National Ignition Facility Implosion Research Articles

Modeling ablator defects as a source of mix in high-performance implosions at the National Ignition Facility

Recent indirect drive inertial confinement fusion implosions on the National Ignition Facility (NIF) [Spaeth et al., Fusion Sci. Technol. 69, 25 (2016)] have crossed the threshold of ignition. However, performance has been variable due to several factors. One of the leading sources of variability is the quality of the high-density carbon (HDC) shells used as ablators in these experiments. In particular, these shells can have a number of defects that have been found to correlate with the appearance of ablator mix into the hot spot and a degradation in nuclear yield. These defects include pits on the ablator surface, voids in the ablator bulk, high-Z debris from the Hohlraum wall that adheres to the capsule surface, and finally the inherent granular micro-structure of the crystalline HDC itself. This paper summarizes high-resolution modeling of each of these mix sources in two recent high-performance NIF implosion experiments. The simulated impact from a range of individual capsule defects is found to be broadly consistent with the trends seen in experiment, lending credence to the modeling results and the details of the mixing process that they reveal. Interestingly, modeling of the micro-structure inherent to HDC shows that this perturbation source results in considerable mixing of the deuterium–tritium fuel with ablator material during the implosion. The reduction in fuel compression from this mix results in an approximately factor of two reduction in neutron yield in current implosions and emphasizes the importance of mitigating this significant performance degradation.

Hohlraum Reheating from Burning NIF Implosions.

As fusion experiments at the National Ignition Facility (NIF) approach and exceed breakeven, energy from the burning capsule is predicted to couple to the gold walls and reheat the hohlraum. On December 5, 2022, experiment N221204 exceeded target breakeven, historically achieving 3.15MJ of fusion energy from 2.05MJ of laser drive; for the first time, energy from the igniting capsule reheated the hohlraum beyond the peak laser-driven radiation temperature of 313eV to a peak of 350eV, in less than half a nanosecond. This reheating effect has now been unambiguously observed by the two independent Dante calorimeter systems across multiple experiments, and is shown to result from reheating of the remnant tungsten-doped ablator by the exploding core, which is heated by alpha deposition.

Machine learning assisted bayesian inference of mix and hot-spot conditions in NIF implosions

Experiments on the National Ignition Facility (NIF) have provided clear evidence of ablator material mixing into the Hot-Spot, leading to degraded performance. However, inferring the amount of mix and Hot-Spot conditions from typical experimental observations (e.g. x-ray spectra and images) is highly challenging. We have developed an analysis method that utilizes machine learning assisted Bayesian inference to find the probability distributions of the Hot-Spot and mix conditions. This approach uses a neural network, trained on an idealized 2-dimensional representation of the Hot-Spot and mix distribution, and Bayesian inference to find the statistical distributions of Hot-Spot conditions that provide a match with observations. We have tested this method with synthetic data from simulations.

Effects of alpha-ion stopping on ignition and ignition criteria in inertial confinement fusion experiments

With the advent of ignited plasmas at the National Ignition Facility (NIF), alpha physics has become a driving factor in theoretical understanding and experimental behavior. In this communication, we explore aspects of direct alpha-ion heating through comparison of the consequences from the one-fluid and two-fluid models in the hydrodynamic approach. We show that the case with all alpha energy deposited in electrons raises the ignition criteria by ∼4 keV or ∼0.2 g/cm2 in the hotspot relative to the case with all alpha energy deposited in ions. In the case of the recently ignited NIF implosion, 30% of the 3.5 MeV α energy is deposited into the DT fuel ions, for which there is negligible difference between the one-fluid and two-fluid ignition criteria. However, changes in the ion stopping fraction through profile effects and alternate stopping power models could lead to ignition curve shifts of ∼1 keV.

A coded aperture with sub-mean free-path thickness for neutron implosion geometry imaging on inertial confinement fusion and inertial fusion energy experiments.

Inertial confinement fusion and inertial fusion energy experiments diagnose the geometry of the fusion region through imaging of the neutrons released through fusion reactions. Pinhole arrays typically used for such imaging require thick substrates to obtain high contrast along with a small pinhole diameter to obtain high resolution capability, resulting in pinholes that have large aspect ratios. This leads to expensive pinhole arrays that have small solid angles and are difficult to align. Here, we propose a coded aperture with scatter and partial attenuation (CASPA) for fusion neutron imaging that relaxes the thick substrate requirement for good image contrast. These coded apertures are expected to scale to larger solid angles and are easier to align without sacrificing imaging resolution or throughput. We use Monte Carlo simulations (Geant4) to explore a coded aperture design to measure neutron implosion asymmetries on fusion experiments at the National Ignition Facility (NIF) and discuss the viability of this technique, matching the current nominal resolution of 10 µm. The results show that a 10mm thick tungsten CASPA can image NIF implosions with neutron yields above 1014 with quality comparable to unprocessed data from a current NIF neutron imaging aperture. This CASPA substrate is 20 times thinner than the current aperture arrays for fusion neutron imaging and less than one mean free-path of 14.1MeV neutrons through the substrate. Since the resolution, solid angle, and throughput are decoupled in coded aperture imaging, the resolution and solid angle achievable with future designs will be limited primarily by manufacturing capability.

Correlations between asymmetric compression, burn amplification, and hot-spot velocities in inertial confinement fusion implosions

This manuscript examines the correlations between the hot-spot velocity (an observable signature of residual kinetic energy), low-mode implosion asymmetries, and burn amplification in inertial confinement fusion implosions on the National Ignition Facility (NIF). Using a combination of two-dimensional axis-symmetric and three-dimensional radiation-hydrodynamic simulations coupled to neutronics, we find that for typical NIF implosions, the stagnation asymmetry multiplies the observed hot-spot velocity anywhere from 80% to 120%, while burn amplification always increases it. Additionally, we find stagnation asymmetry typically deflects the observed hot-spot flow. The two mechanisms (low-mode implosion asymmetries and burn amplification) can be decoupled, and application of a simple model to a database of cryogenic implosions on the NIF infers the total hot-spot velocity amplification. This finding modifies the interpretation of data collected from inertial confinement fusion experiments and impacts the magnitude and origin of low-mode asymmetries.

Time resolved ablator areal density during peak fusion burn on inertial confinement fusion implosions

Near peak compression, inertial confinement fusion implosions release both deuterium–tritium (DT) fusion gamma rays and neutron induced gamma rays from carbon from the areal density of the remaining ablator shell. The gamma reaction history diagnostic makes a time resolved measurement of both. Across many recent implosions, the carbon gamma ray peak arrives systematically 11 ± 10 ps later compared to DT fusion burn. The timing shift is consistent with the carbon areal density increasing throughout the peak of the fusion burn, implying that the carbon portion of the capsule continues to converge. A model finds that the observed timing shift is consistent with a 4π averaged carbon ablator inward velocity of 80 μm/ns for the contemporary National Ignition Facility implosions. The timing shift is possibly related to the energy balance of the implosion, with the expectation that a high performing, igniting capsule would see the carbon gamma rays arrive before the DT fusion peak.

Understanding asymmetries using integrated simulations of capsule implosions in low gas-fill hohlraums at the National Ignition Facility

Current capsule implosions at the National Ignition Facility (NIF) using high-density-carbon ablators and laser energies close to 2 MJ have shown neutron yields in excess of 50 kJ. Improving on this performance requires understanding of the different degradation mechanisms. For many NIF implosions, nuclear diagnostic signatures have inferred residual hot-spot velocities that correlate with fuel areal density variations consistent with a low-order mode-1 asymmetry. A current working hypothesis attributes these asymmetries to a combination of beam to beam variations in the laser delivery and possibly coupling to target features, such as the diagnostic holes needed for x-ray imaging. Recently, a new source has been identified, thickness variation in the ablator shell. To gain better understanding and eventually mitigate the causes of asymmetries, 3D integrated simulations using the actual delivered laser powers are needed. To capture the effect of the diagnostic holes (DHs) using direct numerical simulation would require significantly large computational resources. Instead, our 3D simulations make use of a subgrid model developed using highly-resolved 2D simulations that include several details of the DH engineering complexity. Simulations of NIF shots using hohlraums without DHs, to isolate the effect of beam-to-beam variations, reproduce fairly well the observed nuclear diagnostic signatures. Similarly, reasonable agreement between data and simulations is also obtained in the presence of diagnostic holes. To account for the remaining discrepancies a sensitivity study of ablator thickness variation showed that 1% thickness asymmetries are comparable in effect to 1% peak drive mode-1 asymmetries. Additionally, this study identified sensitivity to variations in the imbedded doped layer (needed to shield the DT ice from the high energy x-rays generated in the hohlraum) thickness even when the inner and outer surface of the ablator are perfectly spherical.

Benchmarking boron carbide equation of state using computation and experiment.

Boron carbide (B_{4}C) is of both fundamental scientific and practical interest due to its structural complexity and how it changes upon compression, as well as its many industrial uses and potential for use in inertial confinement fusion (ICF) and high-energy density physics experiments. We report the results of a comprehensive computational study of the equation of state (EOS) of B_{4}C in the liquid, warm dense matter, and plasma phases. Our calculations are cross-validated by comparisons with Hugoniot measurements up to 61 megabar from planar shock experiments performed at the National Ignition Facility (NIF). Our computational methods include path integral Monte Carlo, activity expansion, as well as all-electron Green's function Korringa-Kohn-Rostoker and molecular dynamics that are both based on density functional theory. We calculate the pressure-internal energy EOS of B_{4}C over a broad range of temperatures (∼6×10^{3}-5×10^{8}K) and densities (0.025-50 g/cm^{3}). We assess that the largest discrepancies between theoretical predictions are ≲5% near the compression maximum at 1-2×10^{6}K. This is the warm-dense state in which the K shell significantly ionizes and has posed grand challenges to theory and experiment. By comparing with different EOS models, we find a Purgatorio model (LEOS 2122) that agrees with our calculations. The maximum discrepancies in pressure between our first-principles predictions and LEOS 2122 are ∼18% and occur at temperatures between 6×10^{3}-2×10^{5}K, which we believe originate from differences in the ion thermal term and the cold curve that are modeled in LEOS 2122 in comparison with our first-principles calculations. To account for potential differences in the ion thermal term, we have developed three new equation-of-state models that are consistent with theoretical calculations and experiment. We apply these new models to 1D hydrodynamic simulations of a polar direct-drive NIF implosion, demonstrating that these new models are now available for future ICF design studies.

Measurement of the B10(α,n0)13N cross section for 2.2<Eα<4.9MeV and its application as a diagnostic at the National Ignition Facility

The National Ignition Facility (NIF) provides the opportunity to study nuclear reactions under controlled conditions at high temperatures and pressures at a level never before achieved. However, the timescale of the deuterium-tritium (DT) implosion is only a few nanoseconds, making data collection and diagnostics very challenging. One method that has been proposed for obtaining additional information about the conditions of the implosion is to activate a dopant material using the $\ensuremath{\alpha}$ particles produced from the DT fuel as a diagnostic. The yield of the activated material can give a measure of the mixing that occurs in the capsule. One of the reactions that has been proposed is $^{10}\mathrm{B}(\ensuremath{\alpha},n)\phantom{\rule{0.16em}{0ex}}^{13}\mathrm{N}$ as it produces a radioactive reactant product with a convenient half-life of $\ensuremath{\approx}10\phantom{\rule{0.16em}{0ex}}\mathrm{min}$. Although this reaction has several advantages for the application at hand, it has not seen much study in the present literature, resulting in large uncertainties in the cross section. Furthermore, for the current application, the cross section must be well characterized. With this motivation, the $^{10}\mathrm{B}(\ensuremath{\alpha},n)\phantom{\rule{0.16em}{0ex}}^{13}\mathrm{N}$ cross section has been remeasured for $2.2<{E}_{\ensuremath{\alpha}}<4.9\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ with the angle-integrated ground-state cross section reported for the first time. The present results, combined with previous measurements, allow for a determination of the cross section to a significantly higher degree of accuracy and precision than obtained previously and are shown to be consistent with thick-target measurements. Preliminary calculations are performed to test the feasibility of this reaction as a diagnostic for a NIF implosion.

Three-dimensional modeling and hydrodynamic scaling of National Ignition Facility implosions

The goal of an inertially confined, igniting plasma on the National Ignition Facility (NIF) [M. L. Spaeth, Fusion Sci. Technol. 69, 25 (2016)] remains elusive. However, there is a growing understanding of the factors that appear to be limiting current implosion performance. And with this understanding, the question naturally arises: What conditions will ultimately be required to achieve ignition, either by continuing to improve the quality of current implosions, or by hydrodynamically scaling those implosions to larger driver energies on some future facility? Given the complexity of NIF implosions, answering this question must rely heavily on sophisticated numerical simulations. In particular, those simulations must respect the three-dimensionality of real NIF implosions and also resolve the wide range of scales for the many perturbation sources that degrade them. This prospectus article reviews the current state of detailed modeling of NIF implosions, the scaling to ignition from recent experiments that that modeling implies, and areas for future improvements in modeling technique that could increase understanding and further enhance predictive capabilities. Given the uncertainties inherent in any extrapolation, particularly for a process as nonlinear as ignition, there will be no definitive answer on the requirements for ignition until it is actually demonstrated experimentally. However, with continuing improvements in modeling technique and a growing experience base from NIF, the requirements for ignition are becoming clearer.

Approaching a burning plasma on the NIF

The locus of National Ignition Facility (NIF) inertial confinement fusion (ICF) implosion data, in hot-spot burn-average areal density (ρR) and Brysk temperature (T) space, is shown and illustrates that several implosions are nearing a burning plasma state, where α-heating is the dominant source of plasma heating. A formula for diagnosing a burning plasma using measured/inferred data from ICF implosion experiments is given with the underlying derivation. Plotting ICF implosion performance against inferred hot-spot energy illustrates the key need to maximize the delivery of energy to an implosion hot-spot. A very compact analytical equation for α-heating is given, which shows that fundamentally, α-heating provides a discrete “boost” to pVγ of an implosion hot-spot. It is then shown numerically that the analytical expression for the amplification of pVγ is simply related to yield amplification and to other more famous metrics used for inferring yield amplification in experiments. Interestingly, the argument of the pVγ boost equation appears to provide a fundamental ignition condition that implicitly includes the effects of asymmetry, and it also exposes the origin of why there is uncertainty in defining single ignition criteria. The resulting analysis of NIF implosion data indicates that an increase in burn-average hot-spot temperature will be needed in order to ignite, and the strategy being pursued to achieve this goal is outlined.

Modeling and projecting implosion performance for the National Ignition Facility

Steady progress is being made in inertial confinement fusion experiments at the National Ignition Facility (NIF). Nonetheless, substantial further progress is still needed to reach the ultimate goal of fusion ignition. Closing the remaining gap will require either improving the quality of current implosions, increasing the implosion scale (and correspondingly the energy delivered by NIF), or some combination of the two. But how much of an improvement in implosion quality or energy scale is required to reach ignition? To reliably answer this question, an accurate understanding of current and past experiments is first required. Previous modeling efforts of NIF implosions have shown the need to resolve a wide range of scales (from microns to millimeters) as well as a faithful representation of the genuinely three-dimensional (3D) character of the stagnation process. Modeling NIF implosions is further complicated by the many perturbation sources that have been found to influence integrated implosion performance: flux asymmetries from the surrounding hohlraum, engineering features such as support tents and fill tubes, surface defects and contaminants, and more recently the radiation shadow cast by the fill tube on the capsule. A model including all of these effects, and with adequate resolution, challenges current computing capabilities but has recently become feasible on the largest computers. This paper reviews the status of these multi-effect, 3D simulations of NIF implosions, their comparison to experimental data, and preliminary results on scaling these simulations to the threshold of ignition on NIF.

Wavelength-detuning cross-beam energy transfer mitigation scheme for direct drive: Modeling and evidence from National Ignition Facility implosions

Cross-beam energy transfer (CBET) results from two-beam energy exchange via seeded stimulated Brillouin scattering, which detrimentally reduces laser-energy absorption for direct-drive inertial confinement fusion. Consequently, ablation pressure and implosion velocity suffer from the decreased absorption, reducing target performance in both symmetric and polar direct drive. Additionally, CBET alters the time-resolved scattered-light spectra and redistributes absorbed and scattered-light–changing shell morphology and low-mode drive symmetry. Mitigating CBET is demonstrated in inertial confinement implosions at the National Ignition Facility by detuning the laser-source wavelengths (±2.3 Å UV) of the interacting beams. In polar direct drive, wavelength detuning was shown to increase the equatorial region velocity experimentally by 16% and to alter the in-flight shell morphology. These experimental observations are consistent with design predictions of radiation–hydrodynamic simulations that indicate a 10% increase in the average ablation pressure. These results indicate that wavelength detuning successfully mitigates CBET. Simulations predict that optimized phase plates and wavelength-detuning CBET mitigation utilizing the three-legged beam layout of the OMEGA Laser System significantly increase absorption and achieve >100-Gbar hot-spot pressures in symmetric direct drive.

Kinetic physics in ICF: present understanding and future directions

Kinetic physics has the potential to impact the performance of indirect-drive inertial confinement fusion (ICF) experiments. Systematic anomalies in the National Ignition Facility implosion dataset have been identified in which kinetic physics may play a role, including inferred missing energy in the hohlraum, drive asymmetry in near-vacuum hohlraums, low areal density and high burn-averaged ion temperatures (〈Ti〉) compared with mainline simulations, and low ratios of the DD-neutron and DT-neutron yields and inferred 〈Ti〉. Several components of ICF implosions are likely to be influenced or dominated by kinetic physics: laser-plasma interactions in the LEH and hohlraum interior; the hohlraum wall blowoff, blowoff/gas and blowoff/ablator interfaces; the ablator and ablator/ice interface; and the DT fuel all present conditions in which kinetic physics can significantly affect the dynamics. This review presents the assembled experimental data and simulation results to date, which indicate that the effects of long mean-free-path plasma phenomena and self-generated electromagnetic fields may have a significant impact in ICF targets. Simulation and experimental efforts are proposed to definitively quantify the importance of these effects at ignition-relevant conditions, including priorities for ongoing study.

Capsule physics comparison of National Ignition Facility implosion designs using plastic, high density carbon, and beryllium ablators

Indirect drive implosion experiments on the National Ignition Facility (NIF) [E. I. Moses et al., Phys. Plasmas 16, 041006 (2009)] have now tested three different ablator materials: glow discharge polymer plastic, high density carbon, and beryllium. How do these different ablators compare in current and proposed implosion experiments on NIF? What are the relative advantages and disadvantages of each? This paper compares these different ablator options in capsule-only simulations of current NIF experiments and potential future designs. The simulations compare the impact of the capsule fill tube, support tent, and interface surface roughness for each case, as well as all perturbations in combination. According to the simulations, each ablator is impacted by the various perturbation sources differently, and each material poses unique challenges in the pursuit of ignition on NIF.

Simultaneous diagnosis of radial profiles and mix in NIF ignition-scale implosions via X-ray spectroscopy

In a National Ignition Facility implosion, hydrodynamic instabilities may cause the cold material from the imploding shell to be injected into the hot-spot (hot-spot mix), enhancing the radiative and conductive losses, which in turn may lead to a quenching of the ignition process. The bound-bound features of the spectrum emitted by high-Z ablator dopants that get mixed into the hot-spot have been previously used to infer the total amount of mixed mass; however, the typical errorbars are larger than the maximum tolerable mix. We present here an improved 2D model for mix spectroscopy which can be used to retrieve information on both the amount of mixed mass and the full imploded plasma profile. By performing radiation transfer and simultaneously fitting all of the features exhibited by the spectra, we are able to constrain self-consistently the effect of the opacity of the external layers of the target on the emission, thus improving the accuracy of the inferred mixed mass. The model's predictive capabilities are first validated by fitting simulated spectra arising from fully characterized hydrodynamic simulations, and then, the model is applied to previously published experimental results, providing values of mix mass in agreement with previous estimates. We show that the new self consistent procedure leads to better constrained estimates of mix and also provides insight into the sensitivity of the hot-spot spectroscopy to the spatial properties of the imploded capsule, such as the in-flight aspect ratio of the cold fuel surrounding the hotspot.

Hydro-instability growth of perturbation seeds from alternate capsule-support strategies in indirect-drive implosions on National Ignition Facility

Hydrodynamic instability growth of the capsule support membranes (or “tents”) and fill tubes has been studied in spherical, glow discharge polymer plastic capsule implosions at the National Ignition Facility (NIF) [Campbell et al., AIP Conf. Proc. 429, 3 (1998)]. In NIF implosions, the capsules are supported by tents because the nominal 10-μm thick fill tubes are not strong enough to support capsules by themselves. After it was recognized that the tents had a significant impact of implosion stability, new support methods were investigated, including thicker, 30-μm diameter fill tubes and cantilevered fill tubes, as described in this article. A new “sub-scale” version of the existing x-ray radiography platform was developed for measuring growing capsule perturbations in the acceleration phase of implosions. It was calibrated using hydrodynamic growth measurements of pre-imposed capsule modulations with Legendre modes of 60, 90, 110, and 140 at convergence ratios up to ∼2.4. Subsequent experiments with 3-D perturbations have studied instability growth of 10-μm and 30-μm thick fill tubes to compare them with 30-nm thick tent perturbations at convergence ratios up to ∼3. In other experiments, the perturbations from cantilevered fill tubes were measured and compared to the tent perturbations. The cantilevered fill tubes were supported by 12-μm thick SiC rods, offset by 100 μm, 200 μm, and 300 μm from the capsule surfaces. Based on these experiments, 30-μm thick fill tubes and 300-μm offset cantilevered fill tubes were recommended for further tests using layered deuterium-tritium implosions. The effects of x-ray shadowing during the drive and oxygen-induced perturbations during target assembly produced additional seeds for instabilities and were also measured in these experiments.

Core conditions for alpha heating attained in direct-drive inertial confinement fusion.

It is shown that direct-drive implosions on the OMEGA laser have achieved core conditions that would lead to significant alpha heating at incident energies available on the National Ignition Facility (NIF) scale. The extrapolation of the experimental results from OMEGA to NIF energy assumes only that the implosion hydrodynamic efficiency is unchanged at higher energies. This approach is independent of the uncertainties in the physical mechanism that degrade implosions on OMEGA, and relies solely on a volumetric scaling of the experimentally observed core conditions. It is estimated that the current best-performing OMEGA implosion [Regan etal., Phys. Rev. Lett. 117, 025001 (2016)10.1103/PhysRevLett.117.025001] extrapolated to a 1.9 MJ laser driver with the same illumination configuration and laser-target coupling would produce 125 kJ of fusion energy with similar levels of alpha heating observed in current highest performing indirect-drive NIF implosions.

Mitigating the impact of hohlraum asymmetries in National Ignition Facility implosions using capsule shims

Current indirect drive implosion experiments on the National Ignition Facility (NIF) [Moses et al., Phys. Plasmas 16, 041006 (2009)] are believed to be strongly impacted by long wavelength perturbations driven by asymmetries in the hohlraum x-ray flux. To address this perturbation source, active efforts are underway to develop modified hohlraum designs with reduced asymmetry imprint. An alternative strategy, however, is to modify the capsule design to be more resilient to a given amount of hohlraum asymmetry. In particular, the capsule may be deliberately misshaped, or “shimmed,” so as to counteract the expected asymmetries from the hohlraum. Here, the efficacy of capsule shimming to correct the asymmetries in two recent NIF implosion experiments is assessed using two-dimensional radiation hydrodynamics simulations. Despite the highly time-dependent character of the asymmetries and the high convergence ratios of these implosions, simulations suggest that shims could be highly effective at counteracting current asymmetries and result in factors of a few enhancements in neutron yields. For higher compression designs, the yield improvement could be even greater.