Progress toward hydro-equivalent ignition in OMEGA direct-drive DT-layered implosions

Inertial confinement fusion (ICF)^1–3 compresses and heats fuel composed of deuterium (D) and tritium (T) to extreme levels, allowing collisions between the fuel ions to have enough kinetic energy to quantum tunnel through their Coulomb barrier and fuse to produce a 14.1-MeV neutron and a 3.5-MeV $α$ particle. To make the fusion of these particles energy efficient, $α$ particles must collide with the fuel and deposit their energy.^4–6 If this is done so that the heating of the fuel exceeds its energy losses, the target is said to have ignited, leading to runaway energy production in the fuel.

Laser ICF achieves this by cryogenically freezing a layer of DT fuel within a low-Z shell and ablating the surface of the capsule with incident radiation. The ablation pressure accelerates the shell inward at high velocities (300–600 km/s). The central pressure within the capsule increases as the shell is driven inward, slowing the imploding capsule. Upon reaching stagnation, the kinetic energy of the shell is converted into internal energy, producing central temperatures in the low-density (30–100 g/cm³) hotspot of several kiloelectronvolts. When the shell's areal density (⁠ $ρR$⁠) is great enough, the $α$ particles from DT fusion reactions collide with the remaining fuel, depositing their energy and amplifying the fusion reaction rates—a process known as $α$ heating. As performance improves, $α$ heating will become the dominant source of input energy to the system, a state known as the burning-plasma regime. At this point, yield amplification from the $α$ particles rapidly increases absolute yields, making this an important milestone as implosions progress toward ignition. For the system to ignite, it is estimated that the product of the hotspot's temperature and areal density of the fuel must exceed $1.5 g keV/cm2$⁠.^2,7–9

Within laser-based ICF, there are two major approaches to irradiating the capsule and producing these implosions. The first, indirect drive,^5,7,10 mounts its capsules within a high-Z cylinder known as a hohlraum. Laser beams are focused onto the interior surface of the hohlraum, converting laser energy to x rays that fill the chamber's cavity, producing a radiation bath that ablates material off of the capsule surface. While this produces smooth irradiation of the target, it comes at the cost of efficiency. The conversion to x-ray energy, the filling of the hohlraum, and energy losses through the laser entrance holes significantly lower the coupling of laser energy to the fusion capsule.¹¹ Direct-drive ICF seeks to reclaim this efficiency by foregoing the hohlraum and directly illuminating the target surface with laser beams, resulting in about five times more energy coupling to the target. However, this approach faces its own set of challenges.¹² By using coherent laser light rather than incoherent x rays,¹³ implosions become more sensitive to low- and mid-mode perturbations seeded by beam pointing and the tiling pattern of multiple beams^14,15 as well as high-mode modulations from speckling patterns in single-beam spatial profiles.^16–18 Indirect- vs direct-drive ICF is then a trade-off between stability and efficiency. However, they both rely on the same underlying physics, and the recent ignition results in indirect drive^19–21 at the National Ignition Facility (NIF)²² have confirmed the physics of ignition and propagating burn underpinning all ICF research. As this research now turns from achieving ignition to maximizing gain—the energy produced by fusion reactions divided by the input laser energy—it is crucial to investigate paths such as direct drive to improve energy coupling and lower the required input laser energy.

This manuscript provides a summary of the cryogenic direct-drive ICF program performed on the OMEGA laser²³ at the University of Rochester's Laboratory for Laser Energetics, where implosions have now repeatably reached the scaled burning-plasma state.²⁴ Section II A introduces metrics used to evaluate the performance of implosions in ICF and how to scale these metrics between different laser energies.^25,26 Section II B then presents a framework to interpret implosion results through statistical modeling to explain the primary limiters of performance. A brief overview of how the scaled burning-plasma state was reached is provided in Sec. III, describing the implosion design adjustments made to maximize performance in integrated cryogenic implosions. Recent focused physics studies are then presented in Sec. IV, where research is now centered on maximizing the convergence of implosions to improve areal densities through single-variable studies. Many of these platforms are ongoing, and future research plans to enhance convergence and areal densities are discussed in Sec. V alongside other near- to mid-term research avenues. Finally, Sec. VI provides a summary of these results, progress, and future directions.

It should be noted that in addition to the scaled ignition state achieved when $χMJ>1$⁠, a second region of interest lies in $χMJ>0.8$⁠. This is the scaled burning-plasma state where, at full scale, α-particle heating would become the dominant source of energy input into the implosions.^6,10 As stated in Sec. I, this leads to a significant steepening of the slope of scaled yields and allows the projected gain to exceed unity around $χMJ≈0.92$ in direct drive, occurring prior to ignition due to the efficiency of the laser-to-target energy coupling. As will be shown in Sec. III, implosions on OMEGA are now able to consistently reach the scaled burning-plasma state and are nearing projected unity gain.²⁴ 

A great deal of work is focused on developing state-of-the-art, multidimensional models such as draco in 2D¹⁴ and aster-ifriit in 3D.^15,36,37 Research with these models is crucial to understanding the physics of, for instance, the evolution of target defects,³⁸ or the effects of beam polarization on cross-beam energy transfer (CBET) and hotspot morphology.^39,40 Machine-learning models have been developed to provide 3D hotspot reconstructions to better inform decisions between implosions during an experimental campaign.^41,42 These studies have played a large role in the direction of OMEGA's cryo program, and as new models are developed, this role is expected to continue increasing. However, for simplicity of communication, this manuscript will focus on a technique known as statistical modeling.^25,43 This technique provides a framework to understand the dependencies of cryogenic implosions on OMEGA,⁴⁴ and it is possible only because of the large number of implosions performed at this facility.

The statistical model (SM) is a nonlinear piecewise regression applied to the database of OMEGA cryogenic implosions to predict the yield-over-clean (YOC)—that is, the experimental yield divided by the 1D-predicted yield. This enables accurate yield predictions using 1D lilac simulations, accounting for multidimensional effects through statistics rather than 2D and 3D modeling.⁴⁴ As shown in Fig. 1, the statistical model accurately predicts the YOC of implosions with 8% variance around the experimentally measured YOC. This is accurate across a wide range of adiabats (2.5–6.0), convergence ratios (10–25), implosion velocities (250–600 km/s), and drive intensities (⁠ $0.4×1014 to 1.6×1015 W/cm2$⁠). However, understanding the performance of multidimensional parameters such as areal density is currently only possible through higher-dimensional simulations and continues to be a subject of ongoing research.¹⁵ Nonetheless, the success in predicting scalar parameters such as YOC makes statistical modeling a powerful tool for implosion design and a useful framework for interpreting experimental results. While the statistical model's values presented here are specific for OMEGA implosions, this technique and the identified yield dependencies are expected to be extendable to future spherical-direct-drive facilities.

$Ŝ=(αF/3)1.1/(IFAR/20)$ is the stability factor, where $αF$ is the minimum adiabat and $IFAR$ is the in-flight aspect ratio. It is derived both experimentally⁴⁵ and from the nonlinear Rayleigh–Taylor growth rates that amplify surface modulations,⁴⁶ providing a metric of how robust an implosion is to short-wavelength perturbations such as those from laser imprint and target defects.⁴⁷ Targets with higher IFARs have thinner shells in flight, making them more susceptible to perforation. Lower adiabats improve the compressibility of the shells, lowering the ablation velocity, $va∝αF0.6$⁠,³¹ and reducing its stabilizing effects on high-frequency perturbations amplified by the Rayleigh–Taylor instability. As a result, implosions with low stability factors are more susceptible to perforation by short-wavelength modulations, reducing their confinement and overall performance. The piecewise nature of this parameter can be understood as follows. The most unstable implosions have heuristically been found to occur at $Ŝ<0.8$⁠. In this regime, short-wavelength perturbations grow large enough to reach the inner surface of the ice layer, destroying confinement and resulting in degradation factors of $Ŝ0.85$⁠. Above this value, the perturbations are confined within the ice layer, weakening the piston action, but still confining the hotspot, causing the YOC to go as $Ŝ0.4$⁠. Finally, extremely stable implosions with $Ŝ>2.3$ either have low enough IFARs or high enough adiabats that the effects of these short-wavelength perturbations have been almost entirely negated, resulting in no degradation from this factor.

$Ĉ=Rt/RHS$ is the convergence ratio, where $Rt$ is the initial target radius and $RHS$ is the final hotspot radius. The more a capsule converges, the greater its sensitivity to low- and mid-mode perturbations.⁴³ 

$R̂=Rb/Rt$ is related to the beam overlap on target, where $Rb$ is the focused drive beam radius. The phase plates on OMEGA were designed to provide quasi-uniform illumination on an 860-μm-diam target. Due to beam tiling, though, some level of mode-10 perturbations are inevitable.⁴⁰ As this ratio is varied away from 0.87, where the hard-sphere beam-mode pattern is minimized,⁴³ the amplitude of those perturbations increases, resulting in a non-spherical hotspot. For $R̂>0.87$⁠, the degradation from beam overlap goes as $R̂2.3$⁠. As $R̂$ decreases below its ideal, fewer beams overlap on the target, increasing the target's sensitivity to random variations in the power of individual beams (power balance) and laser imprint. The beam-mode tiling pattern on the target rapidly worsens in this regime as well, further degrading performance as $R̂4.2$⁠.⁴³ 

$T̂=Tmax/Tmin$ is the apparent temperature asymmetry, where $Tmax$ and $Tmin$ are, respectively, the maximum and minimum apparent ion temperatures observed with the neutron time-of-flight (nTOF) detectors. This is the only parameter in the statistical model that is not predicted. Rather, it is a posterior correction largely induced by the undesired flow velocity—the bulk motion of the hotspot at stagnation. Such a mode-1 perturbation is caused by unintentional target offsets, beam power imbalance, beam mispointing, and/or the effect of light polarization on CBET.⁴⁰ Detectors along the axis of the flow will see a broadened DT energy peak, giving a greater inferred ion temperature, while detectors perpendicular to it will not see any broadening.^48,49 Because of this, the ratio of the maximum and minimum observed temperatures is a robust measurement of mode-1 asymmetries and flows when it exceeds the statistical variation level, $T̂≥1.14$⁠. Below this level, this correction is ignored as effects from flow velocities become masked by measurement uncertainties in the detectors. Ideal implosions have no flow velocities on stagnation to maximize the conversion of kinetic to internal energy. Any flows represent residual kinetic energy, reducing the overall performance of the implosion.⁵⁰ 

$Ĥ$ is the YOC predicted by 1D lilac simulations when $3He$ is introduced into the capsule vapor. $3He$ results from tritium decay, so the longer the time between when the capsules are filled and when they are imploded, the more $3He$ will exist in the vapor. It has been observed that longer fill times result in more degradation of yield than predicted by lilac. It remains unclear if this is due solely to the $3He$ concentration or if beta decay causes detrimental damage to the ablator.

To summarize, the statistical model predicts that maximum yield-over-clean is achieved by designing implosions with large stability factors (high adiabats and low IFARs), low convergence, targets with outer diameters near 860 μm, low flows, and short fill-to-shot times. However, in 1D, the best-performing implosions have high implosion velocities, low adiabats, high convergence, and high IFARs.²⁴ Overall performance is estimated by multiplying the 1D-predicted yield by the statistical-model-predicted YOC. Therefore, progress is made by balancing these various degradation mechanisms against 1D performance. Navigating this balance to maximize performance is the primary goal of the cryogenic Optimization Campaign.

Using the statistical model's framework alongside multidimensional numerical investigations, several adjustments have been made to implosion designs as part of the Optimization Campaign.²⁴ To begin, the filling cycle—the time from when a capsule is filled with fuel and when it is shot—was reduced from 10 to 3 days, improving the $Ĥ$ term in Eq. (3). Furthermore, as shown in Fig. 2(a), the diameter of the targets increased from 860 to ∼940 μm. This decreases the beam mode $R̂$⁠, which is shown in Eq. (3) to reduce overall stability due to mid-mode asymmetries. However, it also reduces the beam overlap on the target, reducing CBET to increase energy coupling and improve 1D performance. The targets also feature thinner ice layers and ablators. This increases the implosion velocity, further increasing 1D-predicted yields. On the other hand, the combination of larger diameters and thinner shells increases the IFARs, thereby lowering the stability factor $Ŝ$⁠, making these implosions more susceptible to high-mode asymmetries such as laser imprint.

To counteract the increased IFARs, the temporal profiles of the laser pulses have been optimized as well [Fig. 2(b)]. The picket and foot of the laser pulses have increased in power to raise the adiabat of the implosions. Additionally, a double-spike pulse shape is now used, where the main drive reaches maximum power at the beginning and end of the pulse with a reduction in power in the center. This maximizes the energy coupled at the start of the drive, when the shell radius is still large, and conduction zones are relatively small, and maximum compression to be realized at the end of the pulse. By lowering the power in the center, the shell moderately decompresses in flight, lowering the IFAR. This is also expected to reduce hot-electron preheat since hot electrons are only produced during the second spike, though this effect is not captured by statistical modeling. Combined with the increased adiabat set by the picket and foot, this restores the stability factor to provide robust implosions. Additionally, because the implosion velocities are faster, the pulse length is shortened to ∼1.9 ns. This increases the average power, further increasing energy coupling and implosion velocities.

Other experimental techniques have been used to improve implosion performance.⁵¹ Prior to performing cryogenic implosions, the laser beams are pointed to the target chamber center (TCC), and low-mode asymmetries are drastically reduced using precision repointing techniques.⁵² Nonetheless, residual kinetic energy in the hotspot (i.e., mode-1 asymmetry) is still observed in implosions. To address the degradation caused by these flows— $T̂$ in Eq. (3)—targets are now offset from TCC. The distance and direction of this offset are determined by the nTOF-inferred flow velocities during an experiment.⁴⁹ This slightly adjusts the laser intensity profile on the target surface and has been shown to significantly improve flow velocities, symmetry, and overall performance.

Finally, the ablator is now doped with silicon in its outermost layer. This has been shown both numerically and experimentally to boost the absorption of laser energy while suppressing parametric phenomena such as the two-plasmon-decay instability. These instabilities would otherwise generate hot electrons that preheat the target, increasing the target's adiabat beyond its design specification and limiting implosion performance.

These techniques have significantly improved both the hydro-scaled Lawson parameters and fusion yields of cryogenic implosions on OMEGA. Figure 3 shows these metrics extrapolated to 2.15 MJ of driver energy for all performance-focused cryogenic implosions. Applying the target and laser pulse improvements guided by the statistical model more than doubled the extrapolated fusion yield at similar extrapolated Lawson parameters by improving the 3D symmetry and robustness of implosions. Ongoing optimizations brought these implosions closer to the scaled burning-plasma state.⁹ Once silicon dopants were added to the ablators, this trend continued further, and the first implosions with $χMJ>0.8$ were recorded in 2022.²⁴ Recently, several shots have reached the scaled burning-plasma state, achieving a record $χMJ=0.89±0.05$ and an extrapolated fusion yield of $1.5±0.6 MJ$⁠. Much of the improvement to recent implosions is due to a better understanding and control of mode-1 perturbations and increased areal densities through the methods discussed in Sec. IV. Interestingly, it should be noted that several of the points shown in Fig. 3 did not come directly from the Optimization Campaign, but instead came from other cryogenic implosions on longer, 10-day fill cycles. These implosions were designed to explore specific aspects of implosions and are the subject of the following section. Because these implosions reached the scaled burning-plasma state, where a small change to $χMJ$ can lead to a large increase in extrapolated yield, correcting for fuel age predicts large increases to extrapolated performance, resulting in projected gains above unity. These implosions are discussed in Sec. IV C.

Only about a third of the cryogenic experiments performed on OMEGA is part of the Optimization Campaign. The remainder is largely designed to investigate specific aspects of implosions to gain a better understanding of the underlying physics or to explore routes to increased performance. In 2023, many of these experiments focused on exploring methods to produce greater convergence and areal density. Several of these areas remain under active investigation, with new experiments and analyses planned in 2024, and their details will be published in future manuscripts once firm conclusions can be made.

Increasing the confinement of ICF implosions is necessary to achieve high-gain fusion.²⁷ This confinement comes by increasing the areal densities of the implosions, which can be produced through greater convergence. One route to achieving greater convergence is lowering the temperature of the capsule below the DT triple point (∼19 K) by a few degrees Kelvin just before the laser drive—a process known as “subcooling.” Doing so reduces the amount of ice that sublimates into a vapor inside the capsule, lowering the vapor region's density. With lower initial densities, additional compression is required to counteract the drive pressure and reach stagnation.

One-dimensional simulations were performed in lilac, reducing the DT vapor density as a function of subcooling temperature, resulting in greater convergence ratios and areal densities while roughly maintaining yields [Fig. 4(a)]. In these simulations, the areal density increased roughly proportionally to the convergence ratio. Moreover, this was achieved without adjusting the adiabat of the implosions, maintaining the stability factor, $Ŝ$ in Eq. (3). On the other hand, as seen in that same equation, the $Ĉ$ term indicates that the increased convergence is expected to reduce the YOC by exacerbating low- and mid-mode perturbations. Nonetheless, $χMJ$ is more dependent on areal density than yield, and these changes are still expected to improve overall performance.

To test this hypothesis, a series of implosions were performed varying the subcooling temperature. The targets used in these implosions were standard capsules, 931 ± 5 μm in diameter with 7.5 ± 0.1-μm total wall thicknesses, the outer 5.5 μm of which was doped with Si. As shown in Fig. 4(b), the inferred areal densities increased to a point, and the yields decreased approximately as predicted. However, the improvements to areal density were somewhat less than lilac predictions, resulting in only modest improvements to $χMJ$⁠. This is because the inferred flow velocities were all over 100 km/s, limiting the performance of these implosions. One current hypothesis is that the increased convergence increases the growth of mode-1 perturbations, making the targets more sensitive to positioning within the chamber. Using the statistical model [Eq. (3)], if these flows can be corrected in the future, subcooling at −3 K is expected to produce $χMJ≈0.90±0.05$⁠. An enhanced understanding of flow measurements and offset calculations is expected to reduce these flows in upcoming experiments.

A second route to greater convergence and performance is lowering the adiabat of the implosions. Doing so increases the shell density during the acceleration phase, reducing the thickness of the shell and enabling greater compression. As discussed in Sec. II B, this also decreases the stability factor $Ŝ$ and is expected to reduce the YOC as short-wavelength features grow to detrimental levels. Low adiabats are, therefore, expected to be more sensitive to laser imprint.

To test the implosions' sensitivity to imprint at different adiabats, a series of experiments were performed imploding 8-μm-thick, 980-μm-diam. CD shells filled with 42 μm of DT ice.⁵³ These capsules were imploded with 28.5 kJ of UV energy in two pulse shapes: one setting an expected adiabat of 3.5 and the other an adiabat of 5.0. The smoothing-by-spectral-dispersion (SSD) bandwidth fraction was progressively reduced between implosions with each pulse shape. This reduced the smoothing of laser speckle, with the illumination nonuniformity going as $σrms≃20.3(%)/47.5×SSD_fraction+1$⁠, increasing the relative imprint levels.⁵³ 

The yield and areal density measurements, normalized to the full-SSD-bandwidth measurements for each pulse shape, are plotted in Figs. 3 and 4 of Ref. 53 for both adiabats as a function of SSD bandwidth fraction. High-adiabat implosions were robust to SSD fraction with both yield and areal density degrading only when the bandwidth fraction fell below 50%. Low-adiabat implosions, on the other hand, saw immediate degradation as the SSD bandwidth fraction was lowered. This indicates that additional imprint mitigation is required before moving to these lower-adiabat, higher-performance implosion designs.^54–56 

While the statistical model captures many design parameters, it is blind to systematic perturbations from sources such as mounting hardware. It is, therefore, important to examine the impact of these features on implosion performance.

To this end, two experimental campaigns are underway to determine the effects of mounting hardware. Capsules of OMEGA are inserted into the target chamber by gluing the targets to thin stalks that are then held by the Target Positioning System. These two campaigns vary both the size of the glue spot attaching the capsule to the stalk and the diameter of the stalk itself.

The first campaign varied the size of the glue spot from the nominal 26-μm diameter to 70 and 122 μm. The rest of the implosion design was kept constant, using 940-μm-OD targets with 1.9 μm of CD inner- and 5.5-μm CH-Si(6%) outer-layer ablators with 42 μm of DT ice. These targets were driven with $28.1±0.2 kJ$ of laser energy with a standard double-spike pulse shape (SD1505Sv003 as used on top-performing shot 104949). The yield and areal densities were measured and inferred for each shot and normalized by the nominal case. As shown in Fig. 5, the 70-μm glue spots had nearly identical performance as the nominal implosion. Increasing further to 122 μm showed strong degradation in both performance metrics. However, it was suspected that the ice-layer quality was poor on this latter implosion, which could explain this drop in performance. Nonetheless, the nearly identical performance between the nominal 26- and the 70-μm glue spots suggests that the glue spot is not a significant limiting factor in these implosions.

The second campaign, varying the stalk diameter, is ongoing, and preliminary results are not yet conclusive. The target and pulse parameters were identical to the glue-spot scan, and the stalk diameter was reduced on three implosions from the nominal 14-μm diameter to 10 μm. Large flow velocities (⁠ $148±12 km/s$⁠) were observed during the reference implosion using a 14-μm stalk upon stagnation. In general, flows more than 100 km/s have been shown to limit implosion performance, relating to the $T̂$ term in Eq. (3), which makes direct comparisons to small-stalk implosions in this campaign so far unreliable. However, one of the 10-μm implosions, shot 109675, produced a record $χMJ=0.89±0.05$⁠, exceeding the previous record of $χMJ=0.85±0.05$ primarily through an increased areal density of $177±15 mg/cm2$⁠. Additionally, this was on a long, 11-day fill cycle, whereas shot 104949 benefited from a short, 4-day fill cycle. Using the statistical model to correct for fuel age increases the $χMJ$ still further to approximately 0.92 and extrapolated fusion gain above unity. Therefore, while the comparison to other shots in this campaign is not conclusive, preliminary data do align with the hypothesis that reducing the stalk diameter will improve overall performance. However, this was an extremely symmetric implosion with low flow velocities, and its symmetry could also have been the cause of the improved performance. The fact that such high performance was achieved under nonideal conditions supports continuing the investigation into 10-μm stalks further to determine if the stalk or the implosion symmetry had the greatest effect.

In the absence of laser-plasma instabilities (LPIs), it is desirable to drive ICF capsules at greater intensities. Greater intensities produce greater ablation pressures, and because the capsule has maximum surface area early, increasing the intensity at the beginning of the drive increases the acceleration and implosion velocity of the shell. However, the intensity is limited both by LPI, which can lead to hot-electron preheat, and by the maximum power achievable with OMEGA's laser amplifiers. As discussed in Sec. III, silicon dopants reduce LPI, increasing the intensity threshold for preheat to occur and overcoming the first challenge to fielding greater intensities. For the latter challenge, to increase the beam intensity when power is limited, the diameter of the targets must be reduced so that power is deposited over a smaller area. To maintain the $Rb/Rt$ ratio and effectively couple the laser energy to the smaller capsules, new phase plates were developed, producing spots with diameters of approximately 650 μm instead of the full-scale 850 μm typically fielded. Experiments using the combination of smaller targets with smaller phase plates are referred to as “subscale.”

A series of subscale experiments were performed with increased intensity to assess their potential for increased implosion quality and fusion performance. Capsules ∼770 μm in diameter with 6.0- to 7.0-μm-thick Si-doped ablators were filled with ∼36 μm of DT ice. These were driven with pulse shapes based on a hydrodynamic scaling of a previous full-scale implosion (Fig. 6) but with up to $∼50%$ increased intensity on the drive and ∼23 kJ of UV energy. The data for these implosions are still being analyzed, but preliminary analysis suggests that, with little to no optimization, these experiments met or exceeded prior hydro-scaled performance achieved with larger-scale implosions. Further details will be provided in a future publication, but the results have motivated further investigations of these high-intensity experiments.

In the near term, several experiments are planned to continue pursuing increased convergence and areal densities in cryogenic, direct-drive ICF implosions. These include continuing efforts in the subscale, 10-μm-diam stalk, and subcooling platforms as well as more novel designs such as shock-augmented ignition.⁵⁷ In the medium to long term, though, perhaps the greatest limiting factor of current implosions on OMEGA is the adiabat. As stated in Sec. IV B, the minimum adiabat in a high-performance OMEGA implosion is currently around 5. Going below this level sees a rapid decrease in performance due to laser imprint as the stability factor $Ŝ$ is decreased. Thus, new methods to mitigate the effects of laser imprint and improve $Ŝ$ are necessary to reduce the adiabat and see significant performance improvement. To do so, innovations in target development and laser technology are required.

One method to mitigate laser imprint is to coat the exterior of a capsule with a moderate 40- to 80-mg/cm³ foam. By doing so, the density at the ablation front is reduced, resulting in greater ablation velocities and density scale lengths, both of which suppress the Rayleigh–Taylor instability.^55,58 This is the instability that amplifies laser imprint, so by limiting its growth, the effects of laser imprint are lessened. This scheme has been proven numerically to significantly improve the robustness of shells in flight.⁵⁵ The challenge is target fabrication. The foam must be produced in such a way that it does not seed its modulations either due to large filament sizes or low-mode perturbations from large-wavelength nonuniformities. To address this challenge, a two-photon-polymerization (2PP) printing process is under development to enable the creation of designed foams with filaments down to 120–200 nm in diameter. Continuing to develop these capabilities is a key component of future target-based solutions to implosion stability. As these capabilities grow, experiments are planned to test the material properties of the resulting foams, the effects of foam microstructure on areal density perturbation growth, and their robustness against experimental operations such as the filling process.

In addition to lessening the growth of modulations, laser imprint itself can be reduced through target design by taking inspiration from indirect drive. As stated in the introduction, by using x rays to implode the target, indirect drive avoids the complications of laser imprint, but this comes at the cost of efficiency. This is because the incoherence of the x rays produces even illumination, driving a smooth shock into the target. However, this smoothness is only required at early times. After a few hundred picoseconds after the initial shock, a conduction zone forms that exponentially reduces pressure perturbations at the ablation front, drastically reducing laser imprint.¹² Hybrid direct-drive targets combine indirect and direct drive by creating the first shock using x rays produced as a picket hits a thin, high-Z-coated membrane. After the conduction zone forms, and the membrane has dissipated away, beams are then able to directly drive the preconditioned target surface.

This scheme has shown to be effective in planar experiments on OMEGA EP.⁵⁶ Work is now underway to bring these targets to a spherical geometry, where the challenge is supporting the high-Z membrane around the internal capsule. Current designs are investigating the use of low-density (⁠ $∼5 mg/cm3$⁠) foams to support the membrane as well as externally mounted curved membranes to be driven in polar-direct-drive geometries.

Finally, one method to improve the overall stability of implosions is to reduce the IFAR. This requires producing thicker shells in flight, which typically requires poor compression. The wetted foam concept seeks to improve upon this by replacing the inner ice layer of a cryogenic capsule with a low-density foam that is wetted with liquid DT.⁵⁹ Because this layer has a lower density than DT ice, it must be thicker to maintain the same amount of fuel, thereby resulting in a reduced IFAR. Additionally, because the liquid state of DT spans a relatively large temperature range, this also gives greater control over the vapor density of the capsule interior to allow convergence to be adjusted as needed. The same 2PP printing technology as discussed in Sec. V A can be used to produce foams on the inside of the capsules. In addition to continuing to refine the 2PP printing process, this design will be advanced by designing new experimental systems to wet the foams.

In addition to target designs, new laser technology is expected to significantly reduce laser imprint and LPI via broadband laser illumination. By broadening the spectrum of the laser illumination so that $Δω/ω>1%$⁠, where $ω$ is the photon frequency, the resonant drive of LPI is disrupted. This has been shown theoretically and numerically to increase the intensity threshold for hot-electron generation by a factor of 3⁶⁰ while mitigating CBET,⁶¹ significantly increasing the energy coupling of the laser to target up to 90% (Fig. 7).⁶² To validate this bandwidth modeling, the fourth-generation laser for ultra-broadband experiments (FLUX)^63,64 is under construction. When complete, it will produce $Δω/ω>1%$ with a central wavelength around 351 nm, allowing experiments to be performed to directly measure these expected benefits of bandwidth. The outcomes of broadband experiments on this system will provide a step change to implosion performance and will be central to the design of future implosion facilities.

In the past few years, implosions on OMEGA have improved significantly. DT yields over $1014$ are now regularly achieved with extrapolated fusion yields increasing over an order of magnitude from the 50-Gbar campaign in 2016.⁹ The scaled burning-plasma state has now repeatedly been achieved in cryogenic implosions with a maximum $χMJ=0.89±0.05$ and extrapolated fusion yields of $1.5±0.6 MJ$ when scaled to 2.15 MJ of driver energy. These studies now seek to improve the convergence of implosions to maximize areal densities and $χMJ$⁠. While scans varying the SSD smoothing indicate that this is not easily achieved by lowering the adiabat of the implosions due to laser imprint, other techniques such as rapid subcooling are being explored to lower the vapor density and maximize convergence. Using smaller laser focal spots with new phase plates and proportionally smaller targets, the intensities delivered on the target can be increased to improve overall performance. These routes will continue to be explored and expanded upon in the Optimization Campaign and accompanying focused studies in the near term alongside advanced target designs, such as wetted foams, foam overcoats, and hybrid-drive targets. These target innovations will be critical in the OMEGA cryogenic implosion program to mitigate laser imprint with current laser technology. This is crucial to field lower-adiabat designs and significantly improves the confinement, compression, and areal densities of implosions. In parallel, research continues into the effects of increased laser bandwidth and its expected mitigation of laser-plasma instabilities and increased energy coupling. Combined with theoretical and numerical developments and the predictive capabilities of statistical modeling, rapid progress is expected to soon reach scaled gain and ignition on the OMEGA laser. Once achieved, these results will be used to design a future direct-drive facility capable of achieving high-gain thermonuclear burn in the laboratory.

This material is based upon work supported by the Department of Energy (National Nuclear Security Administration) University of Rochester “National Inertial Confinement Fusion Program” under Award No. DE-NA0004144. It is also funded by the DOE Office of FES under Award No. DE-SC0022132 and the National Nuclear Security Administration under Award No. DE-NA0003868. Funding for the targets utilized in this study was provided by General Atomics and funded through the NNSA Contract No. 89233119CNA000063. This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes 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 any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

The authors have no conflicts to disclose.

L. Ceurvorst: Investigation (equal); Writing – original draft (equal). R. Betti: Conceptualization (equal); Formal analysis (equal); Supervision (equal); Writing – review & editing (equal). V. Gopalaswamy: Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). A. Lees: Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). J. P. Knauer: Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). M. J. Rosenberg: Investigation (equal); Supervision (equal); Writing – review & editing (equal). D. Patel: Formal analysis (equal); Writing – review & editing (equal). R. Ejaz: Investigation (equal); Writing – review & editing (equal). C. A. Williams: Investigation (equal); Writing – review & editing (equal). K. M. Woo: Investigation (equal); Writing – review & editing (equal). P. S. Farmakis: Investigation (equal); Writing – review & editing (equal). D. Cao: Investigation (equal); Writing – review & editing (equal). C. A. Thomas: Investigation (equal); Writing – review & editing (equal). I. V. Igumenshchev: Investigation (equal); Writing – review & editing (equal). K. S. Anderson: Investigation (equal); Writing – review & editing (equal). T. J. B. Collins: Investigation (equal); Supervision (equal); Writing – review & editing (equal). R. Epstein: Investigation (equal); Writing – review & editing (equal). A. A. Solodov: Investigation (equal); Writing – review & editing (equal). C. J. Forrest: Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). C. Stoeckl: Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). R. C. Shah: Investigation (equal); Writing – review & editing (equal). V. Yu Glebov: Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). H. McClow: Formal analysis (equal); Writing – review & editing (equal). V. N. Goncharov: Investigation (equal); Supervision (equal); Writing – review & editing (equal). R. K. Follett: Investigation (equal); Writing – review & editing (equal). D. Turnbull: Investigation (equal); Writing – review & editing (equal). K. Churnetski: Investigation (equal); Writing – review & editing (equal). D. H. Froula: Investigation (equal); Supervision (equal); Writing – review & editing (equal). S. P. Regan: Investigation (equal); Supervision (equal); Writing – review & editing (equal). R. T. Janezic: Investigation (equal); Writing – review & editing (equal). C. Fella: Investigation (equal). M. W. Koch: Investigation (equal). W. T. Shmayda: Investigation (equal). M. J. Bonino: Investigation (equal). D. R. Harding: Investigation (equal); Supervision (equal). S. Sampat: Investigation (equal). K. A. Bauer: Investigation (equal). S. F. B. Morse: Project administration (equal); Supervision (equal). M. Gatu Johnson: Investigation (equal). C. Wink: Investigation (equal). R. D. Petrasso: Investigation (equal). C. K. Li: Investigation (equal). J. A. Fenje: Investigation (equal); Supervision (equal). C. Shuldberg: Investigation (equal). J. Murray: Investigation (equal). D. Guzman: Investigation (equal). B. Serrato: Investigation (equal). M. Farrell: Investigation (equal).

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