Effect of the mounting membrane on shape in inertial confinement fusion implosions

At the National Ignition Facility (NIF),¹ scientists are investigating the indirect drive approach to Inertial Confinement Fusion (ICF),^2,3 in which a layered DT-filled capsule is placed inside a high-Z hohlraum, with the goal to achieve fusion ignition and burn. To form a central hot spot with sufficient temperature and areal density to achieve ignition and high gain in ICF requires highly symmetric implosion of the capsule. The hot spot self-emission can be misleading as to the symmetry of the stagnated shell.⁴ Therefore, the shape of the implosion is diagnosed by both time resolved x-ray radiography of the capsule⁵ and imaging of the x-ray hot spot self-emission.⁶ 

In ICF, the growth of the Rayleigh-Taylor Instability (RTI)^7–9 is of concern. It occurs at the interface of two fluids with different densities when the interface is accelerated into the denser fluid. RTI can be seeded by perturbations on the capsule, which can lead to small perturbations growing exponentially and can be detrimental to ICF at two stages.³ RTI can lead to rupturing of the shell during ablation. In the second stage, which occurs when the shell is slowed down by the pressure from the hot spot, RTI can lead to mixing of the dense cold fuel layer with the hot spot, reducing the effective size and deforming the shape of the hot spot.

To quantify the shape of the imploding capsule, images of the imploding shell and of the hot spot are taken, using backlit x-ray radiography and self emission, respectively. The radiography results in a projection of the spherical harmonics Y_lm onto a 2D image. The effects discussed here are azimuthally symmetric and the analysis uses Y_l0 which are the Legendre polynomials P_l. Here, l = 0–8 are considered low mode.

It has been found that the membrane mounting the capsule within the hohlraum interferes with the interpretation of the low mode shape for the low-foot (low adiabat) laser drive. By varying only the membrane thickness, we have isolated the influence of the membrane on the shape of the x-ray emission on a low convergence platform. Here, we correlate the measurements to simulations and discuss the expected impact of the membrane on the performance of high convergence ICF experiments.

The indirect drive target consists of a NIF ignition scale (diameter of 5750 μm and length of 9425 μm)^10,11 hohlraum target modified for backlit imaging.^5,12,13 The backlit imaging technique has been developed⁵ to radiograph the imploding capsule in-flight from a radius of approximately 300 μm to about 150 μm. Probing to even smaller radii is currently being investigated. In this technique two of the NIFs 48 quads are redirected from the hohlraum to a germanium foil located 12 mm from the capsule center in the equatorial plane. This generates 10.25 keV Ge He_α x-rays over a ∼1 mm diameter spot lasting about 2 ns. To provide a line-of-sight from the Ge backlighter foil through the hohlraum to the gated x-ray detector, two 0.9 × 0.83 mm diagnostic holes are cut out of opposite sides of the hohlraum wall and plugged by high-density carbon (HDC) windows.

The length of the cylindrical gold hohlraum was varied between −300 and +1000 μm from the original design length of 9.4 mm. The capsule, with a 1.15 mm outer radius and 0.21 mm thick spherical plastic shell, is filled with 6.7 mg/cm³ of 30% of D₂ and 70% of ³He gas when cooled to 24 K. The hohlraum is driven with a 1.3 MJ, 21 ns long, shaped ignition pulse as described in Ref. 5.

The capsule is held at the center of the hohlraum by two thin plastic membranes that are called tents. On early NIF shots, the tent membrane was 300 nm thick; as technology improved, targets were built with 110 nm, 45 nm, 30 nm, and most recently as thin as 12 nm tents. It should be noted that as the tent becomes thinner it becomes less reliable as a support. An illustration of the capsule mounted within a backlit platform hohlraum can be seen in Figure 1. The tent material is Formvar (polyvinyl formal, C₃₁H₅₆O₁₃) with a density of 1.23 g/cm³. The hydrodynamic perturbation discussed here is seeded around the lift-off ring. In most shots, this ring is circular, at about 45°, and the tent lifts off from the capsule surface at 10°–15° rather than tangentially. In the backlit platform targets, the tent contact along the top and bottom of the capsule is in the shape of an ellipse, with the longer axis along the line of the detector/windows. This is due to the windows in those directions, which prohibit the tent contacting the hohlraum wall at those positions, pulling the lift off point closer to the equator.

To study the case of a non-tent mounted capsule, one shot was performed with the capsule mounted using a thick fill tube. The fill tube, see Figure 1, is used to fill the capsule with gas. Nominally, the fill tube has an outer diameter of 10 μm and is inserted into the capsule with a depth of 30 μm. For the tube-mounted capsule, the diameter was increased to 30 μm and the insertion depth to 100 μm. This thick tube is called a stalk below. The position of the fill tube with respect to the detector's line of sight can be seen in Figure 1 and is about 50° from the radiography axis.

Deviations from sphericity of the implosion in-flight seen in the backlit platform described above are typically described by the Legendre modes. To be more quantitative, the backlit frame is divided into angular sectors, and the radial lineout for each sector is analyzed for the minimum transmission. This radius corresponds approximately to the peak density of the shell. The contours constructed from this radius of all angular sectors are analyzed into a Legendre polynomial series. By repeating the process for all frames, the time evolution of the low mode shape, P₀–P₈, and implosion velocity are obtained for the in-flight shell during the diagnosed phase.⁵ Another metric for the quality of the implosion is the shape of the x-ray self emission of the hot spot. The hot spot is formed when the fuel is heated and compressed to a high average density. A good correspondence exists between the hot spot perimeter and the 17% contour of the x-ray emission.¹⁴ 

Targets containing solid DT or THD fuel layers are more involved to field and prepare and are intended to have high neutron yields. Gas-filled targets called symcaps are used to study implosion dynamics during the acceleration and peak velocity phase.¹³ As it is the total mass of the capsule that dominates the implosion dynamics, in the symcap surrogate, the DT or THD ice fuel layer is replaced by an equivalent mass of plastic. The changes in the target lead to a lower overall convergence of the symcap compared to the layered targets. To test the surrogacy between the two platforms, we have measured the in-flight shape of both symcaps and a backlit layered target. The evolution of P₄, in absolute units of μm, for a symcap and a THD target driven with nominally identical conditions is shown in Figure 2. This shows comparable in-flight shapes at overlapping times, which allows us to use the easier-to-field symcap platform for shape tuning, rather than the more complex layered capsules. The similar evolution between THD and symcap is also observed for the other P modes (P₀–P₈). The time integrated self-emission images show a hot spot size for the THD that is about half that of the symcap; however, the time integrated P₄/P₀ measurements for the THD and symcap shots are comparable within the error bars.

Detailed integrated hohlraum-capsule simulations using HYDRA,¹⁵ which do not include the tent mounting, show the presence of an in-flight diamond-like (positive) P₄ that phase inverts to square-like (negative) P₄ hotspot self-emission image. The simulated images can be seen in the first column of Figure 3, and Fig. 4 shows the resulting P₄ amplitudes (gray symbols). The swing rate is in agreement with the one observed in Ref. 5 and is likely due to early drive asymmetries which lead to residual kinetic energy in the implosion.^4,16

The black symbols in Figure 4 show a summary of the measured P₄/P₀s for the different tent thicknesses, the radiographs, and self emission images, which are shown in Figure 3. The in-flight shell is represented by the squares, and the hot spot emission by the circles. Although the tent feature is obvious in the in-flight radiographs, in the form of a pair of horizontal bands, it does not affect the in-flight P₄ as much as it affects the hot spot P₄. The hot-spot P₄ from self emission is sensitive to the tent as it significantly decreases for the stalk-mounted target. Furthermore, for the stalk shot we observe a swing from a positive in-flight P₄ to negative P₄ in the self emission, which is in agreement with simulations that do not include the tent or the stalk (gray symbols). Even though the simulations do not perfectly capture the shape, i.e., the experimentally observed seems to be more positive, the offset in P₄/P₀ between the time integrated self emission and the in-flight shape matches.

By changing the laser pointing and hohlraum length, the amplitude of the P₄ mode of the in-flight shell can be reduced by moving the location of the outer cones further away from the equator of the hohlraum. To prevent clipping of the outer cones by the laser entrance hole, the hohlraum is lengthened by the same amount as the outer beams move. Tent-less HYDRA simulations show that a hohlraum that is 700 μm longer than the nominal length should minimize the in-flight P₄. This can be seen in Figure 5, red symbols.

A series of experiments with different length hohlraums have been performed with a nominal tent thickness of 45 nm. Typical frames of the backlit images, when the implosion capsule is at a radius of ≈220 μm, are shown in Figure 5 (top row). The measured in-flight P₄s for the different hohlraum lengths are also plotted in Figure 5, black squares. Both simulations and experimental data show a substantial reduction of the in-flight P₄ with hohlraum length, see also Ref. 5. Figure 5 shows that the diamond shape in-flight P₄ can be reduced for longer hohlraum targets, but that the hotspot emission has a more pronounced and persistent P₄. This is in contradiction to the simulations, which do not have tents, and is consistent with the notion that the capsule-support tent is significantly affecting the hot-spot images, although, as discussed previously, it has a negligible effect on the inflight shape analysis.

Though the tent feature in the in-flight shell images does not affect the interpretation of the in-flight shape, it has been shown¹⁷ that it has a significant impact on the areal density and its asymmetries. Clear perturbations, in direct correspondence with the tent features visible in the radiographs, can be seen in the reconstructed mass density maps.¹⁷ For some of the targets, the position where the tents lift off the capsule were measured after target assembly. It should be noted that the latitude at which the tent comes in contact with the shell is not necessarily constant around the target, and that the tent lift-off latitude can therefore vary along the contact ring. For reference, the poles of the capsule lie along the symmetry axis of the cylindrical hohlraum.

Figure 6 shows the latitude of the tent feature in the radiography data as a function of the contact position between tent and capsule in the pre-shot target metrology. Data are shown for three shots, indicated with subscript symbols on the data in the figure. Angles from the radiography data are obtained at two different positions [see Figure 7(a)]: The circles labeled as θ_vert correspond to a measurement along a vertical line out through the center of the radiography image, as indicated by the dashed white line in Figure 7(a). The squares labeled as θ_circ correspond to measurements from the circular line out of the image, as indicated by the solid white line in Figure 7(a). Examples for the vertical and circular line outs can be seen in Figure 8. From these line outs, one can find the position of peak brightness (maximum transmission) of the tent feature indicated with open symbols in Figure 6. Similarly, the position of the maximum slope in the x-ray transmission of the tent feature measured on the side towards the target poles is indicated by solid symbols. (The slope features are marked in the line outs shown below in Figure 8.) Figure 6 shows that the position of the slope closely matches the initial tent lift-off position, obtained from the pre-shot characterization data, filled symbols are on the line—while the position of maximum transmission (peak) tends to be 2°–10° closer to the equator than the tent lift-off position. This offset can be expected for a mechanism where the exploding tent seeds a perturbation on the equator-side of the contact ring.

Early estimates of the tent perturbation were based on simulations using a simplified model of the tent¹⁰ and predicted a tent perturbation less than half as big as is inferred from the observations discussed above. Hammel and coworkers^18,19 are finding that very high-resolution simulations of the actual tent geometry are in good agreement with the observations described here. Detailed discussion of these simulations is beyond the scope of this paper. In order to form preliminary estimates of the impact of the observed tent feature, it is useful to have an approximate model that could be calibrated to the experimental results, and can be used in simulations to estimate the impact of this larger than expected tent perturbation. The feature as seen in Figures 3 and 5 has width of about 70 μm, when the ablation front is at 220 μm; scaled up to the initial radius of 1130 μm, the initial width would be about 350 μm. Simulations were done with an initially 350 μm wide groove, with the shape of a single sinusoidal wave (wavelength 350 μm), of various initial groove depths. A groove depth of about 300 nm produces a perturbation that is in reasonable agreement with the observed 110 nm tent perturbation, as shown in Figures 7 and 8. The position of the groove that best matches the observed feature is typically about 10° closer to the waist, so that the upper edge of the perturbation is close to the tent lift-off position. The groove depth that best matches the tent perturbation varies nonlinearly with the thickness of the tent, as shown in Figure 9. This groove is somewhat bigger than has been discussed previously,²⁰ as improved processing of the backlit images has indicated deeper features²¹ than were originally estimated.

In these simulations, the shape of the core emission is significantly affected by the tent feature. Figure 7(b) shows a simulated time integrated emission image from a simulation with the same groove depth and width as used for Figures 7(a) and 8, located at 40° from the waist. The simulated self emission image is qualitatively similar to the images shown above in Figures 3 and 5, with a 9.6 μm P₄ Legendre amplitude on the 17% contour. The amplitudes of P₄, and of the other modes P₂ and P₆, depend on the angle at which the groove is placed initially, and this location approximately maximizes P₄.

Possible influence of the tent can also be seen in the decrease of the neutron yield. Figure 10 (triangles) shows measurements of the DD neutron yield plotted against the tent thickness. A yield degradation due to the tent thickness is already seen for this low convergence radiography platform, and is expected to be even more pronounced for higher convergence platforms, closer to the ignition design. Indeed, for the equivalent of a 45 nm tent, the mock tent simulations show a reduction in yield from 40% to 60% when going from the low to the high convergence platform, see Figures 10 (circles) and 11. The experimentally observed reduced yield for the 0 nm tent, see Figure 10, which was using a thicker stalk to mount the capsule, is most likely due to the perturbation from the stalk mount.

Simulations initialized with the groove “mock tent” perturbation, described above also show that the tent perturbation has a significant effect on the simulated performance. Figure 10 shows the simulated yield of a typical symcap as the depth of the groove is increased, and Figure 11 a layered DT capsule, showing 15%–60% yield decrement due to the tent. The impact is not dependent on the width of the groove, as shown in Figure 11. The dependence on tent thickness is nonlinear, and the impact is significant for even the thinnest tents.

Because the mounting membranes are very thin, it was originally estimated that the tent would have acceptable impact on the implosion.¹⁰ However, the data suggests that the tents seed RTIs at the capsule surface from the beginning, which grow throughout the implosion until they eventually (nearly) perforate the capsule, as has been seen in detailed simulations¹⁹ and is suggested by the processed radiography images, see, for example, Figure 10 in Ref. 21. The interpretation of RTI seeded by the tent contacts, being responsible for the features, is also supported by data taken with a higher adiabat laser pulse shape. These experiments show no visible tent feature in either radiographs or self emission images.²² 

Simulated high adiabat implosions seeded with a similar groove do not show any visible feature in a radiograph image. The tent feature is not predicted to have a significant effect on the performance of these high adiabat implosions, consistent with their reduced hydrodynamic instability.^22–25 

The effect of the tent thickness has been seen in the measured DD yield and the shape of the hot spot self emission. Furthermore, the position of the tent features in the radiographs matches the tent lift-off positions. These measurements support the interpretation that the tent seeds a perturbation at its lift off positions that leads to a Rayleigh-Taylor instability, which is absent for the stalk case. Due to the reduction of the hydrodynamic instability, the impact of the tent is significantly reduced in higher adiabat implosions.

Simulations using an approximate tent model that was calibrated to the experimental results agree with the observed yield degradation caused by the tent. As expected, they predict a significant reduction in yield moving from a low (15–25) to a high (>25) convergence platform.

The influence of the tent feature on the hot spot emission could explain prior inconsistencies between the in-flight (radiograph) P₄ and the core (hot spot emission) P₄, leading to a reevaluation of the optimum hohlraum length.

This work shows that it is important to use mounting membranes that are as thin as possible, find mitigation strategies, for example, in the form of the laser pulse shapes for less instability growth, or alternative mounting strategies, and to keep this tent effect in mind when interpreting results of self-emission shape measurements.

This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract Nos. DE-AC52-07NA27344 and DE-AC52-07NA27344; LLNL-JRNL-664740.