High-compression implosions based on high density carbon ablator using modified drive and capsule dopant profiles Open Access

Laser-driven inertial fusion experiments at the National Ignition Facility (NIF)¹ have successfully exceeded Lawson's criteria for ignition,² achieving a target gain $G≈0.7$ using the full-scale “HyE” platform.³ More recently, by increasing the drive on the capsule with additional laser energy and controlling known degradation mechanisms, improved compression has been achieved, resulting in a target gain $G≈1.5$⁠.⁴ 

Hydrodynamic instabilities and mixing, however, can degrade both compression and the burn-up fraction. Although recent NIF experiments have surpassed unity gain for the first time in a laboratory setting, the current 5% fuel burn-up fraction remains about four times lower than ideal calculations, indicating that greater gains could be achieved by further improving the fuel areal density (i.e., compression). The degree of compressibility depends on the fuel adiabat, which is determined by the strength and timing of successive shocks in the laser pulse drive.⁵ Imperfections in the target can cause mixing between the shell's layers due to hydrodynamic instabilities at the interface discontinuities, which grow during the implosion. This mixing limits the achievable compression^6–9 and makes it critical to reduce instability growth to increase the fuel areal density and gain. Additionally, mixing of the ablator material into the fuel can quench the burn wave by diluting the D and T concentration, and severe mixing can prevent ignition altogether.

In early subscale experiments using high-density carbon (HDC) ablators and “3-shock” drive pulse shapes (a concept that will be clarified later on), the measured fuel down scattered ratio (DSR) was unexpectedly lower for lower adiabat designs, despite comparable implosion velocities and fuel masses. This observation supported the hypothesis that f, or interface mixing, is responsible for compression degradation, consistent with the equation above.

Recently, we reported the highest recorded fuel compression in implosions utilizing HDC ablators with a tungsten (W)-doped layer at the NIF.¹⁰ This was achieved using a new drive profile, “SQ-n,” characterized by a strong first shock followed by a continuous ramp,^11,12 and a new ablator profile, “W-inner.” The W-inner design positions the W-doped layer near the ablator-ice interface to eliminate one unstable interface, as opposed to the “W-buried” design, which leaves an undoped ablator layer before the interface. This combination successfully mitigated high-mode growth at the ablator-fuel interface^13,14 while reducing the in-flight adiabat.

Here, we expand the previous results by presenting a comparative analysis of sub-scale implosions to explore the limits of compression using different ablator designs coupled with the “SQ-n” pulse.^11,12 The ablator designs studied include variations of the “W-buried” and “W-inner” along with the “continuous gradient” profiles that will be described in detail later.

Our findings indicate that the “SQ-n” ramped pulse consistently outperforms the “3-shock” designs across all ablator profiles studied. Notably, the compression data reveal only a modest dependence on the specific dopant configuration, confirming that the “SQ-n” pulse itself is the primary driver of improved performance. Among the “SQ-n” configurations, the highest compression was achieved with the 0.4% “W-inner” and continuous gradient dopant profiles, demonstrating the superior performance of these designs. Overall, when combined with the DSR measurements discussed earlier, the results confirm the critical role of the continuous ramped pulse in reducing mix. In contrast, the “3-shock HDC” pulse demonstrated limitations in performance, as it was unable to effectively leverage the benefits of the “W-inner” dopant profile. This highlights the importance of the “SQ-n” pulse design in achieving improved compression and mix mitigation.

Finally, the sub-scale “SQ-n” experiments have achieved remarkable compression levels, outperforming full-scale “HyE” implosions at similar adiabat. As areal density scales with target size,¹⁵ these results suggest that the “SQ-n” design could benefit significantly from increased scale, as supported by simulations.

This work enables future larger-scale experiments, using a 1050  $μ$ m inner radius capsule in a 6.4 mm $×$ 11.2 mm hohlraum, to test the physics of the “SQ-n” design on DT fuel in the burn-wave propagation regime, utilizing the most effective dopant profiles identified in this study.

To avoid confusion arising from our nomenclature, which aims to preserve historical acronyms, we clarify that all the experiments mentioned here used capsules with HDC ablators, except for the “CH” experiment discussed in Sec. III. The three pulse designs being discussed are illustrated in Fig. 1. Previous iterations of “3-shock” designs at the NIF utilized either a Bigfoot,^16,17 “3-shock BF,” or a “3-shock HDC”^18,19 pulse shape. The “3-shock BF” design features a 3-shock pulse that combines the first and second shocks at the ablator-fuel interface, meeting the third shock at the inner fuel surface and setting the shell at an adiabat of $α∼4$⁠.^16,17 The “3-shock HDC” design modifies the pulse to collide the three shocks at the inner fuel surface, resulting in an in-flight adiabat of $α∼2.5$⁠.^18,19 For clarity, in the rest of this paper, the term “3-shock” will be used to refer to either “3-shock HDC” or “3-shock BF” when statements apply to both designs. The “SQ-n” design discussed below uses a gently ramped pulse for an in-flight adiabat of $α∼3$⁠.¹¹ The ultimate compression achieved is measured by the shell areal density, $ρR$⁠, which is proportional to the down scattered ratio (DSR),^20–22 defined as the ratio of neutrons with energies between 10 and 12 MeV to non-scattered neutrons with energies between 13 and 17 MeV. The DSR effectively measures the fraction of neutrons produced in the hotspot down-scattered by the cold fuel layer surrounding it.

As noted in Ref. 10, subscale experiments with high-density carbon ablators and the “3-shock HDC” pulse shape resulted in lower measured DSR values compared to companion experiments using a “3-shock BF” pulse shape, despite the “3-shock HDC” having a lower design adiabat. This evidence suggested that the interface mix is the primary cause of compression degradation in the “3-shock HDC” design. Indeed, the implosions experience Richtmyer–Meshkov (RM) growth^23–35 and Rayleigh–Taylor (RT) instability at the ablation front during the acceleration phase and the “3-shock HDC” design was especially vulnerable.^36–40 Despite efforts to suppress high-mode growth during ablation, perturbations persist during implosion deceleration due to the Bell–Plesset effect.^41–44 Instabilities originating from defects in the outer ablator can result in the mix of high-Z materials into the hotspot, increasing radiation losses and potentially preventing ignition or reducing gain. In addition to injecting material into the hotspot, hydrodynamic instabilities at the various interfaces within the capsule can cause mixing material from the ablator into the DT fuel, leading to higher entropy and reduction of compression and ultimately the gain. The “SQ-n” pulse shape was developed to improve stability and reduce the mix.^10–12,35 To ensure melting of the HDC ablator and mitigate the seeding growth of instabilities in the initially crystalline material, the “SQ-n” pulse shape uses a first shock slightly higher, in strength, to the one in the “3-shock HDC,” but replaces the second and third shocks with a gently rising ramp to improve stability. Therefore, the fuel–ablator interface experiences only a single shock followed by a smooth acceleration. This interface acceleration has the effect of turning an otherwise unstable linearly increasing shock-induced RM growth into a stable oscillatory RT one.^23–35 As a result, the fuel is set at a relatively low adiabat of three, while the mix width at the ablator-fuel interface is reduced by more than an order of magnitude with respect to designs based on a “3-shock” drive pulse.^10–12 

During the acceleration phase, the stability of the fuel–ablator interface to the RT growth depends in part on the relative density of the fuel and HDC ablator, and thus the preheat due to hard x rays penetrating deep into the ablator.⁵ The typical way to mitigate this effect is by adding a high-Z doped layer to the ablator to shield hard x rays. However, this approach presents tradeoffs in ablation efficiency and stability at the ablation front that must be considered. In the “3-shock HDC” and “3-shock BF” designs, the dopant is buried inside the ablator, at approximately 5  $μ$ m from the fuel's outer surface.⁸ This creates an additional interface of undoped/doped material near the inner surface that can seed RM and RT growth. In its baseline configuration, the “SQ-n” design uses a dopant distribution known as “W-inner,” where the doped ablator region extends to the fuel–ablator interface.¹⁰ By eliminating one potentially unstable interface and the associated opacity and density discontinuity, simulations predict this design reduces fuel–ablator mixing in “SQ-n” significantly. Table I summarizes the results reported in Ref. 10. Ultimately, the combination of the “SQ-n” pulse and the “W-inner” dopant profile has resulted in a 15%–30% increase in compression with respect to the “3-shock” designs. This is attributed to a reduced fuel ablator mix compared to the “3-shock HDC” design and lower adiabat than the “3-shock BF” design.¹⁰ 

Figure 2 compares the baseline 0.4% “W-inner” dopant profile (a) to the 0.2% “W-buried” profile (b). To ensure stability at the fuel–ablator interface, the “W-inner” requires a higher overall dopant concentration in the ablator than the buried layer dopant distribution, resulting in about twice the dopant density. This, however, leads to a slightly more unstable ablation front compared to the buried layer approach due to enhanced density gradients, which amplify Rayleigh–Taylor instabilities, and to the increased radiative losses that can contribute to instability during the rapid heating and pressure changes of the implosion process. The 0.2% “W-buried” profile constitutes the bulk of the “3-shock HDC” series used as a comparison to the “SQ-n” experiments discussed in Ref. 10 and included in Fig. 3.

To identify the impacts of the “SQ-n” on compression, we carried out a sequence of experiments that involved coupling the “SQ-n” pulse with different variations of ablator dopant profiles. In the first experiment, we utilized a buried layer dopant profile [Fig. 2(c)] with a dopant concentration that matched the baseline 0.4% “W-inner” [Fig. 2(a)]. We aimed to separate the effects of the dopant layer reaching the capsule's internal surface and the increase in dopant concentration. The measured DSR was 3.3% $±$ 0.2%. The corresponding data point is represented by the open diamond in Fig. 3, where it is compared to prior data reported in Ref. 10. This value represents a significant 15% reduction from the compression achieved with the 0.4% “W-inner” and is consistent with the predicted greater mixing of the corresponding 0.4% “W-buried” dopant profile.

It is worth noting that although this experiment resulted in the lowest compression among the “SQ-n” series, it still reached a value of DSR significantly higher than any “3-shock HDC” experiments utilizing buried dopant profiles, as shown in Fig. 3. This result highlights the inherent advantages of the “SQ-n” pulse shape over the “3-shock HDC.”

An alternative method to reduce mixing is to employ a continuous-gradient varying dopant profile. This approach aims to smooth out the dopant concentration jumps present at the interfaces of the typical step-like profiles, as illustrated in Fig. 2(d). The resulting profile is predicted to result in less instability growth at the interfaces compared to the buried layer profile due to the smooth transitions in opacity. This profile maintains a few micrometers of the undoped region at the fuel–ablator interface to enhance control over the fuel–ablator Atwood number. Design simulations with HYDRA⁴⁵ suggest that the presence of an undoped layer adjacent to the fuel leads to reduced pre-heating, thereby requiring a smaller dopant fraction to remain cool and dense compared to the “W-inner” profile. This translates to an 11% reduction in the W dopant areal density, potentially leading to higher implosion velocities.

Accordingly, the step-like 0.4% “W-inner” dopant profile was replaced in the second experiment with a continuous gradient dopant profile, labeled as (d) in Fig. 2. This modification resulted in a DSR of 3.64% $±$ 0.1%, matching the compression achieved by the 0.4% “W-inner” experiments (represented by the open circle in Fig. 3). Therefore, the continuous gradient profile demonstrated comparable compression performance, establishing it as a viable alternative for future HDC designs.

In the third experiment, we deliberately reduced the tungsten concentration in the 0.4% “W-inner” layer by approximately a factor of 2 to match the concentration of the 0.2% “W-buried” layer. The resulting profile, labeled as 0.2% “W-inner,” is shown in Fig. 2(e).

The experiment yielded a DSR measurement of 3.6% $±$ 0.2%, which is represented by an open triangle in Fig. 3. Hence, an approximate 7% loss in compression, as compared to the 0.4% “W-inner” baseline profile, consistent with a theoretically less stable Atwood number. It is worth noting that although reducing the dopant concentration in the “W-inner” layer has significantly reduced compression, it is still higher than what was achieved in previous “3-shock BF” and “3-shock HDC” implosions using a “W-buried” HDC ablator. Interestingly, this ablator configuration also achieved higher DSR than the “3-shock HDC” implosions that utilized either the 0.4% “W-inner” or the reduced-dopant 0.2% “W-inner” profile, as shown in Fig. 3. This observation further strengthens the notion that the smooth acceleration imparted by the “SQ-n” pulse shape improves the robustness of the implosion.

Overall, the sub-scale “SQ-n” experiments have achieved fuel compression levels comparable to the large-scale implosions that have, so far, recorded the highest areal density values on the NIF. These large-scale implosions utilized a “4-shock” pulse shape coupled with a CH ablator, achieving a low adiabat of approximately 1.6 (Ref. 47) and reaching a DSR value of about 4%, as shown in Fig. 3.

Furthermore, the sub-scale “SQ-n” series outperformed companion full-scale “HyE” implosions (with an adiabat of approximately 2.9). Notably, the areal density is predicted to scale proportionally with the target size,¹⁵ which makes the compression levels achieved with the “SQ-n” design even more remarkable. Therefore, these results suggest that the “SQ-n” design should benefit significantly from an increase in scale, as predicted by simulations.

Concurrently with assessing compression through DSR, we conducted spectroscopy measurements to infer the optical depth and mix mass from the emission and absorption features of the tungsten dopant in the ablator.⁴⁸ The spectra were recorded using the Imaging and Spectroscopy Snout, covering a range between 8 and 12.5 keV.⁴⁹ The radiative losses associated with the mix are inferred from the Mg- to F-like 3d-2p W emission features from the hotspot, Ti- and V-like emissions from the outgoing shock, and W L-shell fluorescence and absorption features from the cooler, denser surrounding fuel and remaining shell.^50,51 In what follows, we refer to the mixing of the colder, outer layers of the fuel with the ablator material as “cold mix,” in contrast to “hot mix,” which is the mixing of the ablator into the hotspot. Table II summarizes the results for the different combinations of pulse shape and ablator dopant design.

In companion experiments using the “3-shock HDC” pulse shape, we observed a threefold reduction in radiation associated with the “cold mix” when using the 0.4% “W-inner” dopant profile instead of the 0.4% “W-buried” one. Corroborating our earlier statement and evidence from simulations that by removing an unstable interface, the “W-inner” dopant profile does indeed reduce the fuel–ablator mix. Furthermore, using the “SQ-n” pulse shape with either the 4% “W-inner” or the “continuous gradient dopant” profile achieved an additional 20-fold reduction. The combined effect resulted in a total reduction of 60-fold or more, partly attributed to the higher optical depth of the shell. This observed reduction is consistent with simulations indicating that both these dopant profiles offer greater stability with respect to mixing. Overall, when combined with the DSR measurements discussed earlier, the results confirm the critical role of the continuous ramped pulse in reducing mix. The “3-shock HDC” pulse was unable to leverage the benefits of the “W-inner” dopant profile effectively.

We conclude this section by discussing two key parameters that help in understanding DSR trends: the coast time, $tcoast$⁠,⁵² and the implosion velocity, $vimp$⁠.¹⁰ The coast time is defined in Fig. 1 together with the neutron production bang time, $tBT$⁠, and $tstart$⁠, i.e., the time at which the drive power rises above 300 TW. The final shock trajectory is not sensitive to peak powers above this threshold. The implosion velocity, $vimp$⁠, is derived from measured quantities, also defined in Fig. 1, using the equation $vimp∼R/teff$⁠, where R is the capsule radius. The effective acceleration time, $teff$⁠, is defined as the travel time of the capsule between the last shock passage and the onset of deceleration, typically occurring 0.5 ns before bang time.

We observe that, based on simple physical arguments, the relationship between implosion velocity and coast time is causal, as decreasing the coast time corresponds to increasing the duration of the driver pulse, assuming all other factors remain constant. This in turn means the shell is pushed for a longer interval of time, leading to a higher implosion velocity. The plot of the implosion velocity vs coast time for the set of experiments considered here is shown in Fig. 4. The black dashed line is a fit to data using the equation $vimp=vimpmax−a(tcoast−0.45 ns)2$⁠, derived following Fig. 2 of Lindl et al.,⁵³ together with the 3  $σ$ confidence level shown as a gray shaded area. The fit assumes that all designs would achieve approximately 410  $μ$ m/ns with minimal coast time. The fact that the various designs lie on the same fitting curve is a consequence of them using the same peak power and shell thickness.

As shown, the implosion velocity progressively increases as the coast time decreases. For a coast time of approximately 0.6ns, the rate of increase matches the implosion velocity uncertainty, indicating that further reduction in coast time will not significantly increase the implosion velocity. This coast time marks the onset of saturation for the implosion velocity, beyond which reducing coast time does not increase compression. A similar saturation trend is observed when plotting DSR values vs coast time.

A comparison to Fig. 3 suggests that parametrizing DSR vs implosion velocity is more suitable for describing the trend of DSR in the data presented in this article. This is evidenced by the fact that the DSR values in Fig. 3 do not show any saturation concerning implosion velocity. The physics counterpart of this argument is the equation $DSR∝vimp1.6/α$⁠, for a given fuel thickness, as derived in Ref. 10, where $α$ is the adiabat.

The work discussed here builds upon previously achieved record-high compression results using the “SQ-n” pulse and the “W-inner” dopant profile in sub-scale implosions on the NIF.¹⁰ In this study, we have expanded on those results by measuring the DSR achieved by coupling the “SQ-n” pulse with different dopant profile designs to understand the relative impact of each design feature.

Our findings demonstrate that the “SQ-n” ramped pulse consistently outperforms the “3-shock” designs across all ablator profiles studied, establishing it as a more effective approach for achieving higher compression and mitigating mix in inertial confinement fusion (ICF) experiments. Compression data reveal only a modest dependence on the specific dopant configuration, confirming that the “SQ-n” pulse itself is the primary driver of improved performance. Among the “SQ-n” configurations, the highest compression was achieved with the 0.4% “W-inner” and continuous gradient dopant profiles, highlighting the improved performance of these designs.

The “3-shock HDC” pulse was unable to leverage the benefits of the “W-inner” dopant profile effectively, further underscoring the importance of the “SQ-n” pulse in achieving optimal performance. The sub-scale “SQ-n” experiments achieved remarkable compression levels, even outperforming full-scale “HyE” implosions at similar adiabat. As areal density scales with target size, these results suggest that the “SQ-n” design could benefit significantly from increased scale, as supported by simulations.

These findings pave the way for future larger-scale experiments, utilizing a 1050  $μ$ m inner radius capsule in a 6.4 mm $×$ 11.2 mm hohlraum, to test the physics of the “SQ-n” design on DT fuel in the burn-wave propagation regime. By combining the most effective dopant profiles identified in this study, namely, the “W-inner” and the continuous gradient dopant, with the robust performance of the “SQ-n” pulse, this work represents a significant step toward achieving higher gains and advancing the broader goal of practical fusion energy.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory (Contract No. DE-AC52-07NA27344) and by General Atomics (Contract No. DE-NA0001808). This document was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor Lawrence Livermore National Security, LLC, nor any of their employees make any warranty, expressed or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes.

The authors have no conflicts to disclose.

R. Tommasini: Conceptualization (equal); Data curation (equal); Formal analysis (lead); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (lead). D. T. Casey: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). D. Clark: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). A. Do: Data curation (equal); Formal analysis (equal); Investigation (equal); Validation (equal). K. L. Baker: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Validation (equal); Writing – review & editing (equal). O. L. Landen: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). V. A. Smalyuk: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). C. R. Weber: Conceptualization (equal); Investigation (equal); Methodology (equal). B. Bachmann: Data curation (equal); Formal analysis (equal); Visualization (equal). E. Hartouni: Data curation (equal); Formal analysis (equal); Visualization (equal). S. Kerr: Data curation (equal); Formal analysis (equal); Visualization (equal). S. Khan: Data curation (equal); Formal analysis (equal); Visualization (equal). C. Krauland: Data curation (equal); Formal analysis (equal); Visualization (equal). A. L. Kritcher: Data curation (equal); Formal analysis (equal); Investigation (equal); Validation (equal); Visualization (equal). E. V. Marley: Investigation (equal); Validation (equal); Visualization (equal). M. Millot: Data curation (equal); Formal analysis (equal); Validation (equal); Visualization (equal). J. Milovich: Investigation (equal); Validation (equal); Visualization (equal). R. C. Nora: Investigation (equal); Validation (equal); Visualization (equal). A. E. Pak: Data curation (equal); Formal analysis (equal); Validation (equal); Visualization (equal). D. Schlossberg: Data curation (equal); Formal analysis (equal); Validation (equal). D. J. Strozzi: Investigation (equal); Validation (equal); Visualization (equal). B. Woodworth: Project administration (equal); Resources (equal). A. Allen: Data curation (equal); Resources (equal). S. H. Baxamusa: Resources (equal). T. M. Briggs: Data curation (equal); Formal analysis (equal); Resources (equal). T. Fehrenbach: Data curation (equal); Resources (equal). D. M. Holunga: Data curation (equal); Formal analysis (equal); Resources (equal). A. Nikroo: Resources (equal). C. Kong: Data curation (equal); Resources (equal). C. Wild: Data curation (equal); Resources (equal). M. Stadermann: Resources (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.