Mixing in ICF implosions on the National Ignition Facility caused by the fill-tube

Inertial confinement fusion experiments at the National Ignition Facility¹ (NIF) compress capsules filled with cryogenic fuel to thermonuclear conditions. These capsules are filled in situ with deuterium–tritium (DT) fuel through a small fill-tube (FT) that is attached to the capsule. As a capsule implodes, the fill-tube can induce a perturbation that degrades capsule performance.

The fill-tube has been a concern since the beginning of experiments at the NIF. Initial modeling work suggested that it would induce a mass perturbation and inject ∼30 ng of ablator material into the interior,^2,3 but not inhibit ignition in the Be or CH capsules under consideration at the time.⁴ Dedicated fill-tube experiments on the Z-machine measured the mass perturbation at a convergence ratio of 1.5–2.5, confirming the simulation predictions.⁵ In implosions using CH ablators and a low-foot pulse, bright features were observed in the x-ray emission and seem to correlate with the fill-tube location.⁶ Simulations found that the fill-tube was one of the top perturbation sources in those implosions,⁷ but secondary to the significant degradation caused by the capsule-support “tent” that holds the capsule inside the hohlraum.^8–11 

In implosions using high density carbon (HDC) ablators, the x-ray emission shows a more prominent fill tube feature than seen previously. This is likely due to several reasons: (1) the fill-tube perturbation is worse with HDC than with other ablators,¹² (2) the tungsten (W) dopant in HDC is more radiative than other dopants used previously, (3) diagnostics have advanced to give a clearer time-dependent view of the hot-spot evolution, and (4) problems that were present with other ablators were masking the signature of the fill-tube and have been improved with HDC, which has better symmetry control¹³ and less damage from the tent.

The fill-tube consists of a borosilicate glass tube that is inserted part-way into a hole that is laser-drilled through the wall of the ablator. These tubes have typically been 10 μm in diameter with a 2 μm wall thickness.^14,15 Beginning in 2017, HDC experiments have occasionally used fill-tubes that are 5 μm in diameter to reduce the perturbation. These smaller fill-tube experiments have demonstrated increased fusion performance.^16,17

A radiograph of the capsule-fill-tube assembly is shown in Fig. 1 for a 10 μm diameter fill-tube. For 10 μm fill-tubes, the tube is typically inserted 40–55 μm beyond the outer radius. The hole in the capsule has a diameter of 7–10 μm on the inside and a diameter of 20 μm on the outside of the capsule. Glue fills some of the void between the tube and the wall of the hole and extends beyond the outer capsule radius, wicking up the fill-tube and extending ∼16 μm outward from the fill-tube edge. In DT-ice layered implosions, the interior of the fill-tube also contains DT-ice. Compared to the density of the HDC (3.5 g/cm³), the lower density of the ice (0.25 g/cm³), fill-tube (2.3 g/cm³), and glue (1.2 g/cm³) creates a lower column density (⁠$ρR=∫ρ dr$⁠) region that imposes a significant perturbation on the capsule.

This paper reviews the perturbation that the fill-tube imposes on the implosion, focusing on the simulated impact, with comparisons to data when available. Section II details the dynamics of the early stage of the implosion. The ablation of the fill-tube during the first few nanoseconds and the shock that accelerates down the through-hole can allow a hole to open in the ablator and ablator material to mix into the interior before the implosion reaches its peak velocity. The final stage, when the implosion has reached its maximum compression, is discussed in Sec. III. During peak compression, the fuel has formed a central hot-spot in which the ablator mix interacts with and can degrade its conditions. Section IV shows how the calculated degradation varies as the geometry of the fill-tube is changed. Section V describes how the fill-tube perturbation is included in an integrated implosion where many other degradation sources are present. In Sec. VI, a few options for reducing the fill-tube perturbation are discussed. Final concluding remarks are provided in Sec. VII.

Simulations of the fill-tube suggest that much of the damage to the implosion is caused during the early stage, when the capsule is accelerating toward its final compressed state. The fill-tube can impart a significant perturbation that injects the ablator material into the interior during this stage. The simulations use the radiation hydrodynamics code HYDRA¹⁸ and incorporate as much information about the metrology of the fill-tube as possible, including the tapered through-hole, the fill-tube dimensions and insertion depth, and the glue between the hole and tube. Figure 2(a) shows the initial condition of a 10 μm diameter fill-tube on an HDC capsule with a DT ice layer. This simulation is performed with polar discrete ordinate radiation transport, an angular resolution of 0.015°/zone, and radial resolution of 50 nm near the fill-tube (further refinement has demonstrated convergence). Because of these resolution requirements, these simulations need to be performed in two-dimensions on an axially symmetric grid. Recent work has demonstrated the ability to use adaptive mesh refinement to simulate the fill-tube in 3D.¹⁹ 

As the radiation reaches the capsule, the fill-tube ablates outward and collapses on-axis [Fig. 2(b) at 0.5 ns]. Later in time (1.5 ns), the ablation of the HDC is pushing much of the fill-tube material away from the capsule. At 1.5 ns, the shock wave is beginning to accelerate faster down the low-density hole. By 2.4 ns [Fig. 2(d)], the jet of material has traveled down the hole and is breaking out into the DT ice, well in front of the main shock wave in the ablator. This jet of material initially consists of glass and glue from the fill-tube, but as the perturbation on the ablation front grows larger, eventually the ablator material is swept inward. By the time the shell begins accelerating rapidly inward, 4.6 ns, the hole is ∼20 μm wide. As the capsule converges further, ablation pressure continues to push the ablator material through the hole, into the interior of the shell. Figures 2(g)–2(i) show that the material getting through comes from the ablation front, which is un-doped HDC early on but is from the W-doped layer by 5.6 ns [Fig. 2(h)]. By 6.8 ns, approximately 25% of the injected ablator mass comes from the undoped layer and 75% from the W-doped layer.

Convergence effects cause the hole to close by convergence ratio ∼2 [Fig. 2(i)] and the ablator material stops mixing into the inside of the capsule. A high $ρR$ bump forms on axis outside the pocket of mixed-material. By the time the fuel has reached its maximum velocity, 7.4 ns, the returning shock wave is entering the dense fuel and has begun to compress and stir the pocket of mixed material.

In the scenario above, a hole appeared in the shell very early on (at ∼4 ns), allowing the material to stream into the interior. As the fill-tube has been improved by reducing its diameter to 5 μm, the early time hole is not present, but one develops later in time. Figure 3 shows images from a larger-scale implosion with a 5 μm fill-tube. At 5.5 ns, the fill-tube hole has closed with a small amount of ablator, glass, and glue in the interior, but a perturbation is present on the ablation front. As the implosion continues, this perturbation is amplified by the Rayleigh–Taylor instability and eventually punches a hole through the shell. This type of scenario ultimately injects less material than when the hole is open early on.

To evaluate how well these dynamics are modeled, focused experiments were conducted to measure the $ρR$ perturbation on the shell during the acceleration stage of the implosion. These hydro-growth radiography (HGR) experiments attach the capsule to a gold cone and back-light the shell in-flight to record multiple 2D x-ray images using a gated x-ray detector (GXD).^20–25 In these experiments, a dummy fill-tube is attached in the center of the line-of-sight, allowing its hydrodynamic imprint to be measured.

Figure 4 shows the experimental result²⁶ in (b) from the 10 μm diameter fill-tube at a convergence ratio of 2.1. The radiograph shows a high $ρR$ bump near the center of the image (the original fill-tube location), but surrounding the bump in the experiment is a “spoke” pattern. It is believed that this is caused by the shadow cast by the fill-tube from the x-ray emission of spots on the hohlraum wall of individual laser quads. In these shadows, the differentials in radiation flux will alter the ablation amount, which will imprint a perturbation at early time that is amplified by Rayleigh–Taylor growth on the ablation front. The 2D axisymmetric simulation cannot capture these shadow features, but it does reproduce the central high $ρR$ bump [Fig. 4(a)]. Lineouts of the experimental and simulated images are shown in Fig. 4(c). The magnitude of the central $ρR$ feature is similar between the experiment and simulation. Recall from Fig. 2(i) that ablator mix is already trapped inside the shell at this time, so it is not clear if the additional perturbation caused by the shadow features will introduce additional mix into the hot-spot. Three dimensional simulations include a model of this “spoke” feature, but these spokes do not appear to alter the degradation over the 2D dynamics.²⁷ 

A radiography experiment also measured the reduced impact caused by a 5 μm diameter fill-tube.^28,29 Figure 4(d) shows lineouts from the experiment and from the simulation. The experiment showed that the modulation was significantly reduced and was only faintly noticeable above the noise. The simulation predicts that a higher $ρR$ modulation is still present on-axis, but should be at the level of the noise in the experiment. The experiment also observes a feature later in time, at convergence ratio ∼3, which may be a hole opening in the shell. This may be similar to what is simulated in Fig. 3(c), but further experiments with better resolution are needed to make a conclusion.

These radiography experiments are a useful check against the simulations, but to better constrain the injected mix-mass dynamics, future experiments should focus on the time when the hole opens and closes. Simulations find that the radiograph can look similar at convergence ratio ∼2 between these simulations and simulations of improved designs with reduced injected mix (like the larger glue filet discussed in Sec. VI). A radiograph 1 ns earlier, at the time of Fig. 2(h), is more sensitive to injected mix and can show the presence or absence of a hole. These radiography experiments are currently limited to one high-quality image per experiment. The recently developed fast-gated single line-of-sight (SLOS) camera,³⁰ paired with the <10 μm resolution of the crystal backligher imager,³¹ may enable a high-quality sequence of four images of the fill-tube hole opening and closing.

In the final stage of the implosion, the jet of ablator material mixes in the hot-spot and radiatively cools it. Figure 5 shows density and ion temperature near bang time (the time of peak neutron production) from the 10 μm fill-tube simulation. Approximately 150 ps before bang time [Fig. 5(a)], the capsule is still compressing and the mixed material has cooled only a small region near the edge of the hot spot. As the fuel slows down near bang time [Fig. 5(b)], the mixed region continues inward, sending a cool, dense jet into the center of the hot-spot. In these simulations, the hot-spot reaches a temperature near 6 keV and density near 50 g/cc, but the jet is closer to 1 keV and 200 g/cc.

The jet of mixed material is cooled to these low temperatures by radiative losses. This effect is distinctly visible in x-ray images. Prior to bang-time, the emission from the fill-tube is the brightest feature, glowing on the edge of the hot-spot. Figure 6 shows x-ray emission images for a DT-layered implosion (N161023) compared to a fill-tube simulation. Approximately 150 ps before bang-time [Figs. 6(a) and 6(b)], the higher Z material at the edge of the hot-spot injected by the fill-tube dominates the bremsstrahlung emission (⁠$∝Z3$⁠) of the DT plasma and the localized fill-tube feature exhibits a similar spatial extent between the simulation and experiment. By bang time, the fill-tube emission remains the brightest feature in the simulation as it travels into the center of the hot-spot, but the distinction between the fill-tube and surrounding hot-spot is not as clear in the experiment. This may suggest that three-dimensionality of the experiment stirs the mixed material throughout the hot-spot more than in the 2D simulation.

The conditions that the jet arrives at (∼1 keV and 200 g/cc) can be understood by considering an energy balance. The jet will cool from radiative losses caused by the high Z ablator material contained within. As the jet cools, the density will increase to achieve pressure equilibrium with the surrounding hot-spot. The cooler jet will also conduct energy away from the warmer DT hot-spot. These two competing mechanisms, warming of the jet by conduction and cooling through radiation, will govern the energy balance of the jet and the losses from the hot spot. This balance can be written as

where the first term on the right is the conduction heating of the jet (and losses from the hot spot) and the last term is radiative losses from bremsstrahlung emission. The conduction term depends on the surface area of the jet, while the radiative term depends on its volume. Since a large/dense sphere can be optically thick, it stops the interior radiation from escaping, only the volume near the surface, where the optical depth $≤1$ is included in the radiation loss term. The bremsstrahlung optical depth is³² 

Given a fixed mass of material in the jet, each of these terms can be written as a function of temperature.

The behavior of the conductive heating and radiative loss terms are shown in Fig. 7. This assumes that the jet is a 100 ng stationary sphere embedded in the hot-spot, it remains isobaric, the density behaves like an ideal gas, and the conduction length is set to 1/10 the radius of the jet. If the jet material begins at the hot-spot temperature (5 keV in this analysis), the conduction term is zero and bremsstrahlung losses will cool the jet. This cooling rate slows near 3–4 keV as conduction adds heat to the jet, but ultimately it continues to cool. As the jet cools further, it shrinks, decreasing the conduction term. Near 1–1.5 keV, the jet becomes sufficiently dense that the optical depth reduces the radiative term. Near 1.5 keV the conduction heating of the jet is balanced with the radiative emission and the jet material reaches a steady state temperature with a density near 150 g/cm³. The conditions arrived at using this simple model are in fair agreement with the conditions observed in Fig. 5(b). At this condition, there is a steady loss of energy from the hot-spot of ∼20 J/ns/ng, where conduction heats the jet and then that energy is lost through radiation.

The form of these curves is similar for smaller masses of jet material, shown in Fig. 7(b) for 20 ng, but the radiative curve will reduce faster than the conduction curve since it is proportional to volume rather than area. Therefore, it is possible for the equilibrium to occur when the conduction is ramping up near 4 keV. At this point, the energy loss from the hot spot (the conduction term) is larger, at 120 J/ns/ng; thus, smaller chunks of mass are more damaging (per unit mass) as they equilibrate at higher temperature. This model is meant to be illustrative. A more quantitative treatment would require considering line radiation and the transient/spatial dynamics of conduction, with cold DT surrounding the cold jet.

Given the above model, if turbulent mixing were present, the jet could break into many small pieces and be more radiative. A simple estimate of the Reynolds numbers, however, suggests that the hot-spot is viscous.^33,34 The DT in the hot-spot is at conditions of ∼5 keV and ∼50 g/cc, which has a viscosity of ∼200 cm²/s. The jet is traveling through the hot spot at ∼300 km/s and has a diameter of ∼16 μm. These scales produce a Reynolds number of 240, well under the turbulent mixing threshold of 20 000.^35,36

Diffusive mixing, however, may be occurring in the hot spot. These calculations did not include this effect, but we can get an estimate of its magnitude with a test problem using the Miranda code.³⁷ In this problem, a sphere of ablator is in pressure equilibrium inside a DT hot-spot. The ablator is C with 0.23%Lu (the highest Z material available in these calculations) at 1.4 keV and 250 g/cc, while the hot-spot is 5 keV and 50 g/cc. This problem did not have conduction or radiation included, so without diffusive effects, these materials would remain stationary and in isolation. Figure 8(a) shows that over 200 ps, ablator material diffuses several micrometers from its initial position. This distance is not large enough to pollute a large fraction of the hot-spot, but will change the temperature distribution of the Lu atoms, with some reaching 4–4.5 keV. The emission spectrum caused by this temperature difference will be noticeably different. Figure 8(b) shows the total emissivity of the Lu atoms. The higher temperature Lu atoms increase the L-shell emission near 10–12 keV.

Spectroscopic measurements of W-emission suggest that a diffusive scenario like the one above may be occurring. These measurements see L-shell emission lines consistent with W temperature near 4–5.5 keV, hotter than in calculations without diffusion. As illustrated by the model in Fig. 8, the emission >10 keV is very sensitive to small amounts of hot W atoms, so an emission-weighted temperature measurement, like that arrived at by spectroscopy, will find a higher temperature than a mass-weighted temperature value.

Unlike Miranda, HYDRA does not model plasma diffusivity effects. As a simple test of the possible effects of diffusion in the detailed HYDRA simulation, interface reconstruction can be switched off in HYDRA. This allows the code to act as an implicit-Large Eddy Simulation (ILES)³⁸ and the species concentrations will numerically diffuse as they are advected with the flow. This is only an exploratory test and actually performing fill-tube calculations with explicit species diffusion is a work-in-progress.

Figure 9 shows the result of turning interface reconstruction off shortly before peak velocity. The tungsten temperature and density from calculations with and without interface reconstruction are shown in Figs. 9(b) and 9(c). Without interface reconstruction, the tungsten density reduces as the material spreads over a larger distance of 1–2 μm. This distance is consistent with the extent observed in the diffusion test problem in Fig. 8. Low concentrations of tungsten will heat as they penetrate further into the hot-spot, shown in the lower half of Figs. 9(b) and 9(c) and in the temperature distribution in Fig. 9(d). When interface reconstruction is turned off, there is an order of magnitude more tungsten atoms in the 4–5.5 keV temperature range, suggesting that diffusion is a possible mechanism for producing hot tungsten atoms as inferred from experiment.

Diffusion of tungsten atoms also helps produce better quantitative agreement with x-ray images. Experimentally, it has been observed that the enhanced x-ray emission from the localized fill-tube signature has a fairly consistent ratio of brightness to the background DT hot-spot. In this analysis, a Fourier transform isolates the high-mode components of the image that results from the fill-tube.³⁹ This ratio is shown in Fig. 10 from an experiment and three post-shot simulations (discussed in Sec. VI). Originally, the calculations did not produce enough local x-ray emission compared to the experiments. This was improved by increasing the radiation bin structure, with 10× better energy resolution in the >10 keV bins that are producing these x-ray images. When the calculation includes numerical diffusion, the fraction of the x-ray emission jumps considerably, putting it within the range of the experimental measurement. These calculations find, however, that the yield of the implosion is not changing significantly with these changes. This is because the main x-ray losses from W-mix in the hot-spot come from M-shell emission near 2 keV [see Fig. 8(b)]. These photons will escape the hot-spot, but will be absorbed in the ablator before reaching a detector. The ∼2 keV M-shell emission is not as sensitive to diffusive effects as ∼10 keV L-shell emission.

The perturbation generated by the fill-tube is highly non-linear and sensitive to subtle changes in the geometry of the assembly. Figure 11 shows a sensitivity analysis where various aspects of the fill-tube geometry are changed. In the upper part, an 844 μm inner radius capsule design is studied (shot N161023). This design used a 10 μm fill-tube and a follow-up experiment tested the first 5 μm fill-tube on an HDC capsule. The lower portion shows an increased scale design (910 μm inner radius, N170601) which also tested 5 and 10 μm fill-tube diameters – the 5 μm experiment¹⁶ was the first to produce neutron yields greater than 10¹⁶. The figure shows the yield-over-1D, the mix-mass injected into the hot spot, and the fraction of hot-spot x-ray emission that comes from mix (using the original radiation group structure and interface reconstruction). This x-ray metric tracks the energy that escapes the hot-spot (defined by the 1 keV boundary).

The most sensitive aspect of the fill-tube assembly is the bore hole. This is the laser-drilled hole in the shell through which the fill-tube is inserted. When the hole is increased in the simulations, the extra volume is filled with glue near the tapered part of the hole on the outside and DT ice elsewhere. In the N161023 calculations, increasing the radius of the hole by 1 or 2 μm increases the mix-mass by 50% and 100%. In N170601, a 1 μm increase in the hole size injects ∼4× more mix and ∼4.5 more x-ray loss. This result stresses the non-linear behavior of the fill-tube perturbation. The hole diameter is measured by radiography⁴⁰ with an uncertainty of 1–2 μm. Future work will re-calibrate this measurement to reduce uncertainty.

Increasing the depth which the fill-tube is inserted, from 47 μm from the outer capsule radius to 57 μm, has little change to the degradations. Increasing the outer diameter of the fill-tube from 10 to 12 μm (while leaving the inner diameter fixed and increasing the hole size locally to support the larger outer diameter) actually reduces the degradation. This is likely because the larger fill-tube shadows the region and slows down the development of the hole. The fill-tube appears to counteract some of the potential damage done by the bore hole. This is revealed further in Sec. VI when the fill-tube is removed entirely. Recall, however, from Fig. 4 that the actual shadow has a 3D structure, so a larger fill-tube may become worse in reality.

The glue “filet” that extends beyond the capsule outer radius is another important parameter. Increasing this amount by 4.5–6× reduces the mix mass by half in the 10 μm fill-tube simulations. A similar reduction is observed in the 5 μm simulation by increasing the glue mass by 4.5 and 9×. This is discussed further in Sec. VI.

Subsequent to the 10 μm fill-tube experiment, N161023, the first 5 μm HDC DT was performed (N170226). Along with a reduction in the fill-tube diameter, the hole and glue masses were also reduced. Calculations predict that this change would have reduced the amount of mix mass by half. At the larger scale, a 10 μm fill-tube was tested after the success of the 5 μm N170601 experiment. The 10 μm fill-tube is calculated to increase the mix mass by 2.7× over the 5 μm.

The fill-tube simulations shown above are at very high resolution and cannot be included in combination with other perturbations like low-mode asymmetries in the radiation flux, the capsule-support tent, or surface roughness. To estimate the impact of the fill-tube in the presence of other perturbations, a surrogate perturbation was developed.

Figure 12 shows a comparison of a simulation of a 10 μm fill-tube and of a surrogate perturbation: a Gaussian divot 1 μm deep and 25 μm wide. The dynamics earlier in time show some difference. In Fig. 12(a), we see that at convergence ratio ∼2, the hole in the fill-tube case is already closing, while the surrogate perturbation remains wider. This is because the fill-tube perturbation is highly nonlinear and opens up a hole earlier in the implosion, while the surrogate divot takes longer to develop. But both perturbations inject a similar amount of mix-mass into the hot spot. Figure 12(b) shows that at this time there is a similar volume of ablator material penetrating through the hole. By the onset of deceleration [Fig. 12(c)], both simulations look very similar. The perturbation sends a narrow jet of material inward that has 97 ng of ablator material in the fill-tube case and 108 ng in the surrogate case. A divot 0.5 μm deep and 25 μm wide has been found to compare well with simulations of 5 μm diameter fill-tubes.

The simulated neutron yield drops with the addition of the fill-tube from 6.3 × 10¹⁶ in 1D to 3.8 × 10¹⁶ with a 5 μm fill-tube-surrogate or 2.8 × 10¹⁶ with a 10 μm fill-tube-surrogate. When other degradations to the implosion are present, however, the impact from the fill-tube is not as significant. Figure 13 shows the yield as the injected mix-mass increases. When all known sources of perturbations are included in 2D (low-mode radiation asymmetries, surface roughness, the capsule support tent, and a reduced model of high-mode mixing), the 5 μm fill-tube only reduces the yield by ∼20% over the same simulation without the 5 μm fill-tube. The experiments suggest stronger sensitivity, with a ∼70% improvement going from the 10 μm fill-tube to 5 μm (and 3D simulations are closer to this trend⁴¹) When the high-mode mixing model is removed, the fill-tube has a larger impact. This figure stresses the point that, while the fill-tube is a leading degradation mechanism, others are contributing a similar amount and require simultaneous improvement in order to observe an increase in performance.

As discussed above, it has been demonstrated that reducing the fill-tube size from 10 μm to 5 μm diameter reduces the perturbation and improves performance. Figure 14 shows simulations of each of these fill-tubes. The dimensions in these simulations are taken from actual experiments. The hole in the shell reduced from 10 μm to 21 μm in the 10 μm case to 7–12 in for 5 μm and the 5 μm fill-tube has a wall thickness of 1 μm. In both cases, a jet travels down the hole and breaks out into the fuel before the main shock, shown in Fig. 14(b) at 3.5 ns, but in the 5 μm FT case the ablation front is not developing a significant perturbation. The inward dent on the ablation front in the 10 μm case will be amplified once the shell begins further acceleration inward, which will open a hole and inject mix into the interior. Figures 14(c) and 14(d) show the simulations at 6.0 ns, where the hole in the 10 μm case is beginning to close. The density field in the two cases does not look significantly different, aside from the higher ρR near the axis with the 10 μm fill-tube. The material plot [Fig. 14(d)] shows that significantly more ablator material has entered the inside with the 10 μm fill-tube. In these two simulations, the 10 μm fill-tube injects 74 ng by bang time, while the 5 μm injects 21 ng.

Other modifications can be made to reduce the perturbation caused by the fill-tube other than simply reducing the diameter. A counter-intuitive example is shown in Fig. 15, which shows a 10 μm fill-tube where the glue filet on the outside is increased (from 5 to 14 ng). Figure 15(b) shows that the early shock wave is more distorted by the increased glue filet and acts to push material toward the axis. This inward material flow creates a high ρR bump on-axes [Fig. 15(c)] when the nominal glue case has a low ρR divot on the ablation front. As the shell continues to implode [Fig. 15(d)], the divot is developing into a hole while the increased glue remains as a higher ρR bump, ensuring that ablator mix does not get into the interior. For the capsules studied here, it was found that approximately 3× the typical amount of glue will stop the hole from opening up, and simulations with up to 6× glue showed good improvements. As shown in Fig. 11, increased glue also seemed to improve upon the 5 μm fill-tube.

As shown in Fig. 14(b), reducing the size of the fill-tube does not significantly reduce the jet that injects into the ice before the main shock. A possible mitigation to this is to angle the fill-tube and its hole. A proof-of-concept simulation of this effect is shown in Fig. 16. Since this concept requires a three-dimensional simulation, the fidelity needed to be reduced by simulating only a small sector of the capsule, finely resolving only the region near the fill-tube, and reducing the number of radiation groups from 60 to 9. These changes noticeably alter the ablation front scale length, but the behavior of the shock as it travels through the hole is captured. The initial setup and zoning for one of these simulations are shown in Fig. 16(a). Figure 16 shows that as a 5 μm fill-tube is angled, the extent of the jet that protrudes into the ice is reduced. This effect could eliminate the early mix that gets into the hot-spot, but the later-stage ablation front growth may change. The collapse of the angled hole leaves a low-density region in the ablation that has the potential to seed a perturbation. Additionally, having the tube closer to the ablator may induce more problems from shadowing. Whether the reduction of the early jet by tilting the fill-tube outweighs the potential concerns will ultimately need to be resolved by experiments.

A final idea often arises when considering minimizing the fill-tube perturbation: eliminate the fill-tube. Capsules made of plastic can be filled by embedding the capsule in high-pressure DT and allowing it to diffuse through the ablator.⁴² HDC is not permeable to DT, so this process would not work. Additionally, a hole must be drilled in the capsule anyways to allow the Si mandrel to be chemically etched out and removed. A possible solution is to fill the hole with glue after the mandrel is removed and diffusion fill through this glue plug. A similar process has been demonstrated with Be capsules by pressure filling through the hole and then plugging the hole with glue while still at high pressure.⁴³ 

Unfortunately, simulations do not find this glue-plug concept promising. The glue-filled channel remains lower density than the HDC, allowing the shock to rapidly advance through it, creating a large perturbation. The result ends up looking worse than with a fill-tube. The fill-tube acts to shadow the hole-region, reducing the ablation pressure and the strength of the shock down the channel. Figure 17 shows a simulation of a glue-filled hole, with a hole size typically used for 10 μm fill-tubes. It shows that the hole rapidly opens up and injects a significant amount of mix mass, ∼2× more than the fill-tube simulation in Fig. 2. Simulations of a 5 μm sized hole similarly look worse than a corresponding 5 μm fill-tube simulation. The concept can be improved by increasing the density or opacity of the glue or tilting the hole at an angle. Research and development will be required to determine what glue mixtures can be made, if the diffusion fill or fill-then-plug procedure can successfully make a DT-layered capsule, and if the perturbation is reduced with this approach.

The fill-tube induces a significant perturbation to HDC implosions. Simulations suggest that a hole in the ablator opens up during the implosion, allowing the ablator material to mix into the interior. These simulations appear to agree with experimental signatures of the in-flight perturbation and the late-stage emission from high-Z mix in the hot-spot.

Other experiments could help validate these models. The implosion stage is very dynamic, with the hole opening and closing rapidly over 2–3 ns. A time series of radiographs could confirm if this dynamic is correct. A further unknown is the impact of the 3D shadows that are not incorporated in 2D simulations. Extending the in-flight radiograph technique to later in time can measure if these perturbations break through the shell.⁴⁴ 

In the final stage of the implosion, with high-Z material mixing in the hot-spot, the modeling is more complex and uncertain. The injected mix will experience diffusive and viscous fluxes. The radiation from this mixture will not be in local thermodynamic equilibrium. The jet of material will experience shear stresses and Kelvin–Helmholtz mixing from the surrounding 3D flow. The conditions of the mix and its heating and cooling rate can be better constrained by high-resolution temporally and spatially resolved spectroscopy. To better understand how the fill-tube degrades the performance, an implosion with a second “dummy” fill-tube can be performed. However, this experiment could have the complexity that the two jets of the mix material will interact and not degrade performance additively.

The prospects for improving the fill-tube perturbation seem bright. The improvement seen in going to a diameter of 5 μm has prompted almost all subsequent experiments to use this size, resulting in further records in performance. Initial tests of a 2 μm fill-tube have been conducted, and there is the possibility of going smaller. Plans are in the works to test the tilted fill-tube concept. Increasing the glue mass and doping it with a higher Z are ideas being studied.⁴⁵ 

While simulations suggest that removing the fill-tube will not immediately show a large performance gain, improving other degradations simultaneously will help take advantage of the fill-tube improvements. As implosion designs increase in scale, we can expect the sensitivity to this degradation to increase.

T.B. contributed to the development and metrology of smaller diameter fill-tubes but could not be reached for manuscript approval.

This work was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 and by General Atomics under 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 makes any warranty, expressed 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 Lawrence Livermore National Security, LLC. The views and opinions of the 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.