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.

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 Crystal Backlighter Imager: A spherically bent crystal imager for radiography on the National Ignition Facility

The Crystal Backlighter Imager (CBI) is a quasi-monochromatic, near-normal incidence, spherically bent crystal imager developed for the National Ignition Facility (NIF), which will allow inertial confinement fusion capsule implosions to be radiographed close to stagnation. This is not possible using the standard pinhole-based area-backlighter configuration, as the self-emission from the capsule hotspot overwhelms the backlighter signal in the final stages of the implosion. The CBI mitigates the broadband self-emission from the capsule hot spot by using the extremely narrow bandwidth inherent to near-normal-incidence Bragg diffraction. Implementing a backlighter system based on near-normal reflection in the NIF chamber presents unique challenges, requiring the CBI to adopt novel engineering and operational strategies. The CBI currently operates with an 11.6 keV backlighter, making it the highest energy radiography diagnostic based on spherically bent crystals to date. For a given velocity, Doppler shift is proportional to the emitted photon energy. At 11.6 keV, the ablation velocity of the backlighter plasma results in a Doppler shift that is significant compared to the bandwidth of the instrument and the width of the atomic line, requiring that the shift be measured to high accuracy and the optics aligned accordingly to compensate. Experiments will be presented that used the CBI itself to measure the backlighter Doppler shift to an accuracy of better than 1 eV. These experiments also measured the spatial resolution of CBI radiographs at 7.0 μm, close to theoretical predictions. Finally, results will be presented from an experiment in which the CBI radiographed a capsule implosion driven by a 1 MJ NIF laser pulse, demonstrating a significant (>100) improvement in the backlighter to self-emission ratio compared to the pinhole-based area-backlighter configuration.

Publisher's Note: X-ray shadow imprint of hydrodynamic instabilities on the surface of inertial confinement fusion capsules by the fuel fill tube [Phys. Rev. E 95, 031204(R) (2017)]

This corrects the article DOI: 10.1103/PhysRevE.95.031204.

X-ray shadow imprint of hydrodynamic instabilities on the surface of inertial confinement fusion capsules by the fuel fill tube

Measurements of hydrodynamic instability growth for a high-density carbon ablator for indirectly driven inertial confinement fusion implosions on the National Ignition Facility are reported. We observe significant unexpected features on the capsule surface created by shadows of the capsule fill tube, as illuminated by laser-irradiated x-ray spots on the hohlraum wall. These shadows increase the spatial size and shape of the fill tube perturbation in a way that can significantly degrade performance in layered implosions compared to previous expectations. The measurements were performed at a convergence ratio of ∼2 using in-flight x-ray radiography. The initial seed due to shadow imprint is estimated to be equivalent to ∼50-100 nm of solid ablator material. This discovery has prompted the need for a mitigation strategy for future inertial confinement fusion designs as proposed here.

Development of a krypton-doped gas symmetry capsule platform for x-ray spectroscopy of implosion cores on the NIF

The electron temperature at stagnation of an ICF implosion can be measured from the emission spectrum of high-energy x-rays that pass through the cold material surrounding the hot stagnating core. Here we describe a platform developed on the National Ignition Facility where trace levels of a mid-Z dopant (krypton) are added to the fuel gas of a symcap (symmetry surrogate) implosion to allow for the use of x-ray spectroscopy of the krypton line emission.

Measurement of Hydrodynamic Growth near Peak Velocity in an Inertial Confinement Fusion Capsule Implosion using a Self-Radiography Technique

First measurements of hydrodynamic growth near peak implosion velocity in an inertial confinement fusion (ICF) implosion at the National Ignition Facility were obtained using a self-radiographing technique and a preimposed Legendre mode 40, λ=140  μm, sinusoidal perturbation. These are the first measurements of the total growth at the most unstable mode from acceleration Rayleigh-Taylor achieved in any ICF experiment to date, showing growth of the areal density perturbation of ∼7000×. Measurements were made at convergences of ∼5 to ∼10× at both the waist and pole of the capsule, demonstrating simultaneous measurements of the growth factors from both lines of sight. The areal density growth factors are an order of magnitude larger than prior experimental measurements and differed by ∼2× between the waist and the pole, showing asymmetry in the measured growth factors. These new measurements significantly advance our ability to diagnose perturbations detrimental to ICF implosions, uniquely intersecting the change from an accelerating to decelerating shell, with multiple simultaneous angular views.

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.

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.

Hot-spot mix in ignition-scale inertial confinement fusion targets

Mixing of plastic ablator material, doped with Cu and Ge dopants, deep into the hot spot of ignition-scale inertial confinement fusion implosions by hydrodynamic instabilities is diagnosed with x-ray spectroscopy on the National Ignition Facility. The amount of hot-spot mix mass is determined from the absolute brightness of the emergent Cu and Ge K-shell emission. The Cu and Ge dopants placed at different radial locations in the plastic ablator show the ablation-front hydrodynamic instability is primarily responsible for hot-spot mix. Low neutron yields and hot-spot mix mass between 34(-13,+50)  ng and 4000(-2970,+17 160)  ng are observed.

Extracting core shape from x-ray images at the National Ignition Facility

Measuring the shape of implosions is critical to inertial confinement fusion experiments at the National Ignition Facility. We have developed techniques that have proven successful for extracting shape information from images of x-ray self-emission recorded by a variety of diagnostic instruments for both DT-filled targets and low-yield surrogates. These key results help determine optimal laser and target parameters leading to ignition. We have compensated for instrumental response and have employed a variety of image processing methods to remove artifacts from the images while retaining salient features. The implosion shape has been characterized by decomposing intensity contours into Fourier and Legendre modes for different lines of sight. We also describe procedures we have developed for estimating uncertainties in these measurements.

Demonstration of ignition radiation temperatures in indirect-drive inertial confinement fusion hohlraums

We demonstrate the hohlraum radiation temperature and symmetry required for ignition-scale inertial confinement fusion capsule implosions. Cryogenic gas-filled hohlraums with 2.2 mm-diameter capsules are heated with unprecedented laser energies of 1.2 MJ delivered by 192 ultraviolet laser beams on the National Ignition Facility. Laser backscatter measurements show that these hohlraums absorb 87% to 91% of the incident laser power resulting in peak radiation temperatures of T(RAD)=300 eV and a symmetric implosion to a 100 μm diameter hot core.

X-ray Thomson-scattering measurements of density and temperature in shock-compressed beryllium

We present the first x-ray scattering measurements of the state of compression and heating in laser irradiated solid beryllium. The scattered spectra at two different angles show Compton and plasmon features indicating a dense Fermi-degenerate plasma state with a Fermi energy above 30 eV and with temperatures in the range of 10-15 eV. These measurements indicate compression by a factor of 3 in agreement with Hugoniot data and detailed radiation-hydrodynamic modeling.

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.

Measurement of the absolute hohlraum-wall albedo under ignition foot drive conditions

We present measurements of the absolute albedos of hohlraums made from gold or from high-Z mixtures. The measurements are performed over the range of radiation temperatures (70-100 eV) expected during the foot of an indirect-drive temporally shaped ignition laser pulse, where accurate knowledge of the wall albedo (i.e., soft x-ray wall reemission) is most critical for determining capsule radiation symmetry. We find that the gold albedo agrees well with calculations using the supertransition array opacity model, potentially providing additional margin for inertial confinement fusion ignition.

Temperature measurements of shock compressed liquid deuterium up to 230 GPa

Pyrometric measurements of single-shock-compressed liquid deuterium reveal that shock front temperatures T increase from 0.47 to 4.4 eV as the pressure P increases from 31 to 230 GPa. Where deuterium becomes both conducting and highly compressible, 30< or =P< or =50 GPa, T is lower than most models predict and T<<T(Fermi), proving that deuterium is a degenerate Fermi-liquid metal. At P>50 Gpa, where the optical reflectivity is saturated, there is an increase in the rate that T increases with P.

Accuracy of K-shell spectra modeling in high-density plasmas

We present spectroscopic measurements of the helium-like and lithium-like argon emission supported by Thomson scattering diagnostics on gas bag targets. These data provide critical tests of plasma spectroscopic K-shell models. In particular, we have measured the line radiation in the wavelength region of the He-like Ar 1s(2)-1s3l transition (He-beta) that is of interest for density and temperature measurements of plasmas from gas-filled targets (n(e)</=10(21) cm(-3)), laser ablation targets (n(e)</=10(22) cm(-3)), and inertial confinement fusion capsule implosions (n(e)>/=10(24) cm(-3)). The spectra show lithium-like dielectronic satellites on the red wing of the He-beta line that are temperature sensitive and are known to influence the shape of the Stark-broadened line profiles observed from implosions. To examine the kinetics modeling of this complex, i.e., the He-beta and its associated satellites, we have performed experiments in gas bag plasmas at densities of (0.6-1.1)x10(21) cm(-3) where we independently determine the electron temperature with ultraviolet Thomson scattering. The comparison of the satellite intensities with kinetics modeling shows good agreement for satellites whose upper states are populated by dielectronic capture, but shows discrepancies for inner-shell collisional excited transitions.

Shock-induced transformation of liquid deuterium into a metallic fluid

Simultaneous measurements of shock velocity and optical reflectance at 1064, 808, and 404 nm of a high pressure shock front propagating through liquid deuterium show a continuous increase in reflectance from below 10% and saturating at approximately (40-60)% in the range of shock velocities from 12 to 20 &mgr;m/ns (pressure range 17-50 GPa). The high optical reflectance is evidence that the shocked deuterium reaches a conducting state characteristic of a metallic fluid. Above 20 &mgr;m/ns shock velocity (50 GPa pressure) reflectance is constant indicating that the transformation is substantially complete.

High-Energy X-ray Microscopy Techniques for Laser-Fusion Plasma Research at the National Ignition Facility

Multi-kilo-electron-volt x-ray microscopy will be an important laser-produced plasma diagnostic at future megajoule facilities such as the National Ignition Facility (NIF). However, laser energies and plasma characteristics imply that x-ray microscopy will be more challenging at NIF than at existing facilities. We use analytical estimates and numerical ray tracing to investigate several instrumentation options in detail, and we conclude that near-normal-incidence single spherical or toroidal crystals may offer the best general solution for high-energy x-ray microscopy at NIF and similar large facilities. Apertured Kirkpatrick-Baez microscopes using multilayer mirrors may also be good options, particularly for applications requiring one-dimensional imaging over narrow fields of view.