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

Indirect drive Inertial Confinement Fusion (ICF)^1,2 experiments on the National Ignition Facility (NIF)³ have now been performed using three different ablator materials: glow discharge polymer plastic (CH), high density carbon (HDC), and sputtered beryllium (Be). It has been appreciated for some time that each of these materials has specific advantages and disadvantages as an ICF ablator.^4–8 But in the context of current NIF implosion designs, how do these ablators compare? Has the understanding of their respective strengths and weaknesses changed in the light of NIF experiments? And given current understanding, which appears most likely to reach ignition on NIF? This paper seeks to shed light on these questions by combining modern simulation results with a survey of the current experimental database.

In the context of likely future NIF experiments, attention should be paid to both what experiments have been conducted on NIF to-date and what are promising near-term future directions. For this study, a two-part methodology was therefore adopted: Our understanding of the differences between these ablators was first grounded in modeling specific NIF experiments using the different ablators (“post-shot modeling”).^9–14 By calibrating and/or comparing simulation results with experimental data, confidence can be built that the simulations provide a reasonable picture of current implosion experiments and that extrapolations to future designs using these simulations are meaningful. Based on these post-shot models, extrapolated implosion designs for each ablator were then developed meant to exploit the full power and energy capabilities of NIF.¹⁵ These extrapolated designs aimed both to follow the design directions currently being pursued in NIF campaigns (and so remain relevant to current and near-future experiments) and to stretch these designs to the full potential of NIF and explore by how much (based on current understanding) performance could be improved. At both the post-shot and extrapolation phase of the study, differences between the ablators were identified and possible strengths and weaknesses highlighted.

As a further subdivision of the methodology, each ablator type and implosion design was simulated both in an integrated hohlraum model⁹ and in a higher resolution capsule-only model.¹⁰ Integrated hohlraum simulations model the entire process of an indirect drive NIF implosion experiment. This includes laser propagation through the hohlraum, x-ray conversion at the hohlraum wall and transport to the capsule, and finally, the capsule implosion and fusion burn. These integrated simulations have the advantage of incorporating all of the relevant physics in a single model. However, in modeling both the hohlraum laser conversion and the capsule implosion, they suffer the disadvantage of inadequate resolution of the finest scales of the implosion—if the computational requirements are to remain tractable. To resolve the finer scale features of the implosion, capsule-only simulations focus only on the capsule implosion phase and treat the surrounding hohlraum as a spherical x-ray-emitting boundary. As such, hohlraum simulations aim to model the gross energetics of the implosion, as well as any long-wavelength asymmetry in the x-ray drive, while capsule-only simulations focus on the effect of fine scale features on the capsule (such as the capsule support,^16–19 fill tube,^20,21 and surface defects) and model the aggregate impact of all of these imperfections on implosion performance. For both simulation types, the simulations in this study were run using the well-known radiation-hydrodynamics code HYDRA.²² 

Over the course of this study, differences between the ablators were identified in both types of simulations. The results of hohlraum modeling for each ablator are described in a companion paper.²³ These simulations highlighted the advantages of short laser pulse lengths for maintaining symmetric x-ray drive conditions, as well as the importance of efficient energy coupling from the hohlraum to the capsule. Both of these requirements favor HDC most. Further details of the hohlraum aspects of this study are left to the companion paper²³ and are not repeated here.

This paper focuses on the capsule-specific aspects of the differences between the three ablators. The principal findings from capsule modeling are the following:

1. Current and extrapolated HDC designs show the largest ablation front instability growth as characterized by linear growth factors, beryllium shows the least, and CH is intermediate. Note that these growth factors characterize the relative stability of each design. The impact of hydrodynamic instabilities is the convolution of these growth factors and the surface defects and other perturbation sources characteristic of each ablator. The relative surface quality of each ablator is therefore also important.

2. Based on current metrology, beryllium has the highest surface roughness on both inner and outer surfaces, and HDC has the least. This results in significant simulated short-wavelength mix in current beryllium designs, but this does not appear to be a concern for CH or HDC.

3. The capsule support tent impacts current CH implosions most and HDC implosions least with the beryllium intermediate. Near-term extrapolated designs show that beryllium is most impacted by the tent with HDC and CH comparable.

4. In current designs, the fill tube impacts HDC very strongly (with >50 ng of high-Z ablator material injected into the hot spot), CH is only weakly impacted, and beryllium designs are intermediate. Future designs with 5 μm diameter fill tubes simulate to be only weakly impacted for all ablators.

5. Experiments with CH and HDC ablators are relatively well matched by simulations [within ∼20% in yield, burn-averaged temperature, and neutron down scattered ratio (DSR)], but the most recent beryllium implosion is not. There are signatures of strong mixing in this experiment, however, that are consistent with the concerns raised above and may indicate that additional doping, reducing the laser power to increase remaining mass, or other modifications, will be required in future beryllium designs.

6. Current CH and HDC designs extrapolate to yields of several 10¹⁶ at full NIF power and energy. The beryllium design considered here extrapolates to 10¹⁸ due to its lower adiabat, but this is probably unrealistic due to the dangers already identified from short-wavelength mixing.

Finally, note that each ablator type is known to have fine-scale perturbation seeds beyond the surface roughness and other effects included here. For example, oxidation of CH could cause short-wavelength opacity and density modulations,²⁴ latent material strength in HDC could seed irregularities if the initial shock is not strong enough to completely melt the ablator,²⁵ and crystalline micro-structure or trace argon non-uniformities could play similar roles in sputtered beryllium.⁸ These additional perturbation sources are a subject of active investigation and not addressed here. Additionally, while this paper focuses primarily on the results of simulation comparisons, a comparison of the experimental results on each ablator's stability characteristics is obviously also important. This comparison is beyond the scope of this paper but will be detailed in future work.²⁶ 

This paper is organized as follows. Section II describes post-shot simulations of implosion experiments performed with each ablator type. These simulations illustrate the various and different degradation sources particular to each ablator. Furthermore, the fidelity with which the experiments can be matched by simulations serves as a foundation for extrapolations to future designs. Section III then describes similar simulation results but for extrapolated designs for each ablator. These extrapolations are grounded in the database of past NIF experiments but pushed to the limits of NIF's energy and power capabilities. Finally, Sec. IV summarizes and concludes.

To assess the effect of the different ablator materials on the hydrodynamic stability of the implosion, capsule-only simulations were run for each of the cases discussed in the companion paper.²³ High-resolution capsule-only assessments are particularly important as engineering features used to support and fill the capsule prior to the shot (the “tent” and “fill tube”) are known to be significant degradation sources in current experiments, and the evolution of these perturbations will differ with each ablator type. Furthermore, each ablator has specific surface finish characteristics, as well as internal structure, which can be amplified differently by hydrodynamic instabilities.

In contrast to the hohlraum simulations of the companion paper, these simulations model only the capsule and require an imposed x-ray source to drive the implosions. These x-ray sources were imported from the hohlraum simulations and adjusted as needed to match the implosion shock timing, velocity, and bang time from the hohlraum simulations. Given its importance to implosion stability, the M-band fraction of the x-ray source was also adjusted to be consistent with NIF View Factor measurements.²⁷ Inevitably, this “hand-off” from hohlraum to capsule simulation is imperfect and introduces some small differences in the simulation results; however, these differences were judged small compared to the overall modeling uncertainty.

Since capsule-only simulations model only the capsule, very high grid resolutions can be used, sufficient to resolve even the very small scales of the tent (∼45 nm thick) and fill tube (∼10 μm), in addition to surface roughness. The longer length scale effects of the hohlraum drive asymmetries can also be included by importing asymmetry coefficients from the hohlraum simulations. For each case studied, each perturbation source was simulated in isolation as well as in combination to assess both the dominant effects on performance and how the effects combine to determine overall implosion performance. All simulations used tabular equation of state (EOS) data from the Livermore EOS database (LEOS)²⁸ and tabular opacity data generated by the VISTA and OPAL opacity models.²⁹ Of course, there are uncertainties in these material properties that can influence the results described below. Quantifying the uncertainties in performance projections due to uncertainties in material data is a subject of on-going work but beyond the scope of this study.

Like the hohlraum modeling in the companion paper, simulations were first run of five NIF experiments, representative of each ablator type, in a post-shot mode: N140520 (plastic high foot, CH HF),^30–35 N151020 (low gas fill plastic, CH LGF),³⁶ N161023 (HDC),^37,38 and N170109 (Big Foot, BF—a design that also uses HDC as an ablator).^39,40 At the time this study was begun, the beryllium deuterium-tritium (DT) fueled experiment had yet to occur, so a pre-shot model was constructed of this implosion based on the beryllium 2-D ConA experiment N170227.⁴¹ Note that each ablator also incorporates a small amount of a higher Z dopant to control hard x-ray pre-heating: silicon in CH, tungsten in HDC, and copper in beryllium. These dopants are important in determining the stability characteristics of each design as discussed further below.

Various 1-D implosion characteristics as well as the experimental ion temperature, DSR, and primary yield are summarized in Table I. While these values are similar to those for the corresponding hohlraum simulations, they are not identical. The differences reflect the imperfect process of handing-off an x-ray drive from a hohlraum simulation to a capsule-only simulation, as well as the higher resolution used in the capsule-only simulations. Note that the experimental values in the last column of the table correspond to the beryllium DT shot N170702⁴¹ even though the simulation values are from a pre-shot model based on the 2-D ConA N170227. In particular, more recent modeling suggests that the remaining mass in this experiment may have been lower than listed here due to differences in the as-shot target, possibly exacerbating the instability growth discussed below.

Important 1-D implosion characteristics are shown in the four panels of Fig. 1: inflight density versus radius, ablation front scale length versus ablation front radius, inflight aspect ratio versus ablation front radius, and fuel-ablator Atwood number versus ablation front radius. Each of these quantities is important in determining the 2-D and 3-D stability of the implosion. Note that HDC and Big Foot have the shortest ablation front scale lengths, suggesting the most unstable ablation fronts, while CH and beryllium have slightly longer ablation front scale lengths. Conversely, Big Foot has an always negative fuel-ablator Atwood number, suggesting that there should be no mixing between the ablator and DT fuel inflight. CH, HDC, and beryllium have similar positive Atwood numbers, suggesting some susceptibility to inflight fuel-ablator mixing. Lastly, beryllium has the largest inflight aspect ratio midway through its implosion, suggesting overall the largest potential for instability feed-through from the ablation front to the hot spot.

Figure 2 shows the ablation front linear growth factors for each design at their respective times of peak implosion velocity. These growth factors characterize the amplification of perturbations at the surface of the ablator at the start of the implosion to perturbations at the ablation front at the end of the acceleration phase. HDC has the largest and uniformly positive growth factor spectrum, while both CH implosions have the characteristic positive and negative lobe shape.^21,42 The Big Foot implosion shows much reduced growth compared to HDC. This difference is not due to differences in the Richtmyer-Meshkov (RM)^43,44 phase of growth as, with its shorter pulse length, the RM zero crossing mode number for Big Foot should be at a higher mode number than it is with the longer pulse length HDC design.⁴⁵ Instead, enhanced ablative stabilization during the Rayleigh-Taylor (RT)^46,47 phase of growth due to the higher M-band fraction in the Big Foot's gold-lined hohlraum accounts for much of the enhanced stabilization in the Big Foot design. Finally, the beryllium growth factor spectrum shows the influence of beryllium's higher ablation velocity resulting in multiple RM oscillations and a multi-peak spectrum. The higher ablation velocity also increases ablative stabilization and accounts for the significantly lower overall amplitude of the beryllium growth factors compared to CH and HDC.⁴⁸ 

With respect to finite amplitude perturbations, tent simulations were run for each implosion. These simulations fully resolve the initial tent configuration (using 2048 × 1600 zones in angle and radius), and convergence with respect to zoning was verified for all cases. For the sake of comparison, all simulations were run with an identical tent configuration corresponding to the CH high foot shot N140520: a 45 nm tent thickness with a 14° liftoff angle above tangential at a polar angle of 45°. Figure 3 shows a close-up of the initial tent configuration and zoning. These simulations were run without α-particle deposition to isolate the hydrodynamic evolution of the tent perturbation without the influence of hot-spot self-smoothing when α-particle deposition is included. As shown in Fig. 4, the impact of the tent is clearly the largest for the CH implosions, resulting in an aneurism that completely perforates the dense shell at bang time. The tent aneurism is much reduced in the HDC and Big Foot implosions, especially in the latter due to its higher adiabat and lower converged shell density, while the aneurism in the beryllium implosion is intermediate between HDC and CH.

Fill tube simulations were also run for each case as shown in Figs. 6 and 7. Like the tent simulations, these simulations all used an identical fill tube configuration corresponding to shot N140520, including the ablator fill hole, fill hole counter bore, tube insertion depth, and glue fillet. These simulations used polar S₆ radiation transport on a 30° wedge with 2048 × 1600 zones up to a convergence of approximately three. Zoning tests have verified that this resolution is converged for these μm-scale fill tube features. Figure 5 shows a close-up of the initial fill tube configuration and zoning. After convergence three, the simulation is linked onto a butterfly mesh⁴⁹ with the boundary extended to the full 180° of the capsule. Also, similar to the tent simulations, α-particle deposition was switched off in these simulations. Note that these simulations do not include any effects of fill tube “shadows” as recently identified in HGR experiments⁵⁰ since the precise origin of these shadows is still under study and it is unclear at this time how they could change with ablator choice. Also, detailed comparisons of fill tube simulations to implosion data on NIF suggest that current fill tube simulations underestimate the size and mass of the jet injected by the fill tube, perhaps due to this “shadowing.” Hence, it should be borne in mind that the fill tube simulations described here and below are likely a lower bound on the impact of this feature.

Figure 6 shows the results of the fill tube simulations for each implosion at the time they are linked from the 30° cone to a butterfly mesh. There is an interesting dichotomy between the CH simulation results and the HDC results at this time. In the case of CH, the fill tube has caused an outward-pointed bump to grow at the ablation front with very little mass injected into the interior of the shell. The HDC simulations not only show a small outward-going bump but also a large plume of ablator material (primarily W-doped HDC) injected into the interior of the shell. Watching the simulations evolve in time shows that this plume originates from the fill tube seeding a divot-type perturbation at the ablation front early in time which subsequently opens a hole in the ablator shell. The ablation pressure then pushes a large amount of ablator material through this hole before it closes due to convergence and finally leaves a small outward bump at the ablation front. In contrast, for CH, the fill tube seeds an initially outward bump early in time that only grows in an outward direction and never opens a hole for the significant ablator material to be injected. In this case, the small mass of the injected ablator material originates only form the initial jet of glass and ablator material launched down the fill hole ahead of the first shock. Beryllium represents the intermediate case between CH and HDC. Here, an initially outward-directed bump is again seeded early in time but is flanked by an inward penetrating bubble ring. This ring perturbation grows to nearly penetrate the shell by link time as shown in the lower right panel.

The reason for the range of fill tube effects shown in Fig. 6 appears to be due to the range of densities of these different ablators (1.0, 1.8, and 3.5 g/cm³ for CH, Be, and HDC, respectively) as compared to the density of the glue used to attach the fill tube and fill the fill tube counter bore (1.2 g/cm³). In the case of CH, the glue is a quite close density match to the surrounding CH ablator. Hence, the shock launched into the glue region advances at a very similar velocity to that in the surrounding CH. Coupled with the slightly reduced drive in the neighborhood of the fill tube, this leads to the outward-going fill tube perturbation seen in the upper two panels. For HDC, however, the glue is roughly one third the density of the surrounding ablator, causing the shock to propagate faster through the counter bore region, despite the slightly reduced drive, and this ultimately leads to the divot-type perturbation and subsequent large jet of ablator material described above. Beryllium, with a density close to the average of CH and HDC, again represents an intermediate case.

The impact of the fill tube at bang time for each implosion is shown in Fig. 7. Analogous to the inflight results in Fig. 6, there is very little impact from the fill tube for the CH implosions, while large jets carrying >50 ng of ablator material are seen in the HDC and Big Foot implosions. Again, beryllium represents the intermediate case with ∼15 ng of injected ablator material. This latter injected mass results from the thinning of the shell adjacent to the axial bump, as shown in the last panel of Fig. 6, which ultimately breaks through and injects the ablator material into the hot spot very late in time.

The relative impacts of the tent and fill tube for each implosion are summarized in the histogram in Fig. 8. The vertical scale shows the simulated total yield without α-particle deposition normalized to the 1-D no-deposition yield for each case. The blue bars show the results of the tent simulations described above, and the red bars show the results of the fill tube simulations. For the two CH implosion types, the tent is seen to be the largest degradation source with the fill tube second. For the HDC and Big Foot implosions, these roles are reversed with the tent having little impact and the fill tube being the largest degradation. In the case of beryllium, the two degradation sources are almost equal. These results correspond nicely with the visual size of the perturbations seen in Figs. 4, 6, and 7. Note that these simulations without α-particle deposition dampen the impact from the various perturbation sources. With α-particle deposition included, the effects of the larger degradation sources can be expected to be amplified (as the degradation prevents burn propagation and the yield drops steeply), while the effects of the smaller degradations are reduced as the robustly burning hot spot self-smooths and the effect of the perturbation is burned away. That is, with α-particle deposition included, the small degradations can be expected to become smaller, but the large degradations become larger.

Another factor to consider in comparing these ablators is the potential for short-wavelength fuel-ablator mixing^21,51 driven by the unstable Atwood numbers shown in the lower right panel of Fig. 1. Here, the perturbations dominantly originate from the fine-scale surface roughness inherent to each ablator on both the inside and outside of the shell. Representative surface roughness power spectra for each ablator type are shown in Fig. 9 as functions of Legendre mode number. The solid black line shows the Rev. 3 CH specified surface roughness.⁵² The solid red line shows the measured outer surface roughness for the shell used on the high foot shot N140520. This surface roughness was used for both of the CH ablator design simulations. The solid blue line shows the measured surface roughness for the HDC shell from shot N161023 and used in the HDC and Big Foot simulations, and the solid green line shows the measured outer surface roughness from the beryllium shot N170227 and used in the beryllium simulations. In each case, the dashed lines show the corresponding inner surface roughnesses. In the case of beryllium, a measured surface power spectrum from a representative mandrel was used. For CH and HDC, only the nominal inner power spectra were available. As is evident from the figure, HDC has the smoothest surface, and beryllium the roughest, with CH intermediate between these two.

High resolution wedge simulations using these power spectra as perturbations are shown in Fig. 10 at the time of peak implosion velocity for each design. These simulations resolve Legendre mode numbers up to 1200 and use typically 2048 × 1600 zones on a 15° wedge. For the CH and HDC cases, relatively little instability growth is seen. In the Big Foot case in particular, the always-stable Atwood number shown in Fig. 1 leads to an essentially unperturbed simulation in 2-D. The beryllium simulation, on the other hand, shows significant instability growth at both the fuel-ablator interface and the ablation front. Running simulations with the surface roughness initialized at only the fuel-ablator interface and only the ablator outer surface shows that the larger portion of the growth is seeded by the fuel-ablator interface roughness for this design. Given that the Atwood numbers are similar for CH, HDC, and beryllium, the large initial surface roughness on this internal beryllium interface likely accounts for the large simulated mixing. It may be possible to improve the stability of this interface by increasing the copper dopant in the beryllium and thereby reducing the unstable Atwood number and hence Rayleigh-Taylor growth at the interface. As is well-known, increasing the ablator dopant comes at the cost of reduced implosion velocity as well as increased ablation front instability, and an optimum balance must be found.⁴² 

Finally, Fig. 11 shows the results of 2-D simulations where all of the above effects have been combined, with the exception of short-wavelength fuel-ablator mixing. That is, these simulations include drive asymmetries from the hohlraum, surface roughness, and tent and fill tube effects. For the latter two perturbations, these simulations use surrogate perturbations tuned to reproduce the effects of the resolved simulations described above but with much reduced resolution. These simulations use only 1024 × 400 zones in the case of CH and beryllium and 2048 × 300 zones in the case of HDC and Big Foot but include the full physics of α-particle deposition for accurate modeling of the neutron yield. Note, again, that these simulations do not account for the short-wavelength mix effects shown in Fig. 10. While this is a good approximation for CH, HDC, and Big Foot, this approach is probably inadequate for the beryllium implosion being modeled. Future work will aim to include this effect properly.

For the two CH implosions, the long-wavelength distortions of the hot spot due to hohlraum drive asymmetries appear to be the dominant perturbation source. For the HDC and Big Foot implosions, the fill tube is the dominant perturbation. For the beryllium simulation, intermediate mode perturbations are most prominent followed by a still visible fill tube perturbation. Interestingly, all of these simulations predict yields in the range of 2–7 × 10¹⁵.

The comparison of these combined-effects simulations with experimental data is summarized in Fig. 12. The vertical scale shows the experimentally measured primary neutron yield, burn-averaged hot spot temperature (as measured by the width of the primary neutron spectral feature), and down scattered neutron ratio (DSR) normalized to the simulated value from the simulations shown in Fig. 11. The blue bars show the normalized yields, the red bars the normalized temperatures, and the gray bars the normalized DSRs. For all except the beryllium implosion, the simulations agree with the experimental values to within 25%—in some cases much better—for all three observables. This encouraging level of agreement for CH and HDC lends some confidence to the extrapolations presented in Sec. III. However, the beryllium experiment shows significantly lower yield and compression than predicted in simulations and makes extrapolations of the beryllium design highly uncertain. The disagreement in this case may be due to the short-wavelength mixing effects discussed above and shown in Fig. 10. Recall that this effect was omitted in the simulations shown in Fig. 11 and summarized in Fig. 12. Simulations employing sub-grid mix models tuned to reproduce the high-resolution results, such as in Fig. 10, are underway in order to better account for these effects.

Based on the extrapolated implosion designs presented in the companion paper,²³ capsule-only simulations were run following the same procedures used in the post-shot simulations above. Table II summarizes some of the 1-D characteristics of these designs from the capsule-only simulations. The laser pulse shapes, hohlraum radiation temperatures, and M-band fractions for each design are shown in Fig. 13. As noted above, the x-ray sources for these simulations were extracted from the corresponding hohlraum simulations and then adjusted as necessary to match shock timing and bang time data from the hohlraum simulations. The M-band fractions were also adjusted to be consistent with View Factor data as the M-band fraction has an important influence on implosion stability.

Similar to Fig. 1, Fig. 14 summarizes the inflight density distribution, ablation front scale length, inflight shell aspect ratio, and fuel-ablator Atwood number for the three designs. Notable here is the always-stable Atwood number in the scaled-up HDC design. As shown in Table II and the upper left panel of Fig. 14, this design has relatively high remaining mass compared to the others. This is due to the fact that the ablator opacity is a non-scaling quantity as the capsule dimensions and drive pulse length are increased. This non-scaling property of the ablator may be partially addressed by reducing the dopant added to the ablator as the scale is increased. The effect of reducing the ablator dopant (from 0.24 at. % W—as used in the HDC experiments modeled in Sec. II—to 0.12 and 0.08 at. % W, respectively) is shown by the dashed and dotted curves in Fig. 15. As the dopant is reduced, the fuel-ablator Atwood number increases, increasing the design's susceptibility to fuel-ablator mixing, but the ablation front scale length also increases, reducing the amount of ablation front instability growth. As shown below in Fig. 21, reducing the dopant concentration to one third of the original value does not appear to adversely impact the fuel-ablator stability; however, it significantly improves the ablation front stability by reducing the ablation front growth factors from a peak of 750 with the full dopant to 250 with one third the dopant (Fig. 16). Furthermore, the reduced dopant increases the implosion velocity from 370 km/s to 400 km/s. For these reasons, an implosion design with one third the nominal dopant concentration appears more optimal and was simulated for all of the following comparisons.

Figure 16 compares the ablation front growth factors for the scaled-up designs similar to the post-shot cases shown in Fig. 2. Broadly, the scaled-up growth factors are similar to the post-shot results with uniformly positive growth for the HDC design, positive and negative growth for the CH design, and more RM oscillations in the scaled-up beryllium design. Note again that the growth factor spectrum is shown for the one third dopant case for HDC. With the full dopant concentration, the peak growth factors are 750.

Resolved tent simulations of the three designs are shown in Fig. 17. In contrast to the post-shot results, here the CH design shows the smallest impact from the tent, while beryllium is impacted most, and HDC is intermediate. The large beryllium impact is likely due to the higher convergence of this design and larger deceleration phase RT growth.

Resolved fill tube simulations for each design are shown in Figs. 19 and 20. Unlike the post-shot simulations, here all designs are simulated with a 5 μm diameter fill tube in the configuration of shot N170226. This reduced fill tube diameter has been shown decisively to improve performance in HDC implosions—enabling yields greater than 10¹⁶—, and will be the standard fill tube configuration in future experiments.^53,38 The details of the fill tube configuration and zoning are shown in Fig. 18, to be compared with Fig. 5.

Figure 19 shows the simulated fill tube results at a convergence of three when the high-resolution wedge simulations are linked onto a lower-resolution butterfly mesh. The trends seen in the post-shot simulations are reproduced here, albeit at smaller amplitudes corresponding to the smaller diameter fill tube: The HDC simulation has opened a hole in the shell, although it is not large enough to inject significant mass as with the larger fill tube. The CH simulation shows an outward-directed bump perturbation from the fill tube with again little injected mass, and the beryllium simulation shows an outward-going bump ringed by (several) inward-going bubbles. Figure 20 shows the simulations at their respective bang times. The hot spot perturbations are small for all ablators with little injected mass. Again, note that current simulations appear to under predict the amount of injected mass compared to experiment, so these results should be taken as lower bounds.

Figure 21 shows short-wave length fuel-ablator mix simulations for each design at peak implosion velocity. Even with the dopant reduced to one third, the fuel-ablator mix is not significant for the HDC design, although a one-half dopant design could also be chosen for increased assurance against short-wavelength mix. The CH design appears very stable to fuel-ablator mixing, and again, the beryllium design shows the largest amount of mix, though not quite as severe as in the post-shot results above.

Figure 22 shows lower-resolution simulations with all effects combined, except for short-wavelength mixing, that is, fill tube and tent defects, surface roughness, and flux asymmetries taken from the corresponding hohlraum simulations. By design, all of these implosions have fairly round hot spots. The fill tube impact is more prominent for the HDC and beryllium designs, and the tent impact appears to be minor. The higher convergence beryllium design shows more prominent mid-wavelength deceleration phase instability growth around the hot spot. However, it is notable that this high convergence design nonetheless ignites in the simulation to produce nearly 10¹⁸ neutrons. Note, again, that these results are certainly optimistic. In all cases, the impact of the fill tube is likely underestimated, while in the case of beryllium, the role of short-wavelength mix is probably non-negligible and must be included for an accurate projection of performance in this case. This is a subject of on-going work.

Finally, Fig. 23 compares the relative impact of the various perturbation sources in the scaled-up designs as well as all effects in combination. The vertical scale shows yield over clean. The blue, red, and green bars show the results of separate resolved-tent, fill tube, and hohlraum asymmetry-only simulations with α-particle deposition switched off. The lighter blue bars show simulations with α-particle deposition included and all effects in combination. The various perturbation sources result in relatively little yield degradation individually; however, in combination, all of the perturbation sources result in predicted yield over clean values of 25%–60%.

This paper compares the relative advantages and disadvantages of the three primary ablator materials for NIF ignition designs (CH, HDC, and beryllium) based on up-to-date capsule modeling. The results were compared for simulations of ablation front linear growth factors, the capsule support tent and fill tube, short-wavelength fuel-ablator interface mixing, and simulations with all effects in combination. The simulations were run in both a post-shot mode to model past experiments and a pre-shot or predictive mode to assess the prospects of future designs intended to exploit the full power and energy of NIF. Companion hohlraum simulations were also run for all of the cases considered, and the results are described in a companion paper.²³ 

The principle results of this capsule-only study are the following:

1. Current and extrapolated HDC designs show the largest ablation front linear growth factors, beryllium shows the least, and CH is intermediate.

2. The capsule support tent impacts current CH implosions most and HDC implosions least, but near-term extrapolated designs show that beryllium is most impacted with HDC and CH comparable.

3. In current designs, the fill tube impacts HDC very strongly (with >50 ng of high-Z ablator material injected into the hot spot), CH is only weakly impacted, and beryllium designs are intermediate. Future designs with 5 μm diameter fill tubes simulate to be only weakly impacted for all three ablators.

4. Based on current metrology, beryllium has the highest surface roughness on both the inner and outer surfaces, and HDC has the least. This results in significant simulated short-wavelength mix in current beryllium designs, but this does not appear to be a concern for CH or HDC.

5. Experiments with CH and HDC ablators are relatively well matched by simulations (better than 25% in yield, burn-averaged temperature, and DSR), but the most recent beryllium implosion is not, likely due to strong short-wavelength mixing that is not properly accounted for in current simulations.

6. Current CH and HDC designs extrapolate to yields of several 10¹⁶ at full NIF power and energy. Current beryllium designs extrapolate to 10¹⁸, but this is probably unrealistic due to the uncertainties with respect to short-wavelength mixing noted above.

Note that the relative impacts of the different perturbation sources vary from post-shot models to extrapolated designs. For example, the tent impacts CH most in the post-shot simulations but impacts beryllium most in the extrapolated designs. This variation underscores the important point that the ablator choice is not the single determinant of perturbation growth but that pulse shape and other design choices strongly influence the results. Indeed, selecting the optimal pulse shape is an essential choice in developing better performing designs.

Finally, also note that there are many ablator-specific features such as opacity inhomogeneities from contaminants, material strength effects, and crystalline micro-structure which are not addressed here but deserve attention in future work. The rich experimental database comparing the unique features of these ablators will also be documented in future work.²⁶ 

In conclusion, based on current understanding and the results described above, the HDC ablator design looks best positioned to reach higher yields on NIF in the near term. In fact, implosion designs similar to the scaled-up HDC design discussed here are the subject of active work aiming for higher yield in the very near future. The CH design looks similarly promising, although it absorbs less energy at a given scale than HDC and cannot be driven as efficiently. The future performance of the beryllium design looks most uncertain due principally to the higher surface roughness of current beryllium shells and inadequacies in current modeling. However, the dataset of beryllium implosions on NIF is extremely limited, and more experience will be needed before reliable predictions can be made.

We acknowledge the contributions of the CH, HDC, BF, and Be NIF teams in collecting the experimental data cited in this comparison. We also acknowledge the assistance of the HYDRA development team in running the simulations described here.

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.