Neutron source reconstruction using a generalized expectation-maximization algorithm on one-dimensional neutron images from the Z facility

Magnetized Liner Inertial Fusion experiments have been performed at the Z facility at Sandia National Laboratories. These experiments use deuterium fuel, which produces 2.45 MeV neutrons on reaching thermonuclear conditions. To study the spatial structure of neutron production, the one-dimensional imager of neutrons diagnostic was fielded to record axial resolved neutron images. In this diagnostic, neutrons passing through a rolled edge aperture form an image on a CR-39-based solid state nuclear track detector. Here, we present a modified generalized expectation-maximization algorithm to reconstruct an axial neutron emission profile of the stagnated fusion plasma. We validate the approach by comparing the reconstructed neutron emission profile to an x-ray emission profile provided by a time-integrated pinhole camera.

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.

Evidence of non-Maxwellian ion velocity distributions in spherical shock-driven implosions

The ion velocity distribution functions of thermonuclear plasmas generated by spherical laser direct drive implosions are studied using deuterium-tritium (DT) and deuterium-deuterium (DD) fusion neutron energy spectrum measurements. A hydrodynamic Maxwellian plasma model accurately describes measurements made from lower temperature (<10 keV), hydrodynamiclike plasmas, but is insufficient to describe measurements made from higher temperature more kineticlike plasmas. The high temperature measurements are more consistent with Vlasov-Fokker-Planck (VFP) simulation results which predict the presence of a bimodal plasma ion velocity distribution near peak neutron production. These measurements provide direct experimental evidence of non-Maxwellian ion velocity distributions in spherical shock driven implosions and provide useful data for benchmarking kinetic VFP simulations.

X-ray-imaging spectrometer (XRIS) for studies of residual kinetic energy and low-mode asymmetries in inertial confinement fusion implosions at OMEGA (invited)

A system of x-ray imaging spectrometer (XRIS) has been implemented at the OMEGA Laser Facility and is capable of spatially and spectrally resolving x-ray self-emission from 5 to 40 keV. The system consists of three independent imagers with nearly orthogonal lines of sight for 3D reconstructions of the x-ray emission region. The distinct advantage of the XRIS system is its large dynamic range, which is enabled by the use of tantalum apertures with radii ranging from 50 μm to 1 mm, magnifications of 4 to 35×, and image plates with any filtration level. In addition, XRIS is capable of recording 1-100's images along a single line of sight, facilitating advanced statistical inference on the detailed structure of the x-ray emitting regions. Properties such as P0 and P2 of an implosion are measured to 1% and 10% precision, respectively. Furthermore, T_e can be determined with 5% accuracy.

Measurements of low-mode asymmetries in the areal density of laser-direct-drive deuterium-tritium cryogenic implosions on OMEGA using neutron spectroscopy

Areal density is one of the key parameters that determines the confinement time in inertial confinement fusion experiments, and low-mode asymmetries in the compressed fuel are detrimental to the implosion performance. The energy spectra from the scattering of the primary deuterium-tritium (DT) neutrons off the compressed cold fuel assembly are used to investigate low-mode nonuniformities in direct-drive cryogenic DT implosions at the Omega Laser Facility. For spherically symmetric implosions, the shape of the energy spectrum is primarily determined by the elastic and inelastic scattering cross sections for both neutron-deuterium and neutron-tritium kinematic interactions. Two highly collimated lines of sight, which are positioned at nearly orthogonal locations around the OMEGA target chamber, record the neutron time-of-flight signal in the current mode. An evolutionary algorithm is being used to extract a model-independent energy spectrum of the scattered neutrons from the experimental neutron time-of-flight data and is used to infer the modal spatial variations (l = 1) in the areal density. Experimental observations of the low-mode variations of the cold-fuel assembly (ρL₀ + ρL₁) show good agreement with a recently developed model, indicating a departure from the spherical symmetry of the compressed DT fuel assembly. Another key signature that has been observed in the presence of a low-mode variation is the broadening of the kinematic end-point due to the anisotropy of the dense fuel conditions.

A new neutron time-of-flight detector for yield and ion-temperature measurements at the OMEGA Laser Facility

A new neutron time-of-flight (nTOF) detector for deuterium-deuterium (DD)-fusion yield and ion-temperature measurements was designed, installed, and calibrated for the OMEGA Laser Facility. This detector provides an additional line of sight for DD neutron yield and ion-temperature measurements for yields exceeding 1 × 10¹⁰ with higher precision than existing detectors. The nTOF detector consists of a 90-mm-diam, 20-mm-thick BC-422 scintillator and a gated Photek photomultiplier tube (PMT240). The PMT collects scintillating light through the 20-mm side of the scintillator without the use of a light guide. There is no lead shielding from hard x rays in order to allow the x-ray instrument response function of the detector to be measured easily. Instead, hard x-ray signals generated in implosion experiments are gated out by the PMT. The design provides a place for glass neutral-density filters between the scintillator and the PMT to avoid PMT saturation at high yields. The nTOF detector is installed in the OMEGA Target Bay along the P8A sub-port line of sight at a distance of 5.3 m from the target chamber center. In addition to DD measurements, the same detector can be used to measure the neutron yield and ion temperature from deuterium-tritium (DT) implosion targets in the 5 × 10¹⁰ to 2 × 10¹² yield range. The design details and the calibration results of this nTOF detector for both D₂ and DT implosions on OMEGA will be presented.

3D Simulations Capture the Persistent Low-Mode Asymmetries Evident in Laser-Direct-Drive Implosions on OMEGA

Spherical implosions in inertial confinement fusion are inherently sensitive to perturbations that may arise from experimental constraints and errors. Control and mitigation of low-mode (long wavelength) perturbations is a key milestone to improving implosion performances. We present the first 3D radiation-hydrodynamic simulations of directly driven inertial confinement fusion implosions with an inline package for polarized crossed-beam energy transfer. Simulations match bang times, yields (separately accounting for laser-induced high modes and fuel age), hot spot flow velocities and direction, for which polarized crossed-beam energy transfer contributes to the systematic flow orientation evident in the OMEGA implosion database. Current levels of beam mispointing, imbalance, target offset, and asymmetry from polarized crossed-beam energy transfer degrade yields by more than 40%. The effectiveness of two mitigation strategies for low modes is explored.

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.

Bound on hot-spot mix in high-velocity, high-adiabat direct-drive cryogenic implosions based on comparison of absolute x-ray and neutron yields

In laser-driven implosions for laboratory fusion, the comparison of hot-spot x-ray yield to neutron production can serve to infer hot-spot mix. For high-performance direct-drive implosions, this ratio depends sensitively on the degree of equilibration between the ion and electron fluids. A scaling for x-ray yield as a function of neutron yield and characteristic ion and electron hot-spot temperatures is developed on the basis of simulations with varying degrees of equilibration. We apply this model to hot-spot x-ray measurements of direct-drive cryogenic implosions typical of the direct-drive designs with best ignition metrics. The comparison of the measured x-ray and neutron yields indicates that hot-spot mix, if present, is below a sensitivity estimated as ∼2% by-atom mix of ablator plastic into the hot spot.

Measurements of the temperature and velocity of the dense fuel layer in inertial confinement fusion experiments

The apparent ion temperature and mean velocity of the dense deuterium tritium fuel layer of an inertial confinement fusion target near peak compression have been measured using backscatter neutron spectroscopy. The average isotropic residual kinetic energy of the dense deuterium tritium fuel is estimated using the mean velocity measurement to be ∼103 J across an ensemble of experiments. The apparent ion-temperature measurements from high-implosion velocity experiments are larger than expected from radiation-hydrodynamic simulations and are consistent with enhanced levels of shell decompression. These results suggest that high-mode instabilities may saturate the scaling of implosion performance with the implosion velocity for laser-direct-drive implosions.

Experimentally Inferred Fusion Yield Dependencies of OMEGA Inertial Confinement Fusion Implosions

Statistical modeling of experimental and simulation databases has enabled the development of an accurate predictive capability for deuterium-tritium layered cryogenic implosions at the OMEGA laser [V. Gopalaswamy et al.,Nature 565, 581 (2019)10.1038/s41586-019-0877-0]. In this letter, a physics-based statistical mapping framework is described and used to uncover the dependencies of the fusion yield. This model is used to identify and quantify the degradation mechanisms of the fusion yield in direct-drive implosions on OMEGA. The yield is found to be reduced by the ratio of laser beam to target radius, the asymmetry in inferred ion temperatures from the ℓ=1 mode, the time span over which tritium fuel has decayed, and parameters related to the implosion hydrodynamic stability. When adjusted for tritium decay and ℓ=1 mode, the highest yield in OMEGA cryogenic implosions is predicted to exceed 2×10^{14} fusion reactions.

Thermal decoupling of deuterium and tritium during the inertial confinement fusion shock-convergence phase

A series of thin glass-shell shock-driven DT gas-filled capsule implosions was conducted at the OMEGA laser facility. These experiments generate conditions relevant to the central plasma during the shock-convergence phase of ablatively driven inertial confinement fusion (ICF) implosions. The spectral temperatures inferred from the DTn and DDn spectra are most consistent with a two-ion-temperature plasma, where the initial apparent temperature ratio, T_{T}/T_{D}, is 1.5. This is an experimental confirmation of the long-standing conjecture that plasma shocks couple energy directly proportional to the species mass in multi-ion plasmas. The apparent temperature ratio trend with equilibration time matches expected thermal equilibration described by hydrodynamic theory. This indicates that deuterium and tritium ions have different energy distributions for the time period surrounding shock convergence in ignition-relevant ICF implosions.

An x-ray penumbral imager for measurements of electron-temperature profiles in inertial confinement fusion implosions at OMEGA

Hot-spot shape and electron temperature (T_e) are key performance metrics used to assess the efficiency of converting shell kinetic energy into hot-spot thermal energy in inertial confinement fusion implosions. X-ray penumbral imaging offers a means to diagnose hot-spot shape and T_e, where the latter can be used as a surrogate measure of the ion temperature (T_i) in sufficiently equilibrated hot spots. We have implemented a new x-ray penumbral imager on OMEGA. We demonstrate minimal line-of-sight variations in the inferred T_e for a set of implosions. Furthermore, we demonstrate spatially resolved T_e measurements with an average uncertainty of 10% with 6 μm spatial resolution.

Application of an energy-dependent instrument response function to analysis of nTOF data from cryogenic DT experiments

Neutron time-of-flight (nTOF) detectors are used to diagnose the conditions present in inertial confinement fusion (ICF) experiments and basic laboratory physics experiments performed on an ICF platform. The instrument response function (IRF) of these detectors is constructed by convolution of two components: an x-ray IRF and a neutron interaction response. The shape of the neutron interaction response varies with incident neutron energy, changing the shape of the total IRF. Analyses of nTOF data that span a broad range of energies must account for this energy-dependence in order to accurately infer plasma parameters and nuclear properties in ICF experiments. This work briefly reviews a matrix multiplication approach to convolution, which allows for an energy-dependent change in the shape of the IRF. This method is applied to synthetic data resembling symmetric cryogenic DT implosions to examine the effect of the energy-dependent IRF on the inferred areal density. The results of forward fits that infer ion temperatures and areal densities from nTOF data collected during cryogenic DT experiments on OMEGA are also discussed.

Reconstructing 3D asymmetries in laser-direct-drive implosions on OMEGA

Three-dimensional reconstruction algorithms have been developed, which determine the hot-spot velocity, hot-spot apparent ion temperature distribution, and fuel areal-density distribution present in laser-direct-drive inertial confinement fusion implosions on the OMEGA laser. These reconstructions rely on multiple independent measurements of the neutron energy spectrum emitted from the fusing plasma. Measurements of the neutron energy spectrum on OMEGA are made using a suite of quasi-orthogonal neutron time-of-flight detectors and a magnetic recoil spectrometer. These spectrometers are positioned strategically around the OMEGA target chamber to provide unique 3D measurements of the conditions of the fusing hot spot and compressed fuel near peak compression. The uncertainties involved in these 3D reconstructions are discussed and are used to identify a new nTOF diagnostic line of sight, which when built will reduce the uncertainty in the hot-spot apparent ion temperature distribution from 700 to <400 eV.

Direct-drive laser fusion: status, plans and future

Laser-direct drive (LDD), along with laser indirect (X-ray) drive (LID) and magnetic drive with pulsed power, is one of the three viable inertial confinement fusion approaches to achieving fusion ignition and gain in the laboratory. The LDD programme is primarily being executed at both the Omega Laser Facility at the Laboratory for Laser Energetics and at the National Ignition Facility (NIF) at Lawrence Livermore National Laboratory. LDD research at Omega includes cryogenic implosions, fundamental physics including material properties, hydrodynamics and laser-plasma interaction physics. LDD research on the NIF is focused on energy coupling and laser-plasma interactions physics at ignition-scale plasmas. Limited implosions on the NIF in the 'polar-drive' configuration, where the irradiation geometry is configured for LID, are also a feature of LDD research. The ability to conduct research over a large range of energy, power and scale size using both Omega and the NIF is a major positive aspect of LDD research that reduces the risk in scaling from OMEGA to megajoule-class lasers. The paper will summarize the present status of LDD research and plans for the future with the goal of ultimately achieving a burning plasma in the laboratory. This article is part of a discussion meeting issue 'Prospects for high gain inertial fusion energy (part 2)'.

A novel photomultiplier tube neutron time-of-flight detector

A traditional neutron time-of-flight (nTOF) detector used in inertial confinement fusion consists of a scintillator coupled with a photomultiplier tube (PMT). The instrument response function (IRF) of such a detector is dominated by the scintillator-light decay. In DT implosions with neutron yield larger than 10¹³, a novel detector consisting of a microchannel-plate (MCP) photomultiplier tube in a housing without a scintillator (PMT nTOF) can be used to measure DT yield, ion temperature, and neutron velocity. Most of the neutron signals in PMT nTOF detectors are produced from neutron interaction with a PMT window. The direct interaction of neutrons with the MCP provides negligible contribution. The elimination of the scintillator removes the scintillator decay from the instrument response function and makes the IRF of the PMT nTOF detector faster, which makes the ion temperature and neutron velocity measurements more accurate. Three PMT nTOF detectors were deployed in the OMEGA laser system for the first time to diagnose inertial confinement fusion plasma. The design details, characteristics, and calibration results of these detectors in DT implosions on OMEGA are presented. Recommendations on the use of different PMTs for specific applications are provided.

Tripled yield in direct-drive laser fusion through statistical modelling

Focusing laser light onto a very small target can produce the conditions for laboratory-scale nuclear fusion of hydrogen isotopes. The lack of accurate predictive models, which are essential for the design of high-performance laser-fusion experiments, is a major obstacle to achieving thermonuclear ignition. Here we report a statistical approach that was used to design and quantitatively predict the results of implosions of solid deuterium-tritium targets carried out with the 30-kilojoule OMEGA laser system, leading to tripling of the fusion yield to its highest value so far for direct-drive laser fusion. When scaled to the laser energies of the National Ignition Facility (1.9 megajoules), these targets are predicted to produce a fusion energy output of about 500 kilojoules-several times larger than the fusion yields currently achieved at that facility. This approach could guide the exploration of the vast parameter space of thermonuclear ignition conditions and enhance our understanding of laser-fusion physics.

Calibration of a neutron time-of-flight detector with a rapid instrument response function for measurements of bulk fluid motion on OMEGA

A newly developed neutron time-of-flight (nTOF) diagnostic with a fast instrument response function has been fielded on the OMEGA laser in a highly collimated line of sight. By using a small plastic scintillator volume, the detector provides a narrow instrument response of 1.7 ns full width at half maximum while maintaining a large signal-to-noise ratio for neutron yields between 10¹⁰ and 10¹⁴. The OMEGA hardware timing system is used along with an optical fiducial to provide an absolute nTOF measurement to an accuracy of ∼56 ps. The fast instrument response enables the accurate measurement of the primary deuterium-tritium neutron peak shape, while the optical fiducial allows for an absolute neutron energy measurement. The new detector measures the neutron mean energy with an uncertainty of ∼7 keV, corresponding to a hot-spot velocity projection uncertainty of ∼12 km/s. Evidence of bulk fluid motion in cryogenic targets is presented with measurements of the neutron energy spectrum.