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.

Recent indirect-drive1 inertial confinement fusion (ICF)2 experiments on the National Ignition Facility (NIF)3–5 have for the first time produced target yields exceeding 1 MJ6–8 and target gains exceeding unity,9–12 i.e., more fusion energy produced in the experiment than laser energy used to drive the implosion. These experiments all used high-density carbon (HDC) ablators, a form of synthetic diamond, grown in the form of spherical shells with very high sphericity and fine surface finish and doped with small amounts of tungsten to mitigate the effects of hard x-ray pre-heating.13–15 Experiments intended to repeat the first 1 MJ yield result have shown variability, however, with yields varying by factors of several.16 The leading sources of variability for this class of experiments have been identified as long wavelength asymmetries resulting from ablator shell non-sphericity or imbalance in laser delivery17–19 and capsule quality in the form of fine-scale ablator imperfections.20 These short wavelength ablator imperfections include micrometer-scale pits on the capsule surface, similarly sized voids in the bulk of the ablator shell, and debris on the capsule surface believed to be due to flakes of material from the interior of the surrounding Hohlraum that fall onto the capsule surface and can be detected in pre-shot x-ray imaging. A wide range of high atomic number (high-Z) inclusions have also been identified in the ablator bulk in a number of different morphologies, concentrations, and frequencies. Finally, there is the inherent granularity of the crystalline HDC ablator itself. Recent experiments have used nano-crystalline diamond, which is composed of HDC grains with a characteristic length scale of 100 nm and a mass density of approximately 3.4 g/cm3 bound together by graphitic boundary regions with a characteristic thickness of a few nanometers and a density of 2.2 g/cm3.

The density and/or opacity perturbations introduced by each one of these fine-scale defects can serve as seeds for short-wavelength mixing during the course of the implosion. In the worst case, these defects can cause jets of tungsten-doped ablator material to pollute and radiatively cool the hotspot and strongly degrade neutron yields.20,21 Even without jetting into the hotspot, mixing of ablator material with the adjoining dense deuterium–tritium (DT) fuel can reduce the fuel compressibility and limit the total compression of the implosion and hence limit burn propagation and yield.22–24 While localized jets that transport ablator material into the hotspot are believed primarily to result from localized defects such as pits, voids, and surface debris, more broad-spectrum fuel–ablator mixing is believed to be generated by the HDC crystalline micro-structure and surface roughness. Of course, a high density of small, individual defects can also act collectively to generate broad-spectrum mixing, though shells with these types of multiple defects are generally rejected from use in experiments for precisely this reason.

Both degradation mechanisms, pollution of the hotspot by ablator jets and broad-spectrum mixing degrading fuel compression, are important in understanding the performance of current experiments and avenues for future improvement. This paper describes high-resolution modeling to quantify and understand the impact of representative isolated ablator defects, as well as HDC micro-structure and surface roughness, in two recent NIF implosion experiments. High-Z inclusions could also contribute to observed implosion performance, but they are not addressed here given the broad range of morphologies that have been identified and the more preliminary state of characterizing this type of defect. Quantifying the impact of this type of defect will be a subject of future work. Note that recent modeling has also been done of similar types of defects in the context of direct drive implosions.25 

The two recent NIF experiments that are used as baselines for this study are shots N210808, the first NIF experiment to produce a neutron yield exceeding 1 MJ,6 and N221204, the first experiment to exceed unity energy gain.9 Beyond the significance of these experiments as milestones in implosion performance, these shots are also useful to compare with respect to their susceptibility (or resistance) to degradation by ablator defects. Shot N221204 increased the laser energy to 2.05 MJ from 1.9 MJ on N210808 and thereby could drive a 6 μm thicker ablator layer to similar implosion velocity and adiabat. Figure 1 shows the details of the capsules used for these two experiments. In each pie diagram, the yellow region represents undoped HDC, while the orange region represents the HDC region doped with a small percentage of tungsten. Both shells include a small undoped region between the DT fuel layer (blue) and the tungsten-doped HDC layer. Aside from small fluctuations in the thicknesses of the internal layers and the central DT gas density, the leading differences between N210808 and N221204 are the thicker undoped outer ablator layer in N221204 and higher dopant concentration.

FIG. 1.

Pie diagrams for the capsules used on shots N210808 and N221204. The yellow regions represent the undoped HDC, and the orange regions represent the regions doped with tungsten. The DT ice layer is shown in blue, and the central DT gas region is light blue. Aside from small fluctuations in layer thicknesses and DT gas density, the leading difference is the thicker undoped ablator layer in N221204 and higher dopant concentration.

FIG. 1.

Pie diagrams for the capsules used on shots N210808 and N221204. The yellow regions represent the undoped HDC, and the orange regions represent the regions doped with tungsten. The DT ice layer is shown in blue, and the central DT gas region is light blue. Aside from small fluctuations in layer thicknesses and DT gas density, the leading difference is the thicker undoped ablator layer in N221204 and higher dopant concentration.

Close modal

With its more massive imploding shell and higher implosion kinetic energy, N221204 should be more robust to ablator jets or other degradations that could rob the hotspot of energy density and thwart ignition. The thicker ablator shell might also be anticipated to confer greater resistance to the penetration of these jets or other types of mix from a given sized defect into the hotspot and so further reduce their impact in this thicker-ablator experiment. For these reasons, it is interesting to compare the relative susceptibility of these two implosions to a fixed suite of ablator defects and quantify if N221204 is indeed more resistant to a given perturbation than N210808.

The principal results of this study are the following. Pits on the ablator surface with volumes larger than 4 μm3 result in ablator material injected into the hotspot by the time of peak neutron production (bang time). Interestingly, the thicker-ablator experiment N221204 shows similar or larger injected mass for a given sized surface pit than the thinner-ablator N210808 experiment does. Similarly, voids with volumes larger than 5 μm3 within 10 μm of the ablator surface also lead to hotspot injected mass with again a similar or larger injected mass in N221204 compared to N210808. Hot spot injected mass diminishes rapidly with increasing void depth into the ablator for both shots. An exception is large voids located at the outer boundary of the buried doped layer of the ablator. At this interface, large voids can result in 10 ng of hotspot injected mass for N210808 and more than 20 ng for N221204. For comparison, the capsule fill tube is simulated to inject 64 ng of mass into the hotspot for N210808 and is a known degradation to performance. Thin flakes of gold debris on the ablator surface result in 20–40 ng of hotspot injected mass when the debris exceeds a surface area of 50 μm2. Again, N210808 and N221204 show very similar hotspot injected mass for a given size of surface debris. There is also very little sensitivity to debris thickness with thicknesses of 0.5 and 1.0 μm resulting in essentially the same injected mass as a function of surface area. There is, however, a sensitivity to debris composition with depleted uranium debris resulting in less than half of the injected mass compared to the equivalent sized piece of gold debris. Most of the Hohlraum wall in current experiments is composed of depleted uranium under a thin surface layer of gold, but it is not possible in current x-ray imaging to distinguish if the debris is from the gold surface coating or the underlying depleted uranium wall.

Simulations of the impact of HDC micro-structure show that this intrinsic perturbation source results in considerable mixing of the HDC ablator and DT fuel while the shell is imploding. Again, this result is independent of experiment N210808 or N221204. Importantly, although the DT fuel in both of these shots is heavily mixed with HDC at the time of peak compression, this ablator mixing does not penetrate into the forming hotspot and so—aside from reducing the overall fuel compression—does not interfere with the hotspot ignition process. As the burn wave propagates into the denser fuel region by the time of peak neutron production, however, this mixed material is entrained into the burn region and significantly impacts the total neutron yield. To better assess the impact of this ablator-fuel mixing in realistic implosions, a lower resolution mix model is tuned to these high resolution, ab initio mix simulations. When combined with similar surrogate models for the other known degradation sources (the capsule support tent, the fill tube, surface roughness, etc.), these lower resolution, multi-effect simulations show that the fuel–ablator mix alone results in a factor of two reduction in neutron yield, a clearly significant performance degradation. Equally importantly, these simulations show consistency with experimental measurements of yield, compression, and burn width for several shots when fuel–ablator mix is included vs without and further corroborates that this mixing mechanism is an important factor in current experiments.

Controlled experiments to isolate the impact of each degradation source studied here are impossible given the very small scales and irreproducibility of the defects from shell to shell. While this reinforces the importance of simulation studies such as this, a weakness of the approach is that direct experimental validation of these results is also impossible. However, comparisons with broad trends over many repeated experiments can be used to provide some modeling validation. Broadly, the results presented here are consistent with experimental observations. Ablator shells with measured surface pits greater than approximately 3 μm3 in volume have been observed to show bright x-ray emission from hotspot jets consistent with mix mass entering the hotspot,20 and in some cases, individual surface pits can be correlated in space to subsequent hotspot emission. This experimental threshold for mass injection is in encouraging agreement with the threshold of 4 μm3 found in simulation. Likewise, the observation of high-Z surface particles in pre-shot x-ray imaging has shown a correlation with enhanced hotspot x-ray emission when the particles are approximately 100 μm2 in area or larger, again broadly consistent with the threshold of greater than 50 μm2 found in simulations. Direct correlation of the impact of ablator voids on hotspot emission is lacking; however, experiments prior to N210808 that used HDC shells with thousands of void detections compared to none to few detected in N210808 and its repeat shots showed neutron yields an order of magnitude lower.20,26–28 There is, of course, no means to isolate the effect of HDC micro-structure alone, although a number of focused physics experiments are attempting to measure the growth of the fuel–ablator mix layer directly by x-ray imaging29,30 and nuclear diagnostic techniques.24 Furthermore, recent designs that have specifically attempted to mitigate this and other mixing sources have shown improved compression compared to previous designs consistent with reduced mix.31–36 

Note that all of the simulations described here are two-dimensional (2D). While the nonlinear evolution of the jets seeded by pits, voids, or surface debris and especially the quasi-turbulent mixing seeded by HDC micro-structure will evolve differently in three-dimensional (3D) reality as opposed to the 2D idealizations here, the very fine scales and hence high resolution necessary to model these defects make 3D simulations prohibitive at this time. The multi-effect simulations described in Sec. VII can also be expected to be sensitive to 2D vs 3D differences. The trends that can be extracted from the currently available 2D simulations have nonetheless proven useful in prioritizing targets for implosion experiments and target fabrication research for improved target quality. Properly resolving these ablator defects in 3D will remain a goal for future work.

This paper is organized as follows. Section II describes the Hohlraum modeling that is first used to generate x-ray sources applied to higher resolution capsule-only simulations of individual ablator defects. These Hohlraum simulations adopt an alternate approach compared to most Hohlraum simulations of NIF experiments to improve overall agreement with experimental data, so these details are included here. These simulations are also the first NIF simulations to use the latest equation of state (EOS) model for HDC, Sesame 7835, which also significantly improves the fidelity of the model. Section III then describes the methodology and results of simulations of HDC surface pits for both N210808 and N221204. Sections IV and V describe analogous results for ablator voids and high-Z surface debris for both shots, and Sec. VI describes the methodology and results of HDC micro-structure modeling. Section VII then describes lower resolution simulations that incorporate reduced models of multiple perturbation sources together as applies in actual experiments (surface roughness, the fill tube, micro-structure-seeded fuel–ablator mix, etc.). As already noted, these simulations show that the presence of micro-structure-seeded mix alone results in a factor of two reduction in neutron yield for these recent shots. Section VIII summarizes and concludes.

The high-resolution ablator defect simulations described below begin with lower resolution Hohlraum simulations that model the laser beam propagation, x-ray conversion in the Hohlraum, and capsule implosion. These simulations are used to compute an x-ray source that is used as a boundary condition in subsequent higher resolution capsule-only simulations. Since the modeling approach used here differs from the approach followed by most modeling of NIF Hohlraums, some details of this approach are discussed here.

The baseline Hohlraum model is broadly similar to the models described previously.37,38 The model is run in 2D in the radiation hydrodynamics code HYDRA39 using arbitrary Lagrangian–Eulerian (ALE) hydrodynamics, multigroup detailed radiation transport, and laser ray tracing. The simulation mesh resolves the Kapton windows covering the laser entrance holes at either end of the Hohlraum, the details of the Hohlraum laser entrance hole edge, the gold and depleted uranium layered Hohlraum wall, and the helium Hohlraum gas fill and HDC capsule. Adequate zoning in the Hohlraum wall, adequate photon energy groups, and a large enough number of laser rays are used to numerically converge the x-ray generation by the Hohlraum. Tabular equations of state40–42 are used for the Hohlraum and HDC capsule. The DCA opacity model43 is used for the Hohlraum wall under non-local thermodynamic equilibrium (NLTE) conditions, and tabular opacities44 are used for LTE conditions in the Hohlraum wall and in the capsule and Hohlraum gas fill.

The primary difference in the Hohlraum simulations used here compared to previous modeling is that they do not use multipliers on the laser power to match experimental observables. From the first modeling of NIF DT experiments up until the present, it has been consistently observed that simulations of NIF Hohlraums using Lasnex45,46 or HYDRA, or more recently xRAGE,47 all overpredict the conversion of laser energy into x-rays and consequently overpredict the x-ray drive seen by the imploding capsule. Many hypotheses have been proposed to explain the observed deficit in Hohlraum drive, and, while progress has been made in reducing the deficit between simulation and experiment,38 to-date no definite explanation for the deficit has been found. To model on-going experiments at NIF, the pragmatic approach has then been adopted to simply multiply the incident laser power into the Hohlraum simulation by a factor less than unity and thereby degrade the x-ray drive applied to the capsule. In current experiments, it is typically necessary to reduce the incident laser power by 10%–20% in a time-dependent fashion throughout the laser pulse in order to match shock timing in the implosion as measured by the VISAR diagnostic and the implosion bang time. While this approach accomplishes the immediate goal of matching implosion tuning data, it comes at a noticeable cost in simulation fidelity. Specifically, by reducing the incident laser power from the measured incident power, the plasma filling of the Hohlraum will be cooler than if the full laser power were used. This difference will alter laser beam propagation through the Hohlraum fill and also modify the conditions under which any laser plasma interactions48 occur. Given the importance of laser backscatter in influencing laser coupling to the Hohlraum and especially the importance of cross-beam energy transfer49,50 in controlling the sphericity of the capsule implosion, this change in plasma conditions can be a significant compromise in simulation fidelity, compounding the already compromised predictive capability of the model with respect to implosion timing. More broadly, the predictive capability of this modeling approach is also clearly limited. Without a basis in the underlying physics, laser power multipliers tuned to one type of laser pulse and Hohlraum design cannot be expected to accurately predict the behavior of a Hohlraum experiment using a very different laser pulse shape, Hohlraum geometry, or capsule composition.

Bearing the limitations of the current modeling approach in mind, the approach followed here returned to a technique often employed in Hohlraum modeling from before the completion of the NIF.51 This approach is, instead of degrading the incident laser power into the Hohlraum simulation, to degrade the x-ray emission opacity of the Hohlraum wall to match measured Hohlraum performance. While functionally equivalent to degrading the incident laser power, modifying the Hohlraum wall opacity is a physically more plausible modification to the simulation given that relatively modest reductions in wall opacity, consistent with published uncertainties in emissivity,52–54 prove sufficient to match recent tuning data. This is in contrast to the use of laser power multipliers where multipliers on the laser power an order of magnitude larger than the known uncertainty in laser delivery or backscatter are necessary to match observed performance. As already noted, using the full, as-delivered laser energy in the simulation also provides a better model of Hohlraum plasma conditions making for a more accurate assessment of beam propagation and any laser plasma interaction affects.

Another extremely important advantage of degrading the Hohlraum wall opacity as opposed to degrading the incident laser power to match observed performance is that, by applying separate multipliers in energy for the Hohlraum opacity, it is possible to match both the total measured x-ray flux from the Hohlraum wall and the NLTE or gold M-band emission from the Hohlraum wall (emission at photon energies greater than 1.8 keV). Both of these quantities are measured experimentally using the DANTE diagnostic.55 Since the Hohlraum M-band emission is absorbed deeply inside of the ablating capsule and modifies the ablator density distribution, it is a very strong lever on implosion stability.23 As such, for modeling fine-scale defects that grow due to hydrodynamic instabilities, correctly matching the pre-heat levels experienced by the capsule is important for accurate modeling of defect growth. When matching Hohlraum simulations to experiment by using laser power multipliers, it is not possible to independently match both the total flux and M-band emission. Simulations that are matched to the total flux using laser power multipliers generally overpredict the M-band emission by 20%–30% compared to experiment. In turn, differences in capsule M-band pre-heat of this order can result in factor of two differences in simulated instability growth. That simulations matched to experiment using wall opacity multipliers do not make this error and hence give a much more accurate representation of instability growth rates is a further significant advantage to this approach.

In addition to reducing the wall emissivity, the simulations described here also introduce a multiplier on the Hohlraum wall heat capacity. Recent theoretical work and experiments at NIF56 show that the wall opacity and heat capacity are constrained such that the product of the two should be constant. That is, any decrease in wall emissivity must be accompanied by a compensating increase in wall heat capacity. The simulations here therefore introduce a wall heat capacity multiplier that is the reciprocal of the wall emissivity multiplier. Note that a decrease in emissivity and the accompanying increase in heat capacity both reduce the x-ray fluence from the Hohlraum wall and so both act to improve simulation agreement with data.

A final important difference in the simulations described here compared to previous modeling is that they use the Sesame 7835 EOS table for the capsule ablator, the most recently available EOS for carbon.57 This table improves on the tables used in previous simulations in that Sesame 7835 matches both the first shock Hugoniot for HDC and the subsequently inferred release states for HDC into liquid deuterium as measured at NIF and other facilities.58,59 Notably, the LEOS 9061 and 9069 tables60,61 used in previous modeling match either the first shock Hugoniot of HDC or match the subsequent release into deuterium but not both datasets simultaneously. Given that the experiments considered here begin with a strong first shock transiting the HDC ablator, followed by a release of that ablator as the shock crosses into the DT fuel, matching both shock and release is important for accurate modeling. Since the Sesame 7835 table matches the measured behavior in both of these phases, it significantly improves the fidelity of these simulations.

Using the Sesame 7835 EOS table for HDC and separate Hohlraum wall opacity multipliers for energies less than and greater than 1.8 keV, it is possible to closely match tuning data relevant to the NIF implosion experiments modeled in this study. This is summarized in Fig. 2 that shows a comparison of experimental (black) and simulated (red) VISAR shock velocities at the pole (a) and equator (b) for NIF shot N221128. With appropriate wall opacity multipliers, the simulations match the shock merger times, indicated by the abrupt increases in shock velocity, for the first, second, and third shocks and the speeds of each shock to within the experimental error bars indicated by the thin dashed lines. The only noticeable discrepancy is in the third shock velocity at the pole. Also shown in Fig. 2 is a comparison of experimental and simulated Hohlraum emission for both total x-ray flux (c) and emission in the 2–4 keV band coincident with the gold M-band emission (d). The experimental data taken here for shot N21102462 used the recently commissioned multi-layer mirror63 DANTE diagnostic to reduce the uncertainties in the measured 2–4 keV flux to within the 10% error bars shown. Again, by using separate wall opacity multipliers for energies less than and greater than 1.8 keV, it is possible to match within error bars both the total x-ray flux and 2–4 keV flux as shown. Note that, on matching the VISAR measured shock timing and DANTE total and 2–4 keV flux, the simulation also correctly matches the measured bang time of the DT layered experiments N210808 and N221204.

FIG. 2.

Comparison of simulated observables from tuning experiments (red) to NIF tuning data (black). (a) and (b) Pole and equator shock velocities in surrogate keyhole targets using the VISAR diagnostic. Simulations including Hohlraum wall opacity and heat capacity multipliers show good agreement for shock breakout times and velocities. (c) and (d) Hohlraum x-ray flux measurements with the DANTE diagnostic including the recently commissioned multi-layer mirror for improved resolution of the 2–4 keV gold M-band flux. Again, simulations with appropriate Hohlraum wall opacity and heat capacity multipliers match these data well.

FIG. 2.

Comparison of simulated observables from tuning experiments (red) to NIF tuning data (black). (a) and (b) Pole and equator shock velocities in surrogate keyhole targets using the VISAR diagnostic. Simulations including Hohlraum wall opacity and heat capacity multipliers show good agreement for shock breakout times and velocities. (c) and (d) Hohlraum x-ray flux measurements with the DANTE diagnostic including the recently commissioned multi-layer mirror for improved resolution of the 2–4 keV gold M-band flux. Again, simulations with appropriate Hohlraum wall opacity and heat capacity multipliers match these data well.

Close modal

The Hohlraum wall opacity multipliers used to obtain the simulated agreement in Fig. 2 are summarized in Fig. 3. The black curve shows the total laser power history for shot N210808, the red curve shows the wall opacity multiplier used for photon energies less than 1.8 keV, and the blue curve shows the multiplier for energies greater than 1.8 keV with the multiplier magnitude shown on the right-hand scale. Note that the measured laser backscatter has been removed from the incident laser power that is input into the simulations and shown in the plot. The opacity multiplier for energies less than 1.8 keV shown in red begins with a value of 0.85, briefly increases to 1.0 from 3.0 to 4.5 ns, and then decreases again to 0.85 for the remainder of the simulation. The increase in multiplier coincides with the launch of the second shock and was found necessary for the second shock agreement shown in Fig. 2. Overall, the average multiplier value of 0.85 represents only a fairly modest excursion from the nominal opacity and is consistent with inferred uncertainties.52–54 Though not shown in the figure, there is a constant-in-time multiplier on the Hohlraum wall heat capacity of 1.15 to correspond to the average opacity multiplier of 0.85; it is not currently possible to use time-dependent heat capacity multipliers in HYDRA, though strictly the heat capacity should follow the time dependence of the opacity as described above.

FIG. 3.

Hohlraum wall opacity multipliers used to obtain the match to Hohlraum tuning data shown in Fig. 2. The total laser power including backscatter subtraction is shown in black, the Hohlraum wall opacity multiplier for energies less than 1.8 keV is shown in red, and the multiplier for energies greater than 1.8 keV is shown in blue. Multiplier magnitude is shown with the scale on the right.

FIG. 3.

Hohlraum wall opacity multipliers used to obtain the match to Hohlraum tuning data shown in Fig. 2. The total laser power including backscatter subtraction is shown in black, the Hohlraum wall opacity multiplier for energies less than 1.8 keV is shown in red, and the multiplier for energies greater than 1.8 keV is shown in blue. Multiplier magnitude is shown with the scale on the right.

Close modal

The opacity multiplier for energies greater than 1.8 keV shown in blue begins with a value of 1.0, decreases to 0.5 at 4.5 ns, and then decreases again to 0.1 for the remainder of the simulation. This represents a much larger deviation in opacity from the nominal model than used for the lower photon energies, but this deviation was found necessary for the agreement shown in Fig. 2(d). While it is acknowledged that uncertainties are larger for the NLTE opacities that contribute the majority of the emission at energies above 1.8 keV, these multipliers so far from unity are not currently physically justifiable. Hypotheses are being explored for other physical processes that could lead to a strong reduction in M-band emission (e.g., unmodeled mix at the Hohlraum wall), and more accurate NLTE emission models are also actively being developed that could lead to reduced simulated M-band emission. For the moment, however, this approach must simply be taken as an effective model that reproduces important measured features of Hohlraum performance but cannot currently be justified physically. For purpose of modeling ablator defect impacts as is the focus here, this model reproduces the critical measured features of implosion shock timing, Hohlraum total and 2–4 keV x-ray flux, and implosion bang time.

Section II describes the Hohlraum modeling used to develop x-ray sources for subsequent high-resolution capsule-only simulations. This section now focuses on modeling the first type of isolated ablator defect, surface pits. Measurements of surface pits on HDC shells have historically varied over a considerable range of widths and depths. Shells used in NIF experiments in 2018–2021 included up to thousands of surface pits that could be up to 9 μm in full width and as deep as 1.6 μm. While ablator shells in recent high-performance experiments have had few to no large pits, and many fewer small pits as well, these historical pit sizes have informed the modeling done here. Nonetheless, even for the largest of ablator pits, these pits at micrometer or smaller scales represent very small defects compared to the millimeter scale radii of current capsules. As such, very high-resolution simulations are required to capture accurately the growth of these pits.

An example 2D HYDRA simulation of a 1.6 μm deep and 4.6 μm full width pit is shown in Fig. 4. The simulation begins on a wedge spanning 15° in polar angle using 1444 radial and 2048 angular zones. The pit begins as the small Gaussian shaped defect on the axis of symmetry in the left panel of Fig. 4. There are approximately forty angular zones across the pit at the beginning of the simulation. Simulations with higher and lower zone count were run to verify that the resolution used here is numerically converged. Given that the width and depth of the starting pit are comparable, it was also found that detailed radiation transport was needed to accurately capture the radiation shadowing effect of the pit on itself. Simulations were run with multi-group radiation diffusion, discrete ordinate radiation transport,64,65 and implicit Monte Carlo (IMC) transport.66 The latter two approaches were found to give substantially similar results, while the first resulted in much larger defect growth. The exaggerated growth with diffusive radiation transport can be anticipated since this method leads to the transport of radiant energy directly to the bottom of the pit when a more detailed solution would show this region to be shadowed. The enhanced, early-time ablation that results from this unphysical transport to the bottom of the pit ultimately leads to more rapid perturbation growth and a larger late-time hotspot jet. Since the discrete ordinates approach was faster to solution, used fewer compute resources, and was less prone to numerical noise, it is the approach used for the results below. Various approaches to ALE mesh relaxation were also tested and found not to influence the final result.

FIG. 4.

Simulation of a 1.6 μm deep and 4.6 μm full width pit shown at three different times for shot N210808. Mass density is shown in the upper half of each panel and material region in the lower half. In the lower half of each panel, the DT gas and ice regions are light and dark blue, and the doped and undoped HDC regions are orange and yellow, respectively. The initially small pit on the surface grows to puncture the shell by 8.40 ns allowing the ablation pressure to force HDC material into the shell interior. By 9.15 ns (no-α bang time), as shown in the right panel, a very narrow jet has penetrated the center of the hot spot with a mass of 3.3 ng of ablator material. The jet is confined to the axis in this 2D simulation but can be expected to break up or bend away from the axis in a more realistic 3D flow.

FIG. 4.

Simulation of a 1.6 μm deep and 4.6 μm full width pit shown at three different times for shot N210808. Mass density is shown in the upper half of each panel and material region in the lower half. In the lower half of each panel, the DT gas and ice regions are light and dark blue, and the doped and undoped HDC regions are orange and yellow, respectively. The initially small pit on the surface grows to puncture the shell by 8.40 ns allowing the ablation pressure to force HDC material into the shell interior. By 9.15 ns (no-α bang time), as shown in the right panel, a very narrow jet has penetrated the center of the hot spot with a mass of 3.3 ng of ablator material. The jet is confined to the axis in this 2D simulation but can be expected to break up or bend away from the axis in a more realistic 3D flow.

Close modal

The evolution over time of the perturbation seeded by the pit can be seen in the two right panels of Fig. 4. The middle panel shows the defect evolution at 8.40 ns when the shell is approaching peak implosion velocity. By this time, the pit has grown into a Rayleigh–Taylor bubble that has punctured the imploding HDC and DT shell allowing the high ablation pressure outside of the shell to force HDC ablator material through the hole and into the shell interior. The lower half of the panel shows material region with the yellow and orange regions representing undoped and tungsten-doped HDC, respectively. The upper half of each panel shows mass density.

Shortly past this time, the perturbations seeded by large pits can begin to reflect off of the simulation's boundaries at 15° in polar angle. To avoid this unphysical boundary reflection, the simulation is remapped at this time from the 15° wedge to a full 180° domain by simply extrapolating the boundary velocities, densities, and pressures symmetrically in polar angle. Since the fine-scale, early-time evolution of the initial defect has now completed, the resolution of the mesh is also reduced to 2048 angular zones covering the full 180°. At this step, the mesh topology is also changed from a polar mesh to a multi-block butterfly mesh to optimize the resolution of the subsequent ablator jet penetrating the center of the hotspot.67 Since discrete ordinates transport is not currently available in HYDRA for multi-block meshes, the radiation transport scheme is also changed to multi-group diffusion at this time. Tests using IMC transport on multi-block meshes show that using multi-group diffusion at this stage does not compromise the accuracy of the results. Note that a similar procedure to this has been used for modeling the fill tube impact in NIF implosions for some time.68,69

The right panel of Fig. 4 shows the ablator jet generated by the surface pit at the time of peak neutron production. α-particle stopping is disabled in all of these simulations since it otherwise causes the simulations to give close to 1D yields and very high hotspot pressures that substantially change the jet dynamics. (The combined effects of α-particle stopping along with the multiple perturbation sources that impact realistic implosions are included in the simulations in Sec. VII.) The ablator jet at this time is a very high aspect ratio jet that has crossed the center of the hotspot. In this 2D simulation, the jet is confined to the axis due to symmetry. In 3D reality, of course, this constraint would not apply and the jet could be expected to bend off axis or otherwise break apart due to secondary instabilities or the influence of other hotspot flows.70–72 These effects are clearly beyond the scope of this 2D model.

To quantify the impact of different sized surface pits on the implosion, the total amount of injected ablator mass at no-α bang time was tallied. To tally this mass, the hotspot radius is first defined as the lesser of the radius at the capsule waist (away from the location of the jet) where the density is half of its maximum value and the matter temperature is greater than 1 keV. The injected ablator mass is then the summed mass of all material that is not DT within this radius at the given time. This definition is consistent with the definition used in previous studies.22,73,74

The result of scanning different initial pit widths and depths for shots N210808 and N221204 is shown in Fig. 5 in a plot of hotspot injected mass vs pit volume. As shown in the figure, two pit full widths (4.6 and 9.2 μm) were simulated for each of four pit depths (0.2, 0.4, 0.8, and 1.6 μm). Interestingly, for both shots, the amount of injected mass is ordered by the pit volume independent of the initial pit width or depth. This is to be expected theoretically since the pits are very narrow (5–10 μm) compared to the most hydrodynamically unstable modes at the ablation front (100–300 μm). In this regime, the pits behave essentially as delta function perturbations and so only the volume displaced by the pit affects the ultimate perturbation growth. This argument is not strictly correct given the nonlinearity of the initial pit perturbations but nonetheless is accurate based on the results shown in Fig. 5. Note that this argument also implies that 3D surface perturbations, i.e., non-axisymmetric pits, would evolve similarly to 2D axisymmetric surface perturbations of the same volume as modeled here. The same argument can also be applied to the interior void and surface debris perturbations considered in Secs. IV and V.

FIG. 5.

Hot spot injected mass as a function of pit volume for shots N210808 and N221204. Four pit depths (0.2, 0.4, 0.8, and 1.6 μm) were scanned over two pit widths (4.6 and 9.2 μm). Pit volume orders the hot spot injected mass well for all cases, and a threshold for injected mass of greater than 4 μm3 is seen for both N210808 and the thicker-ablator shot N221204. 15 ng of ablator mass is injected into the hot spot for the largest pits simulated for N210808. For comparison, a simulation of the fill tube for this experiment shows 64 ng of hot spot injected mass.

FIG. 5.

Hot spot injected mass as a function of pit volume for shots N210808 and N221204. Four pit depths (0.2, 0.4, 0.8, and 1.6 μm) were scanned over two pit widths (4.6 and 9.2 μm). Pit volume orders the hot spot injected mass well for all cases, and a threshold for injected mass of greater than 4 μm3 is seen for both N210808 and the thicker-ablator shot N221204. 15 ng of ablator mass is injected into the hot spot for the largest pits simulated for N210808. For comparison, a simulation of the fill tube for this experiment shows 64 ng of hot spot injected mass.

Close modal

As also shown for both shots, the threshold for mass injection is a pit volume greater than 4 μm3. As noted in the introduction, this is surprising since it shows that the thicker ablator experiment N221204 is in fact not more resistant to a jet seeded by the same sized perturbation than the thinner ablator experiment N210808. In fact, for very large amplitude pits, these simulations show N221204 is subject to up to 25 ng of injected mass, more than the 15 ng injected with the same sized pit on N210808. This surprising result is due to the higher tungsten dopant concentration used in N221204. With its higher dopant concentration (approximately 0.63 at. % tungsten for N221204 vs 0.45 at. % for N210808), N221204 has a steeper ablation front and a lower ablation velocity. According to the well-known Takabe formula for linear Rayleigh–Taylor growth,75 both of these effects lead to faster perturbation growth and ultimately a larger hotspot jet. Note that subsequent thicker ablator experiments have used ablators with reduced dopant concentrations more comparable to N210808.

A similar procedure was followed for modeling voids in the bulk of the HDC ablator as that used for the pits on the surface. That is, simulations begin with very high resolution on a 15° wedge but are subsequently remapped to a 180° butterfly mesh to capture the stagnation phase with each phase using the same numbers of radial and angular zones as for pits. Again, tests were run at different mesh resolutions to demonstrate numerical convergence. Different from the case of pits, tests of different radiation transport schemes showed that multi-group diffusion was adequate for void simulations, and this method is used in the void simulations below. This might be expected since the early-time radiation shadowing effect important for pits does not apply to voids.

Figure 6 shows the evolution in time of a simulation of a 20.6 μm3 spherical void located 5.0 μm below the ablator surface. The early-time interaction of the void with the first ablation-driven shock is an example of the classic shock-bubble interaction.76 In this interaction, as seen in the void simulation, the shock runs across the void and collapses it. In the process, misaligned density and pressure gradients at the void surface lead to vorticity generation and a subsequent vortex ring left behind the transmitted shock. Since the void has a lower density than the surrounding ablator, the circulation around this vortex ring is such that the ring propagates to the left in Fig. 6 and effectively follows the shock wave along the z-axis. The velocity of the vortex ring is not sufficient, however, to outrun the encroaching ablation front which eventually catches up to the vortex ring. At this point, the vortex ring acts as a strong seed to ablation front Rayleigh–Taylor growth, which rapidly expands the vortex ring perturbation into a Rayleigh–Taylor bubble that, like the pit defect, punctures the ablator shell inflight. This phase is shown in the middle panel of Fig. 6. The subsequent evolution is again similar to the case of a surface pit with the ablation pressure forcing ablator material through the shell opening and this material eventually forming a jet of material through the hotspot center. As before, the jet is confined to the axis of the simulation due to symmetry, although more complicated evolution can be expected in 3D. Note that these dynamics are qualitatively similar to those reported from xRAGE modeling a similar-sized void in an earlier NIF experiment using an HDC ablator.77 

FIG. 6.

Simulation of a 1.7 μm radius void located 5.0 μm below the ablator surface shown at three times for N210808. As in Fig. 4, the upper half of each panel shows mass density and the lower half shows material region with the DT gas and ice shown in light and dark blue and the doped and undoped HDC in orange and yellow, respectively. By 8.40 ns, the vortex ring perturbation seeded by the collapsing void has grown into a Rayleigh–Taylor bubble that has punctured the imploding DT and HDC shell. This results in a jet of ablator material being forced into the shell interior. By 9.15 ns (no-α bang time), 9.7 ng of ablator material has penetrated the hot spot in a narrow jet.

FIG. 6.

Simulation of a 1.7 μm radius void located 5.0 μm below the ablator surface shown at three times for N210808. As in Fig. 4, the upper half of each panel shows mass density and the lower half shows material region with the DT gas and ice shown in light and dark blue and the doped and undoped HDC in orange and yellow, respectively. By 8.40 ns, the vortex ring perturbation seeded by the collapsing void has grown into a Rayleigh–Taylor bubble that has punctured the imploding DT and HDC shell. This results in a jet of ablator material being forced into the shell interior. By 9.15 ns (no-α bang time), 9.7 ng of ablator material has penetrated the hot spot in a narrow jet.

Close modal

The hotspot injected mass for a range of void volumes (5.6, 9.2, 20.6, and 38.8 μm3) and void depths (5, 10, 20, 40, 60, and 80 μm) is summarized in Fig. 7 for N210808 and N221204. As shown in the figure, the hotspot injected mass is more strongly a function of void depth than it is of void volume. This reflects the exponential sensitivity of ablation front Rayleigh–Taylor growth to time. Voids closer to the surface of the ablator perturb the ablator surface earlier than voids deeper in the shell and so experience exponentially more Rayleigh–Taylor growth than their deeper counterparts, and this leads to the exponential falloff of injected mass with depth. Again, N210808 and N221204 show very similar sensitivity in terms of injected mass vs void size and depth with N221204 in several cases showing more injected mass than N210808. The higher dopant and higher ablation front instability of N221204 compared to N210808 again explains this observation.

FIG. 7.

Hot spot injected mass as a function of void volume and depth below the ablator surface for shots N210808 and N221204. Four void volumes (5.6, 9.2, 20.6, and 38.3 μm3) were scanned over six void depths (5, 10, 20, 40, 60, and 75 μm). Hot spot injected mass decreases rapidly with pit depth into the ablator with only large voids less than 10 μm deep leading to more than a few nanograms of injected mass. An exception is the largest voids located at 60 μm below the ablator surface. These voids are located close to the interface between the doped and undoped ablator layers and couple to the classically unstable density discontinuity there early in time.

FIG. 7.

Hot spot injected mass as a function of void volume and depth below the ablator surface for shots N210808 and N221204. Four void volumes (5.6, 9.2, 20.6, and 38.3 μm3) were scanned over six void depths (5, 10, 20, 40, 60, and 75 μm). Hot spot injected mass decreases rapidly with pit depth into the ablator with only large voids less than 10 μm deep leading to more than a few nanograms of injected mass. An exception is the largest voids located at 60 μm below the ablator surface. These voids are located close to the interface between the doped and undoped ablator layers and couple to the classically unstable density discontinuity there early in time.

Close modal

A final interesting feature of these void simulations is the pronounced increase in injected mass for large voids at a depth of 60 μm below the ablator surface for both shots. This radius corresponds to the outer radius of the tungsten doped region of the ablator. The abrupt change in opacity at this interface leads to a similarly abrupt change in density in the shell before the ablation front has propagated into the doped region and removed this discontinuity. During the time that this interface is unablated, it represents a classically unstable interface to Rayleigh–Taylor instability growth. As these simulations show, for sufficiently large initial voids, this early-phase instability can grow into a large enough perturbation to again ultimately puncture the ablator shell and inject a very large amount of mass. Fortunately, voids of this size are rare in current HDC shells, and they result in a shell being excluded from consideration for experiments for precisely this reason.

A methodology similar to that in Secs. III and IV was also applied to the modeling of high-Z surface debris for N210808 and N221204. As with surface pit modeling, discrete ordinate, IMC, and multi-group diffusive radiation transport were tested, and detailed radiation transport in the form of discrete ordinates was found necessary for accurate debris modeling. Convergence with respect to grid resolution was also tested, and a similar resolution of 1444 radial and 2048 angular zones on the initial 15° polar mesh was found adequate for numerical convergence. With this resolution, a typical sized piece of surface debris has fifty-five by ten zones spanning its breadth and depth. The simulations were likewise remapped onto a butterfly mesh close to peak implosion velocity and run through completion using diffusive radiation transport.

Figure 8 shows the evolution in time of a piece of gold surface debris with a thickness of 0.5 μm and radius of 8.0 μm for a surface area of 200 μm2. The evolution of this type of surface defect is different from that of a surface pit in that, even though the thin piece of debris rapidly ablates and blows off of the ablator surface, it nonetheless leads to a local shadowing of the ablator surface under it. This effect is similar to the shadowing caused by the fill tube22,78 and so leads to the growth of a perturbation resembling a central spike surrounded by a Rayleigh–Taylor bubble in the form of an encircling moat. This perturbation can be seen in the second panel of Fig. 8 and may be thought of as the reciprocal of the perturbation seeded by a surface pit. Similar to the case of a surface pit, however, for a large enough piece of debris, the Rayleigh–Taylor bubble grows large enough to puncture the imploding ablator and fuel shell and cause a jet to enter the hotspot. This jet is ring shaped and wider than the narrow jets seeded by pits and voids but penetrates less deeply into the hotspot. As seen in the right panel of Fig. 8, by the time of peak neutron production, this debris-induced jet has not penetrated beyond the hotspot edge but nonetheless represents a relatively large mass of 41 ng of ablator material injected into the hotspot. The size and shape of this jet are overall similar to the simulated impact of the fill tube for this experiment, which results in 64 ng of ablator mass injected into the hotspot.

FIG. 8.

Simulation of a piece of gold surface debris 0.5 μm thick and 8.0 μm in radius shown at three times for N210808. The upper half of each panel shows mass density and the lower half shows material region with the DT gas and ice shown in light and dark blue and the doped and undoped HDC in orange and yellow, respectively. The surface debris region is colored silver in the left panel but has completely ablated away in the other two panels. By 8.40 ns, the radiation shadowing and reduced ablation rate caused by the gold debris has resulted in a spike-type surface perturbation surrounded by a ring-shaped Rayleigh–Taylor bubble. This bubble results in a broad but shallow jet of ablator mass at no-α bang time (9.15 ns) with a mass of 41 ng as shown in the right panel. Broadly, the evolution of the perturbation seeded by high-Z surface debris is more similar to the fill tube perturbation than to the perturbations seed by surface pits or voids.

FIG. 8.

Simulation of a piece of gold surface debris 0.5 μm thick and 8.0 μm in radius shown at three times for N210808. The upper half of each panel shows mass density and the lower half shows material region with the DT gas and ice shown in light and dark blue and the doped and undoped HDC in orange and yellow, respectively. The surface debris region is colored silver in the left panel but has completely ablated away in the other two panels. By 8.40 ns, the radiation shadowing and reduced ablation rate caused by the gold debris has resulted in a spike-type surface perturbation surrounded by a ring-shaped Rayleigh–Taylor bubble. This bubble results in a broad but shallow jet of ablator mass at no-α bang time (9.15 ns) with a mass of 41 ng as shown in the right panel. Broadly, the evolution of the perturbation seeded by high-Z surface debris is more similar to the fill tube perturbation than to the perturbations seed by surface pits or voids.

Close modal

The impact of a range of different debris sizes and thicknesses is quantified in Fig. 9 using the same metric of hotspot injected mass as in Figs. 5 and 7. As for the previous perturbation types, N210808 and N221204 show very similar sensitivity of injected mass to debris area and thickness with the largest pieces of debris injecting approximately 40 ng of ablator material into the hotspot for both experiments. There is also little sensitivity to debris thickness with 0.5 and 1.0 μm thick pieces of debris showing very similar injected masses. Note that the gold coating on the inside of the Hohlraum wall is 700 nm thick. If the surface debris were flakes of gold wall material that delaminates from the interior Hohlraum wall and attaches to the capsule surface, it would be in the range of the 0.5–1.0 μm as modeled here.

FIG. 9.

Hot spot injected mass as a function of surface debris area and thickness for shots N210808 and N221204. Three debris areas (50, 113, and 201 μm2) and two debris thicknesses (0.5 and 1.0 μm) were scanned for gold debris. Depleted uranium (DU) debris of 1.0 μm thickness was also scanned. The simulations show that for both experiments and for both debris compositions, debris larger than 50 μm2 leads to hot spot injected mass. There is very little sensitivity to the debris thickness, but depleted uranium debris leads to less than half the injected mass compared to an equivalent sized piece of gold debris.

FIG. 9.

Hot spot injected mass as a function of surface debris area and thickness for shots N210808 and N221204. Three debris areas (50, 113, and 201 μm2) and two debris thicknesses (0.5 and 1.0 μm) were scanned for gold debris. Depleted uranium (DU) debris of 1.0 μm thickness was also scanned. The simulations show that for both experiments and for both debris compositions, debris larger than 50 μm2 leads to hot spot injected mass. There is very little sensitivity to the debris thickness, but depleted uranium debris leads to less than half the injected mass compared to an equivalent sized piece of gold debris.

Close modal

Importantly, these simulations show that the threshold for the injection of ablator mass into the hotspot for both shots is a debris area of greater than 50 μm2. This threshold value is again qualitatively consistent with observations from NIF experiments where pieces of debris approximately 100 μm2 or larger are frequently associated with the observation of bright hotspot emission consistent with ablator jets.79 Note that, as discussed further in Sec. VII, multiple degradation sources interact in real NIF experiments and hence a clear threshold, let alone a definitive experimental test of the impact of debris, is not possible with current experimental capabilities.

As already noted, the simulations show a sensitivity to the debris composition. Repeating the simulations of N210808 but with 1.0 μm thick pieces of depleted uranium debris shows less than half of the injected mass with depleted uranium compared to gold debris of the same area. The higher opacity and slightly lower density of depleted uranium compared to gold results in the uranium debris being ablated away from the capsule surface faster and imprinting less of a perturbation, which ultimately leads to the lower hotspot injected mass.

The last type of ablator feature to be considered here is the micro-structure of the crystalline HDC itself. As noted in Sec. I, current experiments use nano-crystalline HDC composed of grains of HDC with a density of approximately 3.4 g/cm3 surrounded by graphic boundary regions of density 2.2 g/cm3. Unlike the localized perturbations represented by pits, voids, and surface debris, this fine-scale variation of the density and material properties of the HDC represents a volumetric perturbation throughout the bulk of the ablator. Hence, instead of seeding high aspect ratio hotspot jets as is the case for the localized defects, micro-structure leads to more broad spectrum mixing of the HDC ablator layers and DT fuel over the full extent of the capsule.

As with the other perturbation sources, very high-resolution simulations are needed to model the perturbation seeded by micro-structure. For the nanometer scale perturbation represented by the grain boundary regions in a millimeter scale capsule, exceptionally high resolutions are required. Indeed, fully resolving this range of scales in full radiation hydrodynamics simulations is currently not possible. Hence, an approximate perturbation approach is adopted here where the ∼5 nm scale density modulation of the graphitic boundary region is de-resolved by a factor of ten to a 50 nm effective boundary region. To conserve the areal density modulation of the boundary regions, the density difference between the boundary region and the full density HDC grains is similarly reduced by a factor of ten. In this model, the effective boundary region is then 50 nm wide but with a density of 3.21 g/cm3 compared to the physical ∼5 nm boundary regions with a density of 2.2 g/cm3. Each individual grain is then modeled as a quadrilateral with 200 nm average size and randomized corners surrounded by the lower density graphitic boundary region.80 The baseline simulations use 7425 radial and 4096 angular zones on a 4° wedge at the capsule waist. Convergence tests described below show that this model effectively captures the impact of the micro-structure seeded mix but at proportionately reduced resolution. Simulations without any perturbations were also run for each case to verify that without perturbations the simulated implosion remains spherically symmetric through stagnation and explosion. As with the simulations of other ablator features, in order to run these simulations to completion, they are remapped from the 7425 × 4096 mesh shortly after peak velocity onto a 10 227 × 2048 mesh and run Eulerian through the stagnation phase. Finally, these simulations also include surface roughness on each capsule interface. Separate simulations with only surface roughness or only the ablator micro-structure show that the micro-structure is the dominant contributor to the resulting mix.

Note that these simulations assume that there is no modulation in the ablator opacity due to the micro-structure other than that due to the reduced density of the boundary regions as compared to the full-density HDC grains. That is, in this model, the tungsten dopant is assumed to be homogeneously distributed between the grains and the boundary regions in the doped layer and not preferentially concentrated in the grains vs the boundary regions or vice versa. At this time, there is no evidence to indicate a difference in tungsten dopant concentration in the boundary regions vs grains. It can be assumed, however, that if there were a difference in dopant concentration between the grains and boundary regions, the resulting opacity modulation would significantly enhance the perturbation already seeded by the micro-structure density modulation.

Note that a novel rescaling procedure for modeling the impact of micro-structure was proposed in Ref. 81. This approach has been shown to be more efficient at capturing the impact of the micro-structure at much reduced grid resolutions than the approach used here. Unfortunately, this more sophisticated rescaling approach has so far proven incompatible with the newer Sesame 7835 EOS table used in this study, and simulations with this rescaling have shown significant growth of numerical noise. For this reason, only the simpler scaling procedure has been used for the results described below, but work is on-going to further improve the model. HDC micro-structure modeling of earlier NIF experiments has also been reported using xRAGE with a somewhat different model of the grain structure.82 

Figure 10 shows three snapshots in time from a micro-structure simulation of N210808. The left panel shows the simulation shortly before peak implosion velocity, the middle panel shows the simulation at the time of peak burn in a no-α simulation (here labeled ignition time), and the right panel shows the simulation at the time of peak burn. In each panel, the left half shows material region, while the right shows material density. Unlike the simulations of the previous perturbation sources, these simulations were run with α-particle stopping included and so account for the effect of hotspot self-heating and ignition. As can be verified from the figure, the 4° wedge used for this simulation is adequate to capture the dominant instability features.

FIG. 10.

HDC micro-structure simulation of N210808 shown at three different times. This simulation scales the graphitic boundary regions between the HDC grains from 5 to 50 nm and adjusts the boundary region densities from 2.2 to 3.21 g/cm3 to conserve the areal density modulation. These simulations also include the effect of surface roughness at all interfaces. In each panel, material region is shown on the left, and mass density is shown on the right. Close to peak implosion velocity (8.65 ns) as shown in the left panel, large modulations have grown at the ablation front near the top of the figure and fingers of HDC (yellow and orange) have penetrated deep into the DT (blue). By ignition time (no-α bang time) at 9.20 ns as shown in the center panel, the dense DT fuel is heavily mixed with HDC ablator material, but this material has not entered the lower density, high temperature hot spot. By peak burn in this α-on simulation (9.30 ns) as shown in the right panel, the burn wave has propagated into the mix DT-HDC region, and the mix begins to impact the total neutron yield.

FIG. 10.

HDC micro-structure simulation of N210808 shown at three different times. This simulation scales the graphitic boundary regions between the HDC grains from 5 to 50 nm and adjusts the boundary region densities from 2.2 to 3.21 g/cm3 to conserve the areal density modulation. These simulations also include the effect of surface roughness at all interfaces. In each panel, material region is shown on the left, and mass density is shown on the right. Close to peak implosion velocity (8.65 ns) as shown in the left panel, large modulations have grown at the ablation front near the top of the figure and fingers of HDC (yellow and orange) have penetrated deep into the DT (blue). By ignition time (no-α bang time) at 9.20 ns as shown in the center panel, the dense DT fuel is heavily mixed with HDC ablator material, but this material has not entered the lower density, high temperature hot spot. By peak burn in this α-on simulation (9.30 ns) as shown in the right panel, the burn wave has propagated into the mix DT-HDC region, and the mix begins to impact the total neutron yield.

Close modal

Already by the time of 8.65 ns, as shown in the left panel of Fig. 10, considerable mixing has developed throughout the imploding shell. Large modulations are seen at the ablation front at the top of the figure (roughly corresponding to a density of 5 g/cm3), and long fingers of doped and undoped ablator material (yellow and orange) are seen penetrating through the majority of the dense DT fuel layer. These fingers of hot ablator material result in local heating of the surrounding DT and hence decompression of the fuel layer. Notably, these fingers do not penetrate beyond the dense fuel layer into the hotspot, and this localization of the mix is seen to continue to ignition time as shown in the middle panel. In this panel, the DT fuel and remaining ablator shell have stagnated around the igniting hotspot at a density of several hundred g/cm3. The fingers of ablator material entrained in the DT fuel have been further mixed due to the passage of the stagnation shock through the mix layer but have not entered the low-density, high-temperature hotspot. By the time of peak burn, however, as shown in the right panel, the burn wave has propagated through this dense fuel, and the mixed layer of ablator and DT has been entrained in the low-density, high-temperature burn region. In combination, the fuel decompression due to mix and the entrainment of mix material into the burn region after ignition result in a factor of two reduction in simulated yield and 8% reduction in peak DT areal density compared to the equivalent simulation run without any perturbations. An analogous simulation for the thicker ablator experiment N221204 shows very similar evolution of its mixing layer compared to N210808 and a similar factor of two degradation in yield compared to its unperturbed counterpart.

An interesting feature of these simulations is that much of the mixing shown in Fig. 10 is driven by instability growth local to the inner undoped–doped interface in the ablator. This is illustrated in Fig. 11 with a sequence of snapshots in time progressing from top to bottom. The top figure shows the simulation at 6.30 ns shortly before the ablation front propagates into the doped layer. At this time, the ablation front and the doped–undoped interface (orange–yellow) near the top of the figure are both essentially unperturbed. The inner undoped–doped interface shows visibly nonlinear instability growth, however, with micrometer-scale bubbles and secondary Kelvin–Helmholtz instabilities mixing the doped–undoped regions (yellow–orange). Note that the fuel–ablator interface (blue–yellow) is also almost unperturbed at this time. This evolution continues in the middle panel (6.88 ns) as the ablation front progresses through the doped layer and the undoped–doped mixing layer takes on a quasi-turbulent character. The largest bubbles from the undoped–doped interface have also begun to imprint on the fuel–ablator interface (blue–yellow) at this time. By the last time shown in the figure (7.52 ns), the mixing layer has effectively grown to encompass the entire shell thickness and emphasizes the importance of the local stability of this undoped–doped interface on stability of the entire shell. Note that, for this reason, more recent designs have removed this inner interface and used ablators that include only a single doped layer adjacent to the DT fuel followed by an outer undoped region.31–36 Very recent radiography experiments aimed at directly measuring fuel–ablator mixing also appear to corroborate the undoped–doped interface as a significant sources of mixing.30 

FIG. 11.

Evolution of the mixing layer from the simulation shown in Fig. 10 but at earlier times. At the earliest time (6.30 ns) shown in the top panel, the ablation front and doped–undoped interface (orange–yellow interface in material region) are unperturbed, but nonlinear Rayleigh–Taylor mixing has already set in at the undoped–doped interface (yellow–orange interface). This localized mixing continues to grow in the center panel at 6.88 ns and imprint on the fuel–ablator interface (blue–yellow interface). By 7.52 ns in the bottom panel, the undoped–doped mixing has grown to encompass almost the entire shell.

FIG. 11.

Evolution of the mixing layer from the simulation shown in Fig. 10 but at earlier times. At the earliest time (6.30 ns) shown in the top panel, the ablation front and doped–undoped interface (orange–yellow interface in material region) are unperturbed, but nonlinear Rayleigh–Taylor mixing has already set in at the undoped–doped interface (yellow–orange interface). This localized mixing continues to grow in the center panel at 6.88 ns and imprint on the fuel–ablator interface (blue–yellow interface). By 7.52 ns in the bottom panel, the undoped–doped mixing has grown to encompass almost the entire shell.

Close modal

As already emphasized, these micro-structure simulations stress the limits of mesh resolution currently achievable in simulations. To test the numerical convergence of these simulations, the results of a mesh refinement study are shown in Fig. 12. The left panel shows the results of the nominal simulation near the time of peak implosion velocity, as already shown in Fig. 10, and the middle panel shows the result of doubling the mesh resolution but holding the boundary region perturbations fixed, i.e., the same 50 nm de-resolved boundary regions are used for both cases. The density modulations in both cases can be seen to be similar at this time with similar ablation front perturbations and similar fingers of ablator material penetrating into the dense DT fuel. The right panel compares the span-wise averaged densities from the two 2D simulations (red and blue) against the equivalent 1D simulation (black) at similar times. The radial locations of the density maxima in the three simulations do not exactly align due to jitter in the timing when the data are output from the three simulations. The peak densities of the two 2D simulations are quite close, however, and the extent of the mixing layer in both cases (evident by comparison to the 1D simulation) is quite similar. For a flow of the complexity shown in Figs. 10 and 11, exact agreement cannot be expected, but overall these simulations show reasonable convergence of the 2D results with respect to mesh resolution.

FIG. 12.

Mesh resolution test for the simulation shown in Fig. 10. The left panel shows the result close to peak velocity from Fig. 10. The middle panel shows the same time from an analogous simulation using the same initial micro-structure perturbations but double the mesh resolution. Qualitatively, the mix evolution in the higher resolution simulation is similar to the nominal resolution with strong modulations at the ablation front at the top of the figure and long fingers of HDC ablator material (yellow and orange) penetrating deep into the DT fuel (blue). The right panel compares span-wise averaged densities from the left two panels (red and blue) against the density from the equivalent 1D simulation at the same time (black). Jitter in the timing when the data are output from each simulation results in the translation of the density profiles in radius. The mixing and decompression in the averaged density of the 2D simulations are similar for the two resolutions.

FIG. 12.

Mesh resolution test for the simulation shown in Fig. 10. The left panel shows the result close to peak velocity from Fig. 10. The middle panel shows the same time from an analogous simulation using the same initial micro-structure perturbations but double the mesh resolution. Qualitatively, the mix evolution in the higher resolution simulation is similar to the nominal resolution with strong modulations at the ablation front at the top of the figure and long fingers of HDC ablator material (yellow and orange) penetrating deep into the DT fuel (blue). The right panel compares span-wise averaged densities from the left two panels (red and blue) against the density from the equivalent 1D simulation at the same time (black). Jitter in the timing when the data are output from each simulation results in the translation of the density profiles in radius. The mixing and decompression in the averaged density of the 2D simulations are similar for the two resolutions.

Close modal

Figure 13 shows a further convergence test where now, in addition to the mesh resolution, the width of the graphitic boundary regions between HDC grains is varied from twice that of the nominal case in Fig. 10 (left panel) to half of that of Fig. 10 (right panel). Since the mesh resolution is being varied by the same factors, the number of zones per boundary region is held constant in this test. To save computational resources, the wedge angle was reduced from 4° to 2° in the highest resolution case. As described above, it is not currently possible to resolve the physical ∼5 nm grain boundary width, so the simulations in Figs. 10–12 de-resolved this to a 50 nm boundary region with appropriately scaled density. The simulations in Fig. 13 therefore assess the validity of this approximation. Good qualitative convergence is found between the 100 nm boundary region case on the left, the 25 nm boundary region case on the right, and the baseline 50 nm boundary region case in the middle. Overall, these two convergence tests in Figs. 12 and 13 show limited sensitivity to modeling choices around the nominal and suggest reliable results for the baseline model of Fig. 10.

FIG. 13.

Tests of varying the boundary region size compared to the nominal micro-structure simulation shown in Fig. 10. The nominal simulation close to the time of peak implosion velocity from Fig. 10 is repeated in the middle panel. The result of doubling the boundary region size and reducing the mesh resolution by half is shown in the left panel. The right panel shows the result of halving the boundary region size and doubling the mesh resolution. Only a 2° wedge was simulated in this case to conserve compute resources. In each case, the boundary region density is scaled to conserve the appropriate areal density modulation. As in Fig. 12, qualitatively similar mixing is seen independent of the boundary region size choice suggesting that the mixing results in these simulations are relatively insensitive to the modeling choices in mesh resolution and boundary region size.

FIG. 13.

Tests of varying the boundary region size compared to the nominal micro-structure simulation shown in Fig. 10. The nominal simulation close to the time of peak implosion velocity from Fig. 10 is repeated in the middle panel. The result of doubling the boundary region size and reducing the mesh resolution by half is shown in the left panel. The right panel shows the result of halving the boundary region size and doubling the mesh resolution. Only a 2° wedge was simulated in this case to conserve compute resources. In each case, the boundary region density is scaled to conserve the appropriate areal density modulation. As in Fig. 12, qualitatively similar mixing is seen independent of the boundary region size choice suggesting that the mixing results in these simulations are relatively insensitive to the modeling choices in mesh resolution and boundary region size.

Close modal

Sections III–VI have described modeling of individual fine-scale features in two recent high performing NIF implosions. In an actual NIF experiment, of course, no single degradation source is present in isolation, but a number of degradations act in combination to determine implosion performance. In particular, as multiple perturbations are added on top of one another, the sensitivity of yield or other experimental observables to any one perturbation decreases.70 To address the more realistic impact of the individual degradations modeled in isolation in Secs. III–VI, this section describes lower resolution simulations where multiple effects are added in combination through the use of surrogate perturbation models and so develops a more realistic picture of actual implosion performance.

Lower resolution surrogate models have been developed over many years to facilitate modeling multiple degradation sources for NIF implosions.83–86 Typical surrogate models that are included in NIF implosion modeling are the capsule support tent87,88 and the fill tube,22,68,69,78,89 along with direct modeling of surface roughness and any asymmetries in the x-ray flux incident on the capsule. For these familiar degradation sources, similar surrogate models to those described previously are used and will not be detailed further here. The important degradation to be added here is the high-mode fuel–ablator mix due to ablator micro-structure as modeled in isolation in Sec. VI. Previous simulation studies86 accounted for fuel–ablator mixing but seeded only by interface roughness and so underestimated the magnitude of this effect on integrated implosion performance. In addition, for implosions where large surface pits or surface debris were present, the effect of jetting of ablator material into the hotspot as modeled in Secs. III–V also needs to be taken into account.

As described in Sec. VI, the principal impact of micro-structure-driven fuel–ablator mixing is heating and decompression of the DT fuel during the implosion phase, followed by pollution of the DT fuel during the burn propagation phase out of the hotspot. To account for both of these effects in lower resolution simulations, HYDRA's time-dependent interface mix models are used. Figure 14 shows a sequence of three different times during the implosion of N210808. The left panel shows the density profiles from the 1D simulation in black contrasted against the span-wise average density from the 2D micro-structure simulation from Fig. 10 in gray. The mixing and decompression in the 2D simulation is evident. To capture this mixing effect at lower resolution, the right panel shows the 1D simulation rerun with interface mixing added. These results use HYDRA's time-dependent mix source whereby the user can specify a particular amount of mix at a particular interface with the mixed mass increasing according to a user-specified time dependence. Consistent with the 2D results shown in Fig. 11, the mix models used in Fig. 14 include both mixing between the undoped and doped HDC regions, followed by mixing between the undoped HDC and DT fuel. As shown in the figure, by adjusting the magnitude of the time-dependent mix at each of these interfaces independently, fairly close agreement between the span-wise average density from the 2D micro-structure simulation (gray) and the 1D simulation including mix (red) is possible.

FIG. 14.

Comparison of the span-wise averaged density from the 2D micro-structure simulation (gray) of Fig. 9 with the 1D equivalent (black) at three different radii. Both the DT fuel and the neighboring HDC ablator are seen to be decompressed due to the mixing in the 2D simulation. By applying a tuned mix model to the 1D simulation at the fuel–ablator and undoped–doped interfaces (red), good agreement between the 2D averaged densities and the 1D mixed densities is possible.

FIG. 14.

Comparison of the span-wise averaged density from the 2D micro-structure simulation (gray) of Fig. 9 with the 1D equivalent (black) at three different radii. Both the DT fuel and the neighboring HDC ablator are seen to be decompressed due to the mixing in the 2D simulation. By applying a tuned mix model to the 1D simulation at the fuel–ablator and undoped–doped interfaces (red), good agreement between the 2D averaged densities and the 1D mixed densities is possible.

Close modal

Having tuned a lower resolution interface mix model to capture the effect of micro-structure-driven mixing, this model can now be added to the familiar perturbations of the support tent, fill tube, surface roughness, and x-ray flux asymmetries in 2D full-sphere simulations. As with previous multi-effect simulations,86 these simulations use 476 radial and 2048 angular zones over 180° and include the detailed physics of Monte Carlo burn product transport as well as NLTE emission from any high-Z material injected into the multi-keV hotspot. The model is applied to NIF experiments N210808 and N221204 as modeled above. As an example of an experiment where localized defects led to jetting of ablator material into the hotspot, the model is also applied to shot N211121, a repeat experiment of N210808. While N210808 and N221204 both used very high quality ablator shells free from any large pits, voids, or debris,20 N211121 used a shell with several large defects. Specifically, the capsules for N210808 and N221204 both had no surface pits larger than 3 μm3 and no detected high-Z surface debris. N210808 had no detected interior voids, while N221204 had a single void detection, and that void had a volume of less than 10 μm3. The capsule used for N211121 was from the same production batch as N210808 with similar high quality with respect to pits and voids; however, N211121 had six high-Z particles detected on its surface. Note that other simulation studies90 have reported a 17% lower fill tube injected mass for N211121 than N210808. Since, as described below, the addition of surface debris leads to an estimated 200% increase in the hotspot mix mass for N211121, the small differences in fill tube simulated impact between N210808 and N21121 are neglected here.

Figure 15 compares simulated vs experimental neutron yield from multi-effect simulations on the left, and on the right simulated vs experimental neutron down-scatter ratio (DSR), a measure of the compression of the DT fuel averaged over the duration of the burn.91 In each panel, the gold circles show the results of 2D simulations where the effect of micro-structure-driven mix is neglected, and the blue triangles show the results of simulations where this mix is included. For both N210808 and N221204, the addition of micro-structure-driven mix results in roughly a factor of two degradation in neutron yield. As expected, the addition of micro-structure-driven mix in N210808 reduces the fuel compression and brings the N210808 simulated DSR into agreement with experiment. For the higher yield experiment N221204, the simulated DSR actually slightly increases with the addition of micro-structure driven mix likely due to the reduced burn in this case and hence lower fuel decompression at peak burn time. In either case, both simulated DSR values agree with the measured DSR from experiment when mix is included, while the simulated yields of N210808 and N221204 both trend well compared to experiment.

FIG. 15.

Comparison of primary neutron yield Y13-15 (left) and neutron down-scattered ratio DSR (right) between simulation and experiment for shots N210808, N221204, and N211121. Gold circles represent the results of 2D multi-effect simulations where fuel–ablator mixing as modeled in Sec. VI is neglected, blue triangles show the results with fuel–ablator mixing included, and the red squares show the results for N211121 adding 100 ng of hot spot mix. The N210808 and N221204 simulations with fuel–ablator mix included both agree with the experimental DSR values and trend well with the observed neutron yields. Without fuel–ablator mix, the simulated yields are a factor of two higher than experiment. The N211121 simulation with fuel–ablator mix and 100 ng of hot spot mix also agrees with the experimental DSR and trends with the observed neutron yield. N211121 had four large debris detections, which, based on the results of Sec. V, should have injected approximately 100 ng of ablator material into the hot spot and is consistent with the results of these multi-effect simulations.

FIG. 15.

Comparison of primary neutron yield Y13-15 (left) and neutron down-scattered ratio DSR (right) between simulation and experiment for shots N210808, N221204, and N211121. Gold circles represent the results of 2D multi-effect simulations where fuel–ablator mixing as modeled in Sec. VI is neglected, blue triangles show the results with fuel–ablator mixing included, and the red squares show the results for N211121 adding 100 ng of hot spot mix. The N210808 and N221204 simulations with fuel–ablator mix included both agree with the experimental DSR values and trend well with the observed neutron yields. Without fuel–ablator mix, the simulated yields are a factor of two higher than experiment. The N211121 simulation with fuel–ablator mix and 100 ng of hot spot mix also agrees with the experimental DSR and trends with the observed neutron yield. N211121 had four large debris detections, which, based on the results of Sec. V, should have injected approximately 100 ng of ablator material into the hot spot and is consistent with the results of these multi-effect simulations.

Close modal

The simulation of N211121 including micro-structure-driven mix (blue triangle) disagrees with both the experimental yield and DSR. Although N211121 was intended as a direct repeat of N210808, it had six surface particle detections and four of those had areas greater than the 50 μm2 predicted to result in hotspot injected mass. Consistent with each of these four large particles injecting approximately 25 ng of ablator material into the hotspot as shown in Fig. 9, the 2D simulation of N211121 was rerun including both micro-structure-driven mix and 100 ng of pre-loaded hotspot mix. As shown by the red squares in Fig. 15, accounting for the hotspot mix due to surface particulates on N211121 significantly improves the agreement between simulation and experiment. The simulated DSR for this shot now matches experiment within the error bars like N210808 and N221204, while all three shots now trend with the experimental yield. Note that the addition of 100 ng of hotspot mix to the simulation of N211121 increases the DSR (red square) compared to the case with only fuel–ablator mix (blue triangle), whereas the addition of fuel–ablator mix decreases the simulated DSR compared to the case with no mix (gold circle). The reason for hotspot mix increasing the DSR is that the hotspot mix radiatively cools the hotspot and so allows slightly higher convergence of the dense DT shell leading to higher DT areal density.

Note that, in this pre-loaded hotspot mix modeling, the 100 ng of hotspot mix for N211121 is simply mixed into the DT gas and inner 3.5 μm of DT ice at the start of the simulation. At bang time, this prescription results in the mix being spread nearly uniformly through the resulting hotspot. This modeling approach obviously omits the time-dependent injection of the mix into the hotspot as well as the localization of the mix into individual jets spread around the hotspot as suggested in the single debris simulations shown in Fig. 8. Unfortunately, due to the 2D axisymmetry of these multi-effect simulations, there is no means to spread multiple jets around the hotspot while still including the important effects of the fill tube, tent, and x-ray flux asymmetries. Similarly, there is currently no way in HYDRA of mimicking the time-dependent arrival of the mix into the hotspot. Short of running much more costly high-resolution 3D simulations where multiple jets can be spread over the full solid angle of the implosion and account for the time-dependent arrival of the mix, the prescription of uniformly distributing the mix in the hotspot from the start of the simulation represents the only option for modeling this effect. Nevertheless, the result of the N211121 simulation including hotspot and micro-structure-driven mix and the simulations of N210808 and N221204 with micro-structure-driven mix are broadly consistent with the observed yield and DSR. Taken together, these results suggest a plausible explanation of the observed performance for both “clean” experiments like N210808 and N221204 and experiments that suffered from defect-induced mix as was N211121. Overall, these results lend credibility to the individual defect modeling results from Secs. III–VI.

This paper has described high-resolution modeling of fine-scale ablator defects in recent high-performance NIF implosion experiments with HDC ablators. These fine-scale defects have been correlated with mixing of ablator material into the hotspot and are believed to be a leading contributor to the variability seen in recent experiments by up to factors of several in neutron yield. Specifically, high resolution simulations were run of pits on the ablator surface, voids in the bulk of the ablator, and thin flakes of debris on the ablator surface composed either of gold or depleted uranium, both constituents of the Hohlraum wall. Simulations were also run modeling the inherent crystalline micro-structure of the HDC. These simulations were run for two recent NIF experiments: N210808, the first NIF experiment to exceed 1 MJ of yield, and N221204, a follow-up experiment that used an additional 150 kJ of laser energy compared to N210808 and a 6 μm thicker ablator. Since the higher laser energy and thicker ablator used on N221204 are expected to confer greater resistance to perturbations seeded by pits, voids, and other defects, it is interesting to assess the relative resilience of these two experiments to each of these perturbation sources.

The simulations show that pits on the surface of the HDC ablator with volumes greater than 4 μm3 lead to injected mass into the hotspot, and that pit volume orders the amount of injected mass for a range of different pit widths and depths. This result is in encouraging agreement with experimental observation where pits larger than approximately 3 μm3 have been correlated with mass injection and enhanced hotspot x-ray emission.20 Interestingly, both shots simulated in this study, N210808 and N221204, show similar sensitivity in terms of hotspot injected mass to pit volume. That is, the thicker ablator and higher drive energy of N221204 do not appear to confer any increased resistance to the growth of perturbations seeded by surface pits.

Simulations of ablator voids show that voids with volumes greater than 5 μm3 and within 10 μm of the ablator surface lead to tens of nanograms of hotspot injected mass. Injected mass decreases rapidly for voids that are deeper into the ablator bulk with the exception of very large voids close to the doped–undoped interface in the interior of the ablator. Large voids at this interface can couple to the classically unstable Rayleigh–Taylor growth at this interface early in time and lead to more than 20 ng of injected mass. Again, the thicker ablator experiment N221204 shows similar to or greater mass injected for the same sized void compared to N210808.

Simulations of gold or depleted uranium debris on the capsule surface show that debris greater than 50 μm2 in area leads to hotspot injected mass with similar amounts for both N210808 and N221204. Again, this compares favorably with the sensitivity inferred from experiments where debris on the capsule surface with an area of 100 μm2 or greater has been correlated with enhanced hotspot x-ray emission indicating injected ablator mass.

Simulations of the inherent HDC micro-structure show that this volumetric perturbation source can contribute to significant instability growth at the ablation front as well as in the interior of the shell during the implosion. In particular, the interface between the inner undoped region of HDC and the buried tungsten-doped layer is found to be particularly susceptible to micro-structure seeded instability growth and appears to dominate the evolution of mixing in these simulations. This result especially motivates recent designs that have sought to eliminate or otherwise reduce the growth at this internal undoped–doped interface. Again, both N210808 and N221204 show similar levels of mixing due to HDC micro-structure.

Finally, an assessment was made of the impact of these perturbation sources when they are combined with the many other effects that simultaneously degrade NIF implosions, e.g., the capsule support tent, the fill tube, surface roughness, and x-ray flux asymmetries. By tuning an interface mix model to match the mixing seen in direct simulations of HDC micro-structure, the effect of this mix can be accounted for in lower-resolution, multi-effect simulations. It is found that, even in the presence of other degradation sources, the micro-structure-seeded mix results in a factor of two yield degradation for both N210808 and N221204. For a third experiment, N211121, where several large pieces of debris were observed on the capsule surface, it is found that the estimated hotspot injected mass from these debris based on high-resolution simulations is in agreement with the hotspot mix mass that degrades the yield and compression consistent with experiment in lower-resolution, multi-effect simulations. Taken together, these results suggest overall consistency of the modeling with experiment and a consistent picture of the performance of recent HDC ablator implosion experiments on NIF.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 and General Atomics under Contract No. 89233119CNA000063.

The authors have no conflicts to disclose.

D. S. Clark: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). T. Fehrenbach: Data curation (supporting); Investigation (supporting); Writing – review & editing (equal). C. Kong: Data curation (supporting); Investigation (supporting); Writing – review & editing (equal). M. Millot: Data curation (equal); Investigation (equal); Writing – review & editing (equal). J. Milovich: Formal analysis (supporting); Investigation (supporting); Methodology (supporting); Writing – original draft (supporting). A. Nikroo: Data curation (equal); Investigation (equal); Writing – review & editing (equal). R. C. Nora: Investigation (equal); Methodology (equal); Writing – review & editing (equal). A. E. Pak: Data curation (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). M. S. Rubery: Data curation (equal); Investigation (equal); Writing – review & editing (equal). M. Stadermann: Data curation (equal); Investigation (equal); Writing – review & editing (equal). P. Sterne: Data curation (equal); Investigation (equal); Writing – review & editing (equal). A. Allen: Data curation (supporting); Investigation (supporting); Writing – review & editing (supporting). C. R. Weber: Investigation (equal); Methodology (equal); Writing – review & editing (equal). C. Wild: Data curation (supporting); Investigation (supporting); Writing – review & editing (equal). S. H. Baxamusa: Data curation (equal); Investigation (equal); Writing – review & editing (equal). J. Biener: Data curation (equal); Investigation (equal); Writing – review & editing (equal). M. M. Biener: Data curation (equal); Investigation (equal); Writing – review & editing (equal). T. Braun: Data curation (equal); Investigation (equal); Writing – review & editing (equal). S. Davidovits: Investigation (equal); Methodology (equal); Writing – review & editing (equal). L. Divol: Investigation (supporting); Writing – review & editing (equal). W. A. Farmer: Investigation (equal); Methodology (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.

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