy gain in the laboratory.

The first measurements of soft x-ray flux from ignition scale Hohlraums at the National Ignition Facility using DANTE (invited).

The first 96 and 192 beam vacuum Hohlraum target experiments have been fielded at the National Ignition Facility demonstrating radiation temperatures up to 340 eV and fluxes of 20 TW/sr as viewed by DANTE representing an ∼20 times flux increase over NOVA/Omega scale Hohlraums. The vacuum Hohlraums were irradiated with 2 ns square laser pulses with energies between 150 and 635 kJ. They produced nearly Planckian spectra with about 30±10% more flux than predicted by the preshot radiation hydrodynamic simulations. To validate these results, careful verification of all component calibrations, cable deconvolution, and software analysis routines has been conducted. In addition, a half Hohlraum experiment was conducted using a single 2 ns long axial quad with an irradiance of ∼2×10(15) W/cm(2) for comparison with NIF Early Light experiments completed in 2004. We have also completed a conversion efficiency test using a 128-beam nearly uniformly illuminated gold sphere with intensities kept low (at 1×10(14) W/cm(2) over 5 ns) to avoid sensitivity to modeling uncertainties for nonlocal heat conduction and nonlinear absorption mechanisms, to compare with similar intensity, 3 ns OMEGA sphere results. The 2004 and 2009 NIF half-Hohlraums agreed to 10% in flux, but more importantly, the 2006 OMEGA Au Sphere, the 2009 NIF Au sphere, and the calculated Au conversion efficiency agree to ±5% in flux, which is estimated to be the absolute calibration accuracy of the DANTEs. Hence we conclude that the 30±10% higher than expected radiation fluxes from the 96 and 192 beam vacuum Hohlraums are attributable to differences in physics of the larger Hohlraums.

Radiation-driven hydrodynamics of high- hohlraums on the national ignition facility.

The first hohlraum experiments on the National Ignition Facility (NIF) using the initial four laser beams tested radiation temperature limits imposed by plasma filling. For a variety of hohlraum sizes and pulse lengths, the measured x-ray flux shows signatures of filling that coincide with hard x-ray emission from plasma streaming out of the hohlraum. These observations agree with hydrodynamic simulations and with an analytical model that includes hydrodynamic and coronal radiative losses. The modeling predicts radiation temperature limits with full NIF (1.8 MJ), greater, and of longer duration than required for ignition hohlraums.

Axial heterogeneity and filtered-load dependence of proximal bicarbonate reabsorption.

A theoretical model was developed to examine the role of physical and chemical factors in the control of bicarbonate reabsorption in the renal proximal tubule. Included in the model were axial and radial variations in the concentrations of HCO3-, CO2 and related chemical species in the tubule lumen and epithelial cells. Relations between these concentrations and the solute fluxes across the brush border and basolateral membranes were also included, as were reaction rate and equilibrium expressions to describe the various buffering processes in the lumen and cells. The two most critical membrane parameters, the rate constant for H+ secretion at the brush border and the effective permeability of HCO3- at the basolateral membrane, were evaluated by comparing model predictions with available free-flow micropuncture data in the rat. It was found that the experimental observations could be explained only by decreasing one or both of these membrane parameters with axial position, suggesting a progressive decrease in HCO3- reabsorptive capacity along the tubule. For single nephron filtered loads of HCO3- up to about 1,400 pmol/min, absolute bicarbonate reabsorption was predicted to increase nearly in proportion to filtered load, whereas it was calculated to be relatively constant at higher filtered loads, irrespective of how filtered load was assumed to be varied. These predictions are in excellent agreement with most of the available micropuncture data in rats, as is the prediction that HCO3- reabsorption should change in parallel with CO2 partial pressure in the filtrate, at a given filtered load of HCO3-. Certain discrepancies between the model predictions and experimental observations are evident at very high filtered loads, and the implications of these are discussed in terms of possible adaptive responses of the tubule.

Analysis of the factors influencing peritubular PCO2 in the rat.

We have developed a mathematical model to assess the relative contributions of several factors to the high CO2 partial pressures observed in rat peritubular capillaries. This model is based on a single nephron and focuses specifically on the CO2 partial pressure differences (delta PCO2) between peritubular capillaries and the afferent arteriole. The model is formulated by writing steady-state mass balances for the glomerulus, proximal tubule, and peritubular capillaries in addition to equilibrium relationships for CO2, HCO3-, blood protein buffers, and hemoglobin carbamino compounds. Principal input parameters include glomerular blood flow rate, rates of HCO3- and water reabsorption, and the rate of metabolic CO2 production. Under conditions representative of normal Munich-Wistar rats, the model predicts delta PCO2 to be 4.1 mmHg, in approximate agreement with experimental observations reported elsewhere. Metabolic CO2 production is responsible for roughly half of this predicted delta PCO2, the remainder being attributable to reabsorption processes. In examining the sensitivity of delta PCO2 to changes in physiological conditions, we consistently found it to be inversely related to glomerular blood flow rate. The influence of changes in HCO3- reabsorption on delta PCO2 is variable and highly dependent on the arterial acid-base status and the ratio of HCO3- reabsorption to water reabsorption.

Proximal HCO3- reabsorption and the determinants of tubular and capillary PCO2 in the rat.

Studies were carried out in Munich-Wistar rats to define the CO2 partial pressure (PCO2) profile in the surface tubules and capillaries of the kidney and to relate these measurements to proximal tubular HCO3- reabsorption, renal blood flow, and O2 consumption. In euvolemic rats, PCO2 in Bowman's space (BS) was 12.5 mmHg higher than in arterial blood, indicating CO2 addition to the arterial tree as it traverses the cortex. PCO2 further rose by 3.9 mmHg between the efferent arteriole (EA) and the peritubular capillaries (PC) (P less than 0.01) and by 4.9 mmHg between BS and the early proximal tubule (EP) (P less than 0.01). In studies with paired measurements, PCO2 in EP was 1.8 mmHg higher than in the adjacent PC (P less than 0.05). HCO3- reabsorption in EP (first 0.4-1.25 mm) was 579 pmol X min-1 X mm-1 (34.3 +/- 4.6% of the filtered load). By use of a model of facilitated diffusion of CO2 across the cell, the trans-epithelial PCO2 gradient in EP can be accounted for by the CO2 generated from HCO3- reabsorption, assuming an intracellular pH of 7.3. In the vascular compartment, roughly half the rise in PCO2 between the afferent arteriole (estimated to equal BS PCO2) and PC can be accounted for by metabolic CO2 production and half by titration of blood buffers by reabsorbed HCO3-.

Analysis of PCO2 variations in the renal cortex. I. Single nephron.

A mathematical model was developed to predict differences in CO2 partial pressure between afferent arterioles and peritubular capillaries, based on the flow rate and composition of afferent arteriolar blood. Buffering reactions in blood were described by use of conditions of chemical equilibrium and electroneutrality in separate plasma and red cell compartments, with inclusion of such factors as the effect of hemoglobin oxygenation (alkaline Bohr effect) and formation of carbamino compounds. Steady-state mass balance equations allowed the prediction of peritubular capillary blood composition based on the inputs of blood from the efferent arteriole and the addition of water, CO2, NaHCO3, and NaCl derived from tubule reabsorbate. Models developed previously to describe the rates of glomerular filtration, and of proximal tubule reabsorption of HCO3- and CO2, were combined with the peritubular capillary model to allow realistic simulations for a single superficial nephron. The predicted difference of 5.5 mmHg between the CO2 partial pressures in peritubular capillaries and afferent arterioles (delta PCO2) was in good agreement with values reported for normal Munich-Wistar rats. For a given afferent arteriolar blood composition, the calculated delta PCO2 generally decreased with increasing blood flow rate. At a given blood flow rate and afferent PCO2, delta PCO2 decreased as afferent plasma HCO3- concentration was increased. When afferent PCO2 was varied at constant blood flow rate and HCO3- concentration, delta PCO2 changed in parallel with afferent PCO2.

Analysis of PCO2 variations in the renal cortex. II. Countercurrent exchange.

In an effort to explain the relatively high values of CO2 partial pressure (PCO2) that have been measured in the superficial renal cortex of the rat, we developed a mathematical model based on the concept of countercurrent exchange between blood vessels. The model includes the possibility of exchange of CO2 between interlobular arteries and veins throughout the cortex, and between "terminal" arterioles and venules (those associated with the most superficial nephrons). The effect of countercurrent exchange is to amplify the increases in PCO2 that occur in the microcirculation of individual nephrons, which are due to the addition of metabolic CO2 and reabsorbed HCO3- and CO2 to peritubular capillaries. The model is formulated in terms of correlations that describe blood buffering equilibria in peritubular capillaries and in interlobular arteries and veins, and steady-state mass balances for the interlobular vessels. By use of physically reasonable vascular permeability values, simulations for the normal euvolemic Munich-Wistar rat yielded values of the surface-to-arterial PCO2 difference (delta PCO2) comparable to previously measured values. Predicted variations in delta PCO2 with afferent arteriolar blood flow rate and systemic arterial PCO2 were also in accord with available data. These results suggest that the amplifying effect of countercurrent exchange is in fact adequate to explain the high values of PCO2 measured in surface structures. The solutions to the mass balance equations are in closed analytical form and can be readily adapted to describe countercurrent exchange in the renal cortex of solutes other than CO2.

Performance of large-aperture optical switches for high-energy inertial-confinement fusion lasers.

We describe the design and performance of large-aperture (>30 cm × 30 cm) optical switches that have demonstrated, for the first time to our knowledge, active switching of a high-energy (>5 kJ) optical pulse in an inertial-confinement fusion laser. These optical switches, which consist of a plasma-electrode Pockels cell (PEPC) and a passive polarizer, permit the design of efficient, multipass laser amplifiers. In a PEPC, plasma discharges on the faces of a thin (1-cm) electro-optic crystal (KDP or KD*P) act as highly conductive and transparent electrodes. These plasma electrodes facilitate rapid (<100 ns) and uniform charging of the crystal to the half-wave voltage and discharging back to 0 V. We discuss the operating principles, design, optical performance, and technical issues of a 32 cm × 32 cm prototype PEPC with both KDP and KD*P crystals, and a 37 cm × 37 cm PEPC with a KDP crystal for the Beamlet laser. This PEPC recently switched a 6-kJ, 3-ns pulse in a four-pass cavity.