Design of first experiment to achieve fusion target gain > 1

Fusion offers the promise of clean and limitless energy, which could be the long-term answer to rapidly growing global energy demands. However, net fusion energy gain has not yet been realized in the laboratory due to the difficulties in creating and confining the extreme plasma conditions needed for fusion to occur. Overcoming the electrostatic repulsion of the fusion reactants requires tens of millions of degrees, and creating these conditions in the laboratory has previously required more heating energy, or driver energy, than is produced from fusion. Generating more fusion energy delivered to the target is an important milestone in the quest for fusion energy and has been a long-standing goal of all fusion energy approaches. On December 5, 2022, we have finally achieved that goal in an experiment on the National Ignition Facility (NIF)¹ in Livermore, CA, which was also the last remaining milestone for the National Ignition Facility (NIF).² Since then, we have repeated this result and achieved target gain exceeding unity five times to date at the NIF.

In the laser indirect-drive approach,^3–8 lasers are shined onto the inside of a Au-lined Depleted Uranium (DU) cylindrical cavity (Hohlraum) to generate a $∼$3 million degree x-ray radiation bath. A hollow diamond sphere containing a cryogenically frozen layer of DT, with a DT gas core, is suspended inside the Hohlraum using a thin membrane (capsule support “tent”). The x-ray radiation cavity heats the outside of the diamond shell causing it to expand radially outward which launches (implodes) the fuel and a fraction of the diamond mass radially inward, doing mechanical PdV work on the fuel and squeezing it to smaller volumes, which results in an increase in compression and temperature, see Fig. 1.

A main challenge is doing sufficient work on the central plasma to ignite the fuel. For this to occur, extreme temperatures are required to balance energy losses in the system, e.g., Bremsstrahlung x-ray losses, conduction losses, and explosion phase losses. Self-heating from the alpha particles that are born in the fusion reactions is required to increase the plasma temperature to ignition conditions [D + T $→$ n (14.1 MeV)+⁴He (3.5 MeV)]⁹ which requires achieving sufficient hotspot densities to stop the alpha particles in the central hot plasma. Once the central hot plasma ignites, a burn wave propagates through a cooler denser shell of DT fuel that both initially does work on the implosion and confines the plasma long enough to enable “burning-up” of the remaining cooler denser DT fuel. The plasma is confined for $∼$100 ps via its own inertia and then explodes under the extreme pressure of the fusing plasma. On December 5, 2022, $∼$4% of the DT fuel present in the experiment was “burned,” up, or “fused,” creating energetic neutron particles. This paper describes the design that enabled this result together with simulated projections for future improvements.

Early designs at the NIF⁸ using plastic (CH) capsules to hold the DT fuel suffered from hydrodynamic instabilities seeded by the “capsule support tent”¹¹ which caused capsule material to enter the hot-fusing plasma and radiate energy away. Increasing the laser power in the early part of the laser pulse (“CH HiFoot”) resulted in increased stability¹² but was ultimately also limited by the tent perturbation. Introducing diamond (High Density Carbon (HDC)) ablators^13–17 reduced sensitivity to the tent perturbation due to its higher density (⁠ $∼$3.5 g/cm³) and also made symmetry control easier due to shorter laser pulses. Due to the higher density of HDC, thinner ablators could be used, which reduces the transit time of multiple shocks moving through the ablator and fuel, resulting in shorter laser pulses.

The early hohlraum designs were also limited by laser plasma interactions¹⁸ which resulted in inefficiency of driver coupling to the hohlraum. This was mainly a result of a high level of helium gas fill that was used to hold back the expanding wall plasma, but resulted in increased levels of Stimulated Raman Scattering (SRS). Reducing the helium gas fill density inside the hohlraum^19–21 resulted in lower levels of laser backscatter and an increase in hohlraum efficiency, which enabled fielding larger case-to-capsule-ratio (CCR) hohlraums and making symmetry easier to control without the use of intentional cross-beam-energy-transfer (CBET).^18,22

While imploding the capsules, it is important to control the time-varying radiation flux symmetry within the hohlraum to $∼$1%, to efficiently do work on the implosion.^23–26 The laser–wall interaction causes the hohlraum wall to ingress into the path of laser beams which makes controlling symmetry a main challenge. A main method for controlling symmetry is using CBET to move energy between laser beams by tuning the frequency of the density perturbation caused by the ponder-motive pressure from the interference pattern of the laser beams. Changing the relative wavelength of the overlapping laser beams changes the frequency of this perturbation and creates a refractive index modulation which acts as a Bragg scatter and redirects the incoming laser light. Previously, using this technique in hohlraums with high levels of He gas fill resulted in increased levels of laser-backscatter and loss of symmetry control.²⁷ Development of CBET in low-gas-filled hohlraums^28,29 has been instrumental in enabling symmetry control for reduced CCR target designs.

The HYBRID-E design^30–35 was one of a series of designs³⁶ aimed to increase the energy delivered to the hotspot plasma by increasing the scale (S) of the implosion 10%–15% while maintaining the hotspot pressure required for inertial confinement fusion and other critical implosion properties, within the current limitations of the NIF. Driving larger scale implosions to similar velocities as smaller scale implosions while using the same amount of laser energy requires developing more efficient smaller hohlraums with less radiation loss. This results in a smaller case to capsule ratios (CCR), or smaller hohlraum diameter for a given capsule size, which is more challenging for controlling implosion symmetry. Advancements in symmetry control using CBET in low-gas-filled hohlraums^28,29 and development of a semi-empirical model for late-time hohlraum symmetry³⁷ calibrated against years of experimental data were instrumental in the design of HYBRID-E. Even with a more efficient hohlraum, design tradeoffs were necessary between key implosion metrics and what could be achieved using a laser-driven hohlraum. It was expected that the simulations (HYDRA³⁸) coupled with past experimental data could get close in determining the scale of implosion that would best balance these tradeoffs. Since simulations cannot predict to the degree of precision required to delicately balance the hohlraum and implosion design tradeoffs and achieve ignition, testing two implosion scales (initial inner radius of 1050 and 1100  $μ$m) was part of the initial HYBRID-E experimental plan.

The larger scale diamond capsule was initially tested in HYBRID-E but suffered from simultaneously trying to control the implosion velocity, coast-time, and symmetry.³¹ Following these experiments, a burning plasma^32,33 was achieved by reducing the initial scale of the diamond capsule by only 50  $μ$m, enabling more optimal balancing of these tradeoffs. Then, further reducing the size of the laser entrance holes, holes at the ends of the hohlraum where the laser beams enter, resulted in an even more efficient hohlraum which produced the same radiation temperature at lower laser power due to lower radiation losses. This enabled increasing the laser pulse length to improve the implosion properties³⁹ and couple more driver energy to the implosion which led to the first experiment to achieve scientific ignition⁴⁰ on August 8, 2021 [NIF shot No. N210808]^34,41,42 and the first to produce >1 MJ of fusion energy, see Fig. 2.

On December 5, 2022 (shot #N221204),^35,43–45 fusion energy target gain exceeding unity was achieved, where the fusion energy produced was greater for the first time than laser energy on target, after a symmetry correction from September 19, 2022 (fusion energy of 1.22 MJ and target gain of $∼$60%), by making additional design changes to the HYBRID-E platform.^35,43–45 A thicker diamond ablator was fielded to couple $∼$8% more available laser energy^46,47 to the implosion and increase the areal density of the DT fuel and capsule at maximum compression which leads to higher yield amplification and fuel burn-up fraction. The extra laser energy was enabled through upgrades to the optics damage mitigation and reprocessing. The new capability of NIF delivered 150 kJ additional laser energy (2.05 MJ) compared to prior experiments (1.9 MJ) at a maximum laser power of 440 TW, see Fig. 2 for laser power as a function of time for N210808 compared to N221204. The fusion energy produced was exceeded on July 29, 2023 (N230729) in this design using a higher quality diamond capsule, achieving $∼$3.88 MJ of fusion energy and a target gain of $∼$1.9×.

Figure 1 shows a schematic of the target and laser design. Laser beams are pointed onto the inside of a gold-lined Depleted Uranium (DU) cylindrical can (hohlraum), 11.24 mm length × 6.4 mm diameter, in four distinct laser sets defined by their angle of incidence (inner beams: 23° and 30° and outer beams: 44° and 50°). The laser heating of the hohlraum creates a radiation oven that is $∼$3 × 10⁶ K (>300 eV), see Fig. 1(bottom right). Compared to N210808, the laser energy was increased from 1.92 to 2.05 MJ at constant peak laser power (⁠ $∼$440 TW), see Fig. 1 (top right), and the early part of the laser pulse was extended to maintain the shock timing for the thicker capsule.

The radiation drive is absorbed in the outer region of a hollow diamond spherical capsule (1050  $μ$m inner radius and $∼$85  $μ$m thick) sitting in the center of the hohlraum, which contains the DT fuel (65  $μ$m thick ice layer with a DT gas core). The x-ray absorption heats and ablates the diamond which expands radially outward, causing the remaining diamond capsule and DT fuel to accelerate inward at extreme implosion velocities (⁠ $vimp∼$ 380–400 km/s). Compared to the N210808 HYBRID-E design, the diamond ablator thickness was increased by $∼$5.75  $μ$m (N221204) and 6.9  $μ$m (N230729) to provide higher energy coupling of the radiation drive to the hotspot, higher total areal density at peak compression, and improved stability. See Ref. 35 for additional design details. The thicker diamond ablator was used to make optimal use of the extra drive at the end of the pulse which would have otherwise not coupled significantly more driver energy to the implosion. Figure 1 (bottom right) shows the simulated implosion radius vs time for the 2.05 MJ laser pulse and the $∼$6  $μ$m thinner N210808 diamond ablator compared to the thicker (“as-shot”) N221204 diamond ablator. The thicker ablator causes the capsule to remain larger longer and absorb more of the extra drive at the end of the pulse, which would not have coupled significantly more to the thinner shell implosion. A thickness increase in $∼$6  $μ$m was initially chosen to balance the improvement in both ignition margin and total areal density. See Table I for a comparison of simulated key implosion metrics for the extended 2.05 MJ drive and same capsule thickness as N210808 vs using a $∼$6  $μ$m thicker capsule. Future experiments will test the limits of thicker capsule implosions in this platform to further increase yield-amplification (extra yield from self-heating).

The symmetry of the radiation drive becomes more difficult to control with longer laser pulses and more time for the plasma to fill the hohlraum which reduces the energy coupling to the hotspot.²³ To adjust the symmetry, the amount of laser energy transfer from the “outer” to the “inner” beams (CBET) was increased by further detuning the relative wavelengths of these beams (⁠ $Δλ$ = Inner beam—Outer beam before laser frequency tripling),^18,22,28,29 where $Δλ$ = 1.8  $Å$ for N210808 and $Δλ$ = 2.75  $Å$ for N221204. Figure 1 (left) shows radiation hydrodynamics simulations of N221204 (right) and N210808 (left) at 6 ns after the start of the laser pulse, together with the calculated positions of the material boundaries [gold-lined depleted uranium hohlraum (orange), HDC ablator (light gray), and the position of the ice-gas interface (red)]. Simulated laser rays are also shown, where the color corresponds to normalized laser powers after CBET. Precisely adjusting the powers on the inner and outer laser cones during the entire laser pulse [Fig. 1(top right)] enabled controlling fluctuations in the radiation drive uniformity which can induce $ρ$R variations in the compressed fuel. Detailed radiation hydrodynamic simulations using HYDRA³⁸ with inline CBET⁴⁸ were used to design these inner and outer powers. These simulations were benchmarked against a series of “tuning” experiments, see the  Appendix.

The first experimental test of this new design with 2.05 MJ of laser energy (N220919) was limited in the amount of CBET “allowed” due to risk of laser damage from Stimulated Brillouin Scattering (SBS)⁴⁹ of the incident laser light back out of the hohlraum into the optics assembly. This resulted in a drive deficit at the waist of the hohlraum and an oblate hotspot, see Fig. 2. Increasing the amount of transfer through wavelength separation by 0.25 Angstroms from 2.5 Angstroms to 2.75 Angstroms and readjusting the time-dependent laser powers enabled achieving a round hotspot on N221204. On July 29, 2023 (N230729), a new diamond capsule “batch” was tested which had a lower amount of tungsten dopant, $∼$ 0.4% vs $∼$ 0.62% tested on N221204, see Fig. 3 for a pie-diagram of the diamond capsules noting the differences for these experiments. Due to the thicker ablator the early part of the laser pulse was extended by $∼$ 30 ps and a slightly higher wavelength separation of 2.9 Angstroms was used to correct symmetry for the extra diamond “payload.” Thicker capsules take longer to implode and sample a longer duration of the pole-hot radiation flux asymmetry which drives the hotspot more oblate. Increasing the wavelength separation counteracts this by making the drive more waist-hot earlier in the pulse. Small extrapolations in symmetry are predicted for these changes using radiation-hydrodynamic simulations and experimentally measured sensitivities. However, there is a larger uncertainty in extrapolating to higher levels of CBET in this regime and the chosen wavelength separation was too large, producing a prolate implosion, see Figs. 2 and 3.

Shot N230729 also had a worse mode one symmetry compared to N221204 (107 vs 36 km/s), largely due to an imbalance in laser delivery, aligned with other sources of mode one asymmetry (capsule non-uniformity, DT thickness non-uniformity, non-axially symmetric diagnostic windows). The impact of the combined sources of mode one asymmetry is measured as a net hotspot velocity, or speed at which the hotspot is moving in one direction. The measured hotspot velocity is amplified as the temperature rises for igniting implosions that are expanding during peak neutron production. We estimate this effect as well as the impact on performance for the measured level of mode one on N230729, see Fig. 5.

The lower tungsten dopant capsule fielded on N230729 was predicted to have lower performance (by up to 40%) compared to the higher tungsten dopant capsule of N221204 primarily due to the lower calculated total areal density which causes enhanced expansion through the thin spots following ignition which limits confinement. Thin spots in the dense shell are a result of low-mode asymmetries. Therefore, the level of reduction in the performance for the lower tungsten doped capsules increases with the level of low mode asymmetry. This can be seen in Fig. 4 (top) which shows the performance of the N210808 design (black), N221204 design (red), and N221204 design with lower tungsten concentration diamond capsules (blue stars) as a function residual kinetic energy, the amount of left over work that was not done on the hotspot as a result of the low mode asymmetries creating an inefficient piston. The higher optical depth capsules have more margin against RKE in the yield range where we are currently operating, with the symmetry-performance “cliff” at larger levels of RKE.

The amount of RKE in Fig. 4 (top) includes the simulated time-varying modes one, two, and four of the radiation drive but may overestimate the level of fluctuation in the P2 flux asymmetry, or P2 “swing” [e.g., Fig. 4 (bottom)]. Historically, simulations are benchmarked against in-flight radiography measurements (at implosion radii of $∼$200  $μ$m) which calibrate the level of P2 swing before the experiment, but at the time of writing this paper, a calibration experiment for N221204 had not yet been completed. Figure 4 (bottom) shows the simulated neutron yield (red points) as a function of hotspot oblateness (P2) for the N221204 design. The range of simulated neutron yields at a given level of hotspot oblateness is from taking a plausible range for the P2 swing. The insets are simulated contours at peak compression from $α$-off simulations (simulations where $α$-deposition is artificially turned off (“burn off” or $α$-off)) of the hotspot temperature (left) and density (right) for example points. For the first two experiments (N220919 and N221204) the same diamond capsule batch was used, with the same quality and the measured yield increase as a function of change in hotspot oblateness (blue points) fell within the simulated range.

Post-shot simulations under-predicted the performance of N230729 given the expected degradation from the lower tungsten concentration when matching the measured hotspot P2 asymmetry and mode one hotspot velocity. To better match the observed performance, the level of P2 swing (which is currently unknown) was reduced in simulations. Upcoming tuning experiments will validate the time-varying P2 swing for this design. Using this model for the reduced swing that enables us to match performance for N230729 with the correct observed mode two and one asymmetries, we estimate the impact of the observed mode one.

Figure 5 (middle) shows the simulated fusion energy as a function of simulated hotspot velocity for $α$-off simulations and simulations that include $α$-deposition (“burn on” or $α$-on). These simulations include surface roughness, tent and fill tube perturbation features, and modes one, two, and four of the radiation drive. For higher yield and temperature implosions, the hotspot velocity is amplified as the implosion is burning on expansion, see Fig. 5 (right) for ratio of $α$-off/ $α$-on vs fusion energy. Matching the measured hotspot velocity in burn-on simulations gives a burn-off hotspot velocity (at maximum compression) of $∼$70–75 km/s. This curve shows that reducing the mode one asymmetry could further to routinely achievable levels of < 60 km/s burn-on, increase the yield of N230729 by $∼$30% (>5 MJ). The sensitivity of performance to mode one was benchmarked against the N210808 design, Fig. 5 (left), which experienced large mode one asymmetries from laser fluctuations in repeat experiments. The simulated impact of mode one on the performance for this design (red) was consistent with the measured impact (black points). Note, the mode one present for the N210808 design was also calculated to impact the performance by 25%.

Experiment N230729 is also simulated to have generated more fusion energy with a corrected P2 that is less prolate. Figure 6 shows radiation hydrodynamic simulations of N230729 which match the level of performance (assuming the mode one was anomalous, and reducing it simulations) by picking a different level of P2 swing and matching the measured hotspot shape (left hand side). The simulations show contours at peak compression from $α$-off simulations of the hotspot temperature (left hand side) and density (right hand side). Reducing the level of prolate by decreasing the level of early-time waist-hot drive (a result of the increased wavelength separation compared to N221204) results in a $∼$90% increase in performance with this correction alone, and >7MJ.

Applying this model for the reduced swing, and accounting for as-shot differences in the P2 symmetry for N221204 and N230729, also gives a simulated performance for N221204 of >7MJ with higher dopant tungsten capsules and improved target quality, as well as lower residual kinetic energy (RKE). The difference between this prediction and the measured fusion energy of 3.15 MJ could be due to the reduced diamond capsule quality present for N221204. Experiments to study the impact of capsule quality vs lower tungsten dopant between N221204 and N230729 have bene proposed.

Following these experiments, further extending the laser pulse to 2.2 MJ of laser energy at the same peak power of 440TW (N231029 and N240210), resulted in a record fusion energy produced of 5.2 MJ, record target gain of $∼$2.4×, and record fuel burn-up fraction of $∼$7%. These experiments also increased the diamond ablator thickness by $∼$5  $μ$m compared to N230729. Ongoing work to improve the compressed shell symmetry in this platform, additionally increase the diamond ablator thickness, and increase the fuel burn-up fraction are ongoing.

The design presented in this paper provided more margin for achieving high fusion yields > 1 MJ in the presence of perturbations from non-ideal experimental conditions that reduced performance in the preceding N210808 design. These perturbations are predominantly unintentional low mode asymmetries from capsule non-uniformity or laser non-uniformity and reduced capsule quality that can seed hydrodynamic instabilities and mix ablator material into the hotspot. The hotspot energy density, a metric for ignition margin, was intentionally increased in this design by $∼$20% through an increase in both the hotspot pressure and coupled energy.³⁵ 

Additional margin to these perturbations can be seen in Fig. 7 which shows the fusion energy produced for N210808 (black) and four experiments using the N221204 design (red). The solid bars denote experimental fielding conditions where the yield was not degraded as significantly by low mode asymmetries or high-Z mixing into the hotspot as the repeat experiments of N210808. The dashed red bars denote experiments in the N221204 design which experienced higher levels of low mode asymmetry (P1 or P2), degraded capsule quality (high-Z inclusions), or particles on the capsule. Note, the hotspot velocity being nearly the same for a significantly lower yield, N230618 vs N230729 (see Table II), represents a higher reduction in performance due to the fact that there is amplification of the hotspot velocity at higher yields. The hotspot velocity observed on N230618 was mainly due to non-uniformities in the initial capsule thickness and laser energy delivery, and the hotspot velocity observed on N230729 was mainly a result of an imbalance in laser energy delivery. Even with these perturbations, the N221204 design produced > 1 MJ of fusion energy, whereas the same perturbations applied to the N210808 design (black dashed bars) are simulated to have produced < MJ of fusion energy. The insets above the bars illustrate the main type of perturbation corresponding to that experiment. Table II shows variation in the experimental fielding conditions for the five experiments in the N221204 design shown in Fig. 7.

Ongoing work aims to further increase the compression or coupling of these designs to increase fuel-burn up fraction. This section presents two example methods to improve the performance of the N221204 design, in addition to the suggested higher capsule quality vs N221204 (high-W% $∼$ 0.5% dopant) test and the mode two correction test of N230729.

Lowering the central gas fill density by lowering the “quench”⁵⁰ temperature is predicted to increase convergence and performance of the N230729 design by more than 2×, see Fig. 8. These simulations include the “kitchen sink” (roughness, tent and fill-tube features, and low mode asymmetries) and match the performance of N230729 (left). Lowering the central gas fill density (right) from 0.000 43 to 0.0003 mg/cc increases convergence by $∼$ 4.5%, the ignition margin by 20%, the total areal density by 10%, and the fusion yield by 2.35× (>9 MJ). These simulations also include differences in the DT gas composition with the change in initial temperature. Previous attempts to reduce the central fill density were performed in the N210808 (less stable) design with diamond capsules that had a significant number of defects, which resulted in lower than expected performance and complicated the understanding. Here we propose reducing the central gas fill density in the more stable N230729 design³⁵ which has increased ignition margin and has shown less sensitivity to variations in diamond ablator capsule quality. This adjustment uses the same asymmetries that are present on N230729.

Simulations suggest that the yield can also be substantially increased by further increasing the diamond thickness of the N221204 design using the same hohlraum configuration, laser energy, and adjusted shock timing. Once ignited, having a high total areal density of the fuel and ablator is advantageous for increasing yield amplification and fuel burn-up fraction. The first tests of the thicker ablator higher energy design took a substantial first step but started conservatively in thickness to balance the margin to ignite, increase in total areal density, and the symmetry risk of fielding thicker ablators. Exploring the limits of increase areal density could enhance robustness as well as performance (fusion energy produced and compression at a given yield) by several times, see Fig. 9 and Table III.

Figure 9 shows the simulated neutron yield as a function of increased roughness of the diamond ablator interfaces and ice layer with further increasing the diamond ablator thickness (green points) compared to N221204 and N230729 (red curve) by an additional 4, 6, 8, and 10  $μ$m using the same 2.05 MJ laser energy and hohlraum geometry with adjusted shock timing. A roughness of 5× nominal was applied to match the measured yield for N230729 without including degradation from low-mode asymmetries. For this level of roughness, the yield increases significantly by increasing ablator thickness. While these simulations match yield by increasing interface roughness without including low mode asymmetries, additional studies including low mode asymmetries with nominal roughness also show the same level of impact for thicker ablators at these yield levels. The increase in compression at a given yield is also shown in Fig. 9 (right) via the Down-Scattered-Ratio (DSR) for the thicker diamond ablator simulations (green curve). The increase in DSR as yield increases for the green curve is a result of the thicker ablator designs burning closer to maximum compression in contrast to the expansion phase.

The design changes presented in this paper resulted in the first ever controlled fusion experiment (N221204) to exceed target gain greater > 1, where the fusion energy produced exceeded the laser energy used to drive the target by $∼$1.54×. This design used a thicker diamond capsule (additional $∼$ 7.6% in thickness) together with an extended higher energy laser drive (2.05 MJ of laser energy compared to 1.9 MJ)^46,47 to increase the margin for ignition and enable higher DT fuel burn up fractions compared to N210808. A repeat experiment N230729 achieved the highest yield and gain to date for 2.05 MJ of laser driver energy (3.88 MJ and $∼$1.9× target gain). Further extending the laser drive to 2.2 MJ and increasing the HDC ablator thickness by an additional $∼$ 5  $μ$m has achieved the maximum yield and target gain to date of 5.2 MJ and G $∼$ 2.4×. We have also achieved target gain > 1 on five experiments, demonstrating robust and repeatable target gain. These proof-of-principle experiments demonstrate that there is nothing fundamentally limiting fusion energy gain in the laboratory.

The authors have no conflicts to disclose.

A. L. Kritcher: Conceptualization (equal); Investigation (equal); Software (equal); Supervision (equal); Writing – original draft (equal). D. J. Schlossberg: Data curation (equal); Supervision (equal). C. R. Weber: Methodology (supporting); Software (equal). C. V. Young: Formal analysis (supporting); Software (supporting). O. A. Hurricane: Conceptualization (equal); Supervision (supporting). E. Dewald: Data curation (supporting); Formal analysis (supporting). A. B. Zylstra: Data curation (lead); Supervision (equal). A. Allen: Data curation (supporting). B. Bachmann: Data curation (supporting). K. Baker: Data curation (supporting). S. Baxamusa: Data curation (supporting). T. Braun: Data curation (supporting). G. Brunton: Funding acquisition (supporting); Resources (supporting). D. A. Callahan: Conceptualization (supporting); Methodology (supporting); Software (supporting). D. T. Casey: Data curation (supporting); Formal analysis (supporting); Methodology (supporting). T. Chapman: Data curation (supporting). C. Choate: Data curation (supporting); Resources (equal). D. S. Clark: Formal analysis (supporting); Software (supporting). J.-M. G. Di Nicola: Resources (equal). L. Divol: Formal analysis (supporting). M. J. Edwards: Conceptualization (supporting); Project administration (supporting); Supervision (supporting). S. Haan: Formal analysis (supporting). T. Fehrenbach: Resources (equal). S. Hayes: Resources (equal). D. Hinkel: Methodology (equal); Supervision (supporting). M. Hohenberger: Data curation (supporting). K. Humbird: Software (supporting). N. Izumi: Data curation (supporting). O. Jones: Software (supporting). E. Kur: Software (supporting). B. Kustowski: Software (supporting). C. Kong: Resources (equal). O. L. Landen: Conceptualization (supporting); Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Methodology (supporting). D. Larson: Resources (equal). X. Lepro-Chavez: Resources (equal). J. D. Lindl: Conceptualization (supporting); Formal analysis (supporting); Methodology (supporting). B. J. MacGowan: Formal analysis (supporting). S. MacLaren: Methodology (supporting). M. Marinak: Software (supporting). P. Michel: Formal analysis (supporting). M. Millot: Data curation (supporting); Formal analysis (supporting). A. Nikroo: Resources (supporting). R. Nora: Formal analysis (supporting). A. Pak: Data curation (supporting); Formal analysis (supporting). P. K. Patel: Formal analysis (supporting). J. E. Ralph: Data curation (supporting). M. Ratledge: Resources (supporting). M. S. Rubery: Data curation (supporting); Formal analysis (supporting). N. W. Ruof: Data curation (supporting); Formal analysis (supporting). S. M. Sepke: Software (supporting). M. Stadermann: Resources (equal). D. J. Strozzi: Formal analysis (supporting). T. I. Suratwala: Resources (equal). R. Tommasini: Data curation (supporting); Formal analysis (supporting). R. Town: Resources (equal); Supervision (supporting). Brandon Woodworth: Project administration (equal). B. Van Wonterghem: Resources (equal); Supervision (supporting). C. Wild: Resources (equal).

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

Radiation hydrodynamics simulations (HYDRA)³⁸ were used to model the radiation drive created by the laser-hohlraum interaction as well as the physics of the capsule implosion. These simulations were performed in a two-step process: (1) integrated simulations of the hohlraum and capsule implosion which are benchmarked against experimental data from focused tuning experiments determine the spatially, temporally, and frequency resolved radiation drive surrounding the capsule implosion, and (2) the radiation drive is extracted and applied to higher resolution capsule-only kitchen sink simulations of the implosion to model engineering features with higher fidelity, such as material roughness of the capsule interfaces, a model for the capsule support tent, a model for the DT fill tube,^51,52 non-uniformities in ablator thickness, and DT fuel layer thickness together with low mode non-uniformities of the radiation drive (including mode one, two, and four); see Fig. 10 for a comparison of the simulations to the experimental data.

Simulations include detailed equations of state,^53,54 radiation particle and neutron transport models,^55,56 opacity models,⁵⁷ and electron-ion coupling.^58,59 The radiation drive is modeled with a flux-limited electron heat transport with a limiter of 0.15. An in-line cross beam energy transfer model was used with a saturation clamp on the electron density fluctuations of the ion acoustic wave (⁠ $δn/n$ = 0.002 in until the start of the rise and 0.008 for the rest of the laser pulse). Post-shot simulations use the measured input target conditions and as-delivered laser powers vs time for all beams which can vary from the requested input conditions.

The simulations were adjusted in a common way between experiments to match tuning data and then applied to simulate the DT layered experiments. These adjustments include artificial multipliers on the input laser powers to match the in-flight symmetry, in-flight capsule velocity, and shock velocities along two lines of sight (pole and equator). Shock timing data were obtained immediately prior to N221204 which improved the symmetry model for temporal variations in the radiation drive. Back-scattered laser light due to the interaction of the lasers with the hohlraum wall plasma was energetically low on (N210808 and N221204) and mostly due to Stimulated Brillouin Scattering (SBS)⁴⁹ of the inner beams early in peak laser power.