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.

Stability of perpendicular magnetohydrodynamic shocks in materials with ideal and nonideal equations of state.

Magnetized target fusion approach to inertial confinement fusion involves the formation of strong shocks that travel along a magnetized plasma. Shocks, which play a dominant role in thermalizing the upstream kinetic energy generated in the implosion stage, are seldom free from perturbations, and they wrinkle in response to upstream or downstream disturbances. In Z-pinch experiments, significant plasma instability mitigation was observed with pre-embedded axial magnetic fields. To isolate effects, in this work we theoretically study the impact of perpendicular magnetic fields on the planar shock dynamics for different equations of state. For fast magnetosonic shocks in ideal gases, it was found that the magnetic field amplifies the intensity of the perturbations when γ>2 or it weakens them when γ<2. Weak shocks have been found to be stable regardless of the magnetic plasma intensity and gas compressibility; however, for sufficiently strong shocks the magnetic fields can promote a neutral stability/SAE at the shock if the adiabatic index is higher than 1+sqrt[2]. Results have been validated with numerical simulations performed with the FLASH code.

Effects of Laser Bandwidth in Direct-Drive High-Performance DT-Layered Implosions on the OMEGA Laser.

In direct-drive inertial confinement fusion, the laser bandwidth reduces the laser imprinting seed of hydrodynamic instabilities. The impact of varying bandwidth on the performance of direct-drive DT-layered implosions was studied in targets with different hydrodynamic stability properties. The stability was controlled by changing the shell adiabat from (α_{F}≃5) (more stable) to (α_{F}≃3.5) (less stable). These experiments show that the performance of lower adiabat implosions improves considerably as the bandwidth is raised indicating that further bandwidth increases, beyond the current capabilities of OMEGA, would be greatly beneficial. These results suggest that the future generation of ultra-broadband lasers could enable achieving high convergence and possibly high gains in direct drive ICF.

Predicting hot electron generation in inertial confinement fusion with particle-in-cell simulations.

A series of two-dimensional particle-in-cell simulations with speckled laser drivers was carried out to study hot electron generation in direct-drive inertial confinement fusion on OMEGA. Scaling laws were obtained for hot electron fraction and temperature as functions of laser/plasma conditions in the quarter-critical region. Using these scalings and conditions from hydro simulations, the temporal history of hot electron generation can be predicted. The scalings can be further improved to predict hard x-rays for a collection of OMEGA warm target implosions within experimental error bars. These scalings can be readily implemented into inertial confinement fusion design codes.

Hot-electron preheat and mitigation in polar-direct-drive experiments at the National Ignition Facility.

Target preheat by superthermal electrons from laser-plasma instabilities is a major obstacle to achieving thermonuclear ignition via direct-drive inertial confinement fusion at the National Ignition Facility (NIF). Polar-direct-drive surrogate plastic implosion experiments were performed on the NIF to quantify preheat levels at an ignition-relevant scale and develop mitigation strategies. The experiments were used to infer the hot-electron temperature, energy fraction, and divergence, and to directly measure the spatial hot-electron energy deposition profile inside the imploding shell. Silicon layers buried in the ablator are shown to mitigate the growth of laser-plasma instabilities and reduce preheat, providing a promising path forward for ignition designs at an on-target intensity of about 10^{15}W/cm^{2}.

Diagnosing low-mode (ℓ < 6) and mid-mode (6 ≤ ℓ ≤ 60) asymmetries in the post-stagnation phase of laser-direct-drive deuterium-tritium cryogenic implosions on OMEGA.

Low- and mid-mode perturbations are possible candidates for performance limitations in cryogenic direct-drive implosions on the OMEGA laser at the Laboratory of Laser Energetics. Simulations with a 3D hydrocode demonstrated that hotspot imagers do not show evidence of the shell breakup in the dense fuel. However, these same simulations revealed that the low- and mid-mode perturbations in the dense fuel could be diagnosed more easily in the post-stagnation phase of the implosion by analyzing the peak in the x-ray emission limb at the coronal-fuel interface than before or at the stagnation phase. In experiments, the asymmetries are inferred from gated images of the x-ray emission of the implosion by using a 16-pinhole array imager filtered to record x-ray energies >800 eV and an x-ray framing camera with 40-ps time integration and 20-µm spatial resolution. A modal analysis is applied to the spatial distribution of the x-ray emission from deuterium and tritium cryogenic implosions on OMEGA recorded after the bang time to diagnose the low- and mid-mode asymmetries, and to study the effect that the beam-to-target ratio (Rb/Rt) has on the shell integrity.

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, Te 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.

Development of an x-ray radiography platform to study laser-direct-drive energy coupling at the National Ignition Facility.

A platform has been developed to study laser-direct-drive energy coupling at the National Ignition Facility (NIF) using a plastic sphere target irradiated in a polar-direct-drive geometry to launch a spherically converging shock wave. To diagnose this system evolution, eight NIF laser beams are directed onto a curved Cu foil to generate Heα line emission at a photon energy of 8.4 keV. These x rays are collected by a 100-ps gated x-ray imager in the opposing port to produce temporally gated radiographs. The platform is capable of acquiring images during and after the laser drive launches the shock wave. A backlighter profile is fit to the radiographs, and the resulting transmission images are Abel inverted to infer radial density profiles of the shock front and to track its temporal evolution. The measurements provide experimental shock trajectories and radial density profiles that are compared to 2D radiation-hydrodynamic simulations using cross-beam energy transfer and nonlocal heat-transport models.

The phase-2 particle x-ray temporal diagnostic for simultaneous measurement of multiple x-ray and nuclear emission histories from OMEGA implosions (invited).

Electron-temperature (Te) measurements in implosions provide valuable diagnostic information, as Te is negligibly affected by residual flows and other non-thermal effects unlike ion-temperature inferred from a fusion product spectrum. In OMEGA cryogenic implosions, measurement of Te(t) can be used to investigate effects related to time-resolved hot-spot energy balance. The newly implemented phase-2 Particle X-ray Temporal Diagnostic (PXTD) utilizes four fast-rise (∼15 ps) scintillator-channels with distinct x-ray filtering. Titanium and stepped aluminum filtering were chosen to maximize detector sensitivity in the 10-20 keV range, as it has been shown that these x rays have similar density and temperature weighting to the emitted deuterium-tritium fusion neutrons (DTn) from OMEGA Cryo-DT implosions. High quality data have been collected from warm implosions at OMEGA. These data have been used to infer spatially integrated Te(t) with <10% uncertainty at peak emission. Nuclear and x-ray emission histories are measured with 10 ps relative timing uncertainty for x rays and DTn and 12 ps for x rays and deuterium-He3 protons (D3Hep). A future upgrade to the system will enable spatially integrated Te(t) with 40 ps time-resolution from cryogenic DT implosions.

Three-dimensional hot-spot x-ray emission tomography from cryogenic deuterium-tritium direct-drive implosions on OMEGA.

A three-dimensional model of the hot-spot x-ray emission has been developed and applied to the study of low-mode drive asymmetries in direct-drive inertial confinement fusion implosions on OMEGA with cryogenic deuterium-tritium targets. The steady-state model assumes an optically thin plasma and the data from four x-ray diagnostics along quasi-orthogonal lines of sight are used to obtain a tomographic reconstruction of the hot spot. A quantitative analysis of the hot-spot shape is achieved by projecting the x-ray emission into the diagnostic planes and comparing this projection to the measurements. The model was validated with radiation-hydrodynamic simulations assuming a mode-2 laser illumination perturbation resulting in an elliptically shaped hot spot, which was accurately reconstructed by the model using synthetic x-ray images. This technique was applied to experimental data from implosions in polar-direct-drive illumination geometry with a deliberate laser-drive asymmetry, and the hot-spot emission was reconstructed using spherical-harmonic modes of up to ℓ = 3. A 10% stronger drive on the equator relative to that on the poles resulted in a prolate-shaped hot spot at stagnation with a large negative A2,0 coefficient of A2,0 = -0.47 ± 0.03, directly connecting the modal contribution of the hot-spot shape with the modal contribution in laser-drive asymmetry.

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.

Effect of Strongly Magnetized Electrons and Ions on Heat Flow and Symmetry of Inertial Fusion Implosions.

This Letter presents the first observation on how a strong, 500 kG, externally applied B field increases the mode-two asymmetry in shock-heated inertial fusion implosions. Using a direct-drive implosion with polar illumination and imposed field, we observed that magnetization produces a significant increase in the implosion oblateness (a 2.5× larger P2 amplitude in x-ray self-emission images) compared with reference experiments with identical drive but with no field applied. The implosions produce strongly magnetized electrons (ω_{e}τ_{e}≫1) and ions (ω_{i}τ_{i}>1) that, as shown using simulations, restrict the cross field heat flow necessary for lateral distribution of the laser and shock heating from the implosion pole to the waist, causing the enhanced mode-two shape.

Hot Spot Evolution Measured by High-Resolution X-Ray Spectroscopy at the National Ignition Facility.

Evolution of the hot spot plasma conditions was measured using high-resolution x-ray spectroscopy at the National Ignition Facility. The capsules were filled with DD gas with trace levels of Kr and had either a high-density-carbon (HDC) ablator or a tungsten (W)-doped HDC ablator. Time-resolved measurement of the Kr Heß spectra, absolutely calibrated by a simultaneous time-integrated measurement, allows inference of the electron density and temperature through observing Stark broadening and the relative intensities of dielectronic satellites. By matching the calculated hot spot emission using a collisional-radiative code to experimental observations, the hot spot size and areal density are determined. These advanced spectroscopy techniques further reveal the effect of W dopant in the ablator on the hot spot parameters for their improved implosion performance.

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.

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.

Shock Ignition Laser-Plasma Interactions in Ignition-Scale Plasmas.

We use a subignition scale laser, the 30 kJ Omega, and a novel shallow-cone target to study laser-plasma interactions at the ablation-plasma density scale lengths and laser intensities anticipated for direct drive shock-ignition implosions at National Ignition Facility scale. Our results show that, under these conditions, the dominant instability is convective stimulated Raman scatter with experimental evidence of two plasmon decay (TPD) only when the density scale length is reduced. Particle-in-cell simulations indicate this is due to TPD being shifted to lower densities, removing the experimental back-scatter signature and reducing the hot-electron temperature. The experimental laser energy-coupling to hot electrons was found to be 1%-2.5%, with electron temperatures between 35 and 45 keV. Radiation-hydrodynamics simulations employing these hot-electron characteristics indicate that they should not preheat the fuel in MJ-scale shock ignition experiments.

Direct Measurements of DT Fuel Preheat from Hot Electrons in Direct-Drive Inertial Confinement Fusion.

Hot electrons generated by laser-plasma instabilities degrade the performance of laser-fusion implosions by preheating the DT fuel and reducing core compression. The hot-electron energy deposition in the DT fuel has been directly measured for the first time by comparing the hard x-ray signals between DT-layered and mass-equivalent ablator-only implosions. The electron energy deposition profile in the fuel is inferred through dedicated experiments using Cu-doped payloads of varying thickness. The measured preheat energy accurately explains the areal-density degradation observed in many OMEGA implosions. This technique can be used to assess the viability of the direct-drive approach to laser fusion with respect to the scaling of hot-electron preheat with laser energy.