Probing the seeding of hydrodynamic instabilities from nonuniformities in ablator materials using 2D velocimetry

The performance of the implosion of a DT-fuel-containing capsule at the center of the inertial confinement fusion (ICF) process is highly dependent on minimizing the growth of perturbations seeded at the ablation surface, the fuel-ablator interface, or within the ablator. Rayleigh-Taylor and Richtmyer-Meshkov instabilities during the compression of the fuel can grow large enough to inject cold fuel or ablator material into the hotspot, resulting in a loss of energy available for creating the fusion conditions. These instabilities are seeded by a variety of sources including drive asymmetry, capsule surface roughness, auxiliary components, such as the fill tube and the capsule support structure, and finally internal heterogeneity in the capsule material.¹ The measurements described here examine the early time first shock phase to measure the non-uniformities introduced by surface roughness and ablator heterogeneity. The indirect drive technique currently used by most experiments on the National Ignition Facility (NIF)² reduces the contribution of drive asymmetry by converting the drive laser energy into a generally uniform, nearly thermal x-ray source using a high atomic-number hohlraum.³ Within the hohlraum is a low-Z capsule containing a cryogenic shell of solid deuterium tritium fuel. The x-ray bath ablates the outer surface of this capsule, compressing and heating the fuel. There are currently three leading candidates for capsule materials: a plastic referred to as glow-discharge polymer (GDP), doped with silicon;⁴ tungsten-doped chemical-vapor deposited polycrystalline diamond referred to as high density carbon (HDC);^5,6 and copper-doped beryllium.⁷ Progress has been made in implosion experiments on NIF with all three ablator materials,^8–11 but each has different sources of instability seeding and different degrees of sensitivity to instability growth. Model-based estimates on capsule performance and yield have focused on the seeding of stabilities due to surface roughness of the capsule material, as the contributions from internal heterogeneity were generally considered to be small.^3,12–15 Surface roughness specifications for capsules described by Haan^14,16 are currently being met, but in-flight radiography experiments on imploding capsules¹⁷ have strongly indicated that seeds other than surface roughness may be large enough to become the dominant source for instability growth at the most important modes.^17,18 Complicating the situation, the origin of these heterogeneities is different for each of the three ablator materials. The unusual structure and the overall higher level of non-uniformity observed via radiography in GDP capsule implosions are best understood¹⁹ as the previous theoretical work by Haan et al.,²⁰ and the experimental work by Baxamusa et al.²¹ indicated that significant non-uniformity in ablation can result from non-uniform oxygenation within the outer few μm of the GDP capsules. This is confirmed by the measurements of the two-dimensional shock front velocity²² described here. Beryllium and HDC have more complex microstructures than GDP, and both are acoustically anisotropic.^5,23 This can lead to variations in the shock speed in crystallites of different orientations, potentially seeding instabilities. Additional sources of heterogeneous response include the presence of chemical impurities, particularly argon and oxygen for the beryllium, voids in the deposited material, and static internal stresses in the polycrystalline structure. The current strategy for reducing the impact of internal heterogeneities related to the crystal structure is to fully melt the ablator material on the first shock, requiring 2.6 Mbar for beryllium and >12 Mbar for HDC.^14,24–26 In the case of HDC, this strong shock also raises the entropy of the fuel, making it more difficult to reach the high densities required for ignition. As a part of the effort to understand both the origin and impact of the velocity non-uniformities in all three ablators, we have conducted two-dimensional velocimetry experiments on planar foils of the three ablator materials under conditions similar to the first shock level in beryllium and GDP, and immediately below the first shock level in HDC; the initial results are presented below.

The experiments described here were conducted at the Omega-60 laser facility at the Laboratory for Laser Energetics in Rochester, NY.²⁷ The target design shown in Fig. 1 was used for all three ablator materials, with the witness/fuel proxy material being 40–60 μm thick polymethyl-methacrylate for the warm experiments and 1 mm thick liquid D₂ for the cryogenic experiments. The hohlraum used for the GDP experiments is 2 mm long × 3 mm diameter with a laser entrance hole (LEH) diameter of 1.8 mm. A smaller hohlraum was used for the HDC and beryllium experiments, with an outer diameter of 2.7 mm and an LEH diameter of 1.6 mm.

The primary diagnostic for these experiments is the Omega High Resolution Velocimeter (OHRV), which is a two-dimensional spatially resolving Velocity Interferometry System for Any Reflector (VISAR).²² This instrument provides a velocity map of the perturbed shock front with ∼5 μm spatial resolution and velocity resolution <10 m/s. Recent improvements to the diagnostic have allowed us to approach 4 m/s root mean square (rms) velocity detection limit, which is vital for diagnosing perturbations as low as 10 m/s. Breakout times are determined using a streaked optical pyrometer (SOP),²⁸ which collects the thermal emission at 400 nm as a function of time, as well as timing fiducials from the facility and the OHRV probe laser to determine the timing of the OHRV relative to the breakout from the ablator into the PMMA witness or cryogenic D₂. The OHRV directs a pair of ∼3 ps-duration probe pulses with a wavelength of 400 nm onto the shock front, separated by a precise time interval, typically 100–600 ps, depending on the desired velocity resolution. The instrument then combines the returned pulse pair interferometrically to produce a fringe pattern that provides a spatially resolved map of the optical path difference between the two pulses over the field of view. This can be divided by the time interval between the two pulses to give the position-dependent velocity and the time-averaged over the interval between the two pulses. Each experiment provides a single snap-shot; evolution of the shock over time is inferred from data collected from multiple nominally identical experiments recorded with different diagnostic probe delay times.

The experiments with GDP are described in Ref. 29 and are described here with additional detail. The primary seed for perturbations in GDP is perhaps best understood of the three ablators. In 2015, Baxamusa et al.²¹ confirmed that GDP photo-oxidizes easily enough to result in oxygen non-uniformities on the order of 1 atomic percent (at. %) because of handling and metrology during fabrication. As has been discussed in a theoretical study by Haan et al.,²⁰ this relatively small impurity can have a significant effect on the ablation pressure during the launch of the first shock of the implosion, with regions of higher oxygen having both increased density and opacity relative to the surrounding area. To confirm the magnitude of this effect on the ablation pressure, GDP foils with a deliberate 100‐μm-period oxygen modulation on the hohlraum side were prepared by illuminating the GDP foil through a metal mask with alternating 50 μm clear spaces, and 50 μm opaque bars, as described by Reynolds et al.³⁰ The oxygen perturbation was spatially characterized using phase-shifting diffraction interferometry (PSDI), which measures the optical path difference through the foil,³¹ and Fourier transform infrared spectroscopy (FTIR) was used at isolated locations to determine the peak-to-valley oxygen concentration.³⁰ These measurements were combined with surface topography maps to determine the spatial structure of the oxygen distribution, as shown in Figs. 2(a) and 2(b). Additionally, secondary ion mass spectrometry (SIMS) was used to measure the depth profile of the oxygen concentration in both the masked and unmasked regions of the foil, as shown in Fig. 2(c).²¹ The presence of additional oxygen in the masked regions, relative to the pre-exposure sample, is attributed to inadequacy in keeping the metal mask flush with the GDP foil surface.

The GDP was thermally bonded to a 40–60 μm thick PMMA witness layer in which the shock could be observed, as GDP is opaque to the 400 nm probe wavelength of the OHRV. The shock front in PMMA is optically reflecting, allowing us to obtain a velocity map of the shock front. To study both the magnitude of the perturbation in the shock front as well as the evolution of this perturbation, the probe time of the OHRV was varied from 2.3 ns to 4.21 ns, relative to the start of the drive laser pulse. The resulting velocity maps and profiles are shown in Fig. 3. The three earliest time points, such as 2.3 ns, 2.5 ns, and 2.8 ns, used a 35 μm thick GDP foil, and the other experiments used 50 μm thick GDP. The 100 μm modulation is clear in the velocity maps. Additionally, at early time, the smaller scale structure in the oxygen profile shown in Fig. 2(b) manifests in the velocity as harmonic content at the wavelengths of 50, 33, and 25 μm. The peak-to-valley velocity measured is between 35 and 45 m/s. As expected, the higher harmonic perturbations decay more rapidly than the 100 μm perturbation; by the last two time points, 3.7 ns and 4.21 ns, the 100 μm fundamental feature is dominant.^32,33 Further discussion of the evolution of these modulations can be found in Ref. 29. Additional structure unrelated to the oxygen non-uniformity was observed in Figs. 3(a), 3(d), and 3(f). Through a closer examination of the surface topography maps and the GDP foil fabrication process, this structure was eventually determined to be unique to the foil fabrication process and was a result of ripples in the substrate upon which the GDP was deposited.

Following confirmation of the photo-induced oxygenation,²¹ the target fabrication team began investigating mitigation steps to protect the GDP capsules from heterogeneous surface oxygenation. The leading candidate is a protective coating of 20 nm of amorphous alumina deposited by atomic layer deposition on both surfaces of the GDP capsule; alumina is transparent to light, but oxygen impermeable.³⁴ While the target fabrication team was able to confirm that the alumina coating prevented oxygen uptake, there was some concern that it could introduce non-uniformities under cryogenic conditions. The alumina layers were tested in the cryogenic configuration because it is a better surrogate for a ICF capsule-fuel interface and because the good impedance match between GDP and PMMA in the warm target configuration precludes a good test.

To investigate both the deep release from GDP into D₂ and any potential instability seeding from the alumina coatings, two shots on GDP foils in the cryogenic target configuration were done, one without any protective coating, but otherwise careful protection from light [Fig. 4(a)] and one with the 20 nm alumina protective coating on both surfaces [Fig. 4(b)]. The rms velocity roughness for both shots was 4 m/s, close to detection limit for the OHRV configuration used, and no unaccounted-for structure was observed. While we had anticipated a possible increase in shock roughness due to the larger acoustic impedance difference between GDP and D₂, the velocity rms was lower than the ∼20 m/s observed previously during warm experiments. We believe that this is explained by the decreased handling required for the cryogenic targets relative to the warm targets, which results in less exposure to light during target assembly. Overall, the GDP foils produced the most uniform shock front we have observed thus far, however, careful protection from light exposure and/or oxygen is required.

A quantitative measure of the multi-mode velocity modulations is the velocity spectral density, V_SD, which is obtained from the square root of the azimuthal average of the two-dimensional Fourier-mode power spectrum normalized to enable straightforward extraction of the mode energy within a spectral band of interest

Here, V_rms is the velocity rms (in m/s) obtained from a quadrature sum of all modes within the band between the two spatial frequency limits f_L and f_U. Spatial frequency f is 1/wavelength, with unit of μm⁻¹, and V_SD has unit of (m/s)‐μm. Additional details on the calculation and normalization of the spectral density can be found in the Appendix of Ref. 35. The velocity spectral density for the GDP shots is shown in Fig. 5. This is mostly of interest relative to the other materials, as presented below, although there is a clear signature of the imposed perturbation visible in the spectral density for the modulated samples. Except for the imposed perturbations, the modulations in GDP are much smaller than in Be or HDC. It is quite similar to the previously published results³⁶ despite the difference that these are into liquid D₂ while the previous results were into PMMA. Simulations do not predict a significant difference between the two downstream materials.

In the past few years, sputter-deposited beryllium has become an increasingly utilized capsule material.^37–39 It has low opacity and high density relative to the GDP ablators, and while the current sputter-deposition process does result in a uniform, full-density material, there are potential sources of heterogeneous response.²³ Acoustic anisotropy of the crystal could lead to variation in shock speed as a function of propagation direction relative to the crystal orientation.⁴⁰ This is modeled in detail in Ref. 41 and is likely to be a significant issue if the shock is below melt. Below melt, in Ref. 41, it was estimated to produce hundreds of m/s velocity modulations. Above the melt temperature, it is less likely to be an issue although that has not yet been experimentally verified. Previous measurements of the nonuniformity in beryllium showed minimal structure,⁴² but recent hydrodynamic growth radiography (HGR) results on beryllium capsules at NIF exhibit unusual features not correlated with known perturbation seeds or features, as well as a higher level of roughness than expected.¹⁷ As an improvement over the previous OHRV measurements in the beryllium, two changes were made to the experiment design. The first change was to use beryllium material fabricated using the same process as is currently used in the capsules; the previous experiments used either rolled foils or a sputter deposition that was qualitatively similar to the current process but different, in detail (in particular, the electronic bias, which affects the amount of Ar captured in the Be).The concentration and distribution of chemical impurities introduced during the deposition process, primarily in the form of oxygen and argon, can be highly dependent the deposition process. The second change was to switch from the warm target configuration with release into PMMA to a cryo target configuration with release into liquid D₂, which was not possible during the previous experiments. Finally, as was the case with the GDP measurements described above, the most sensitive velocity measurement OHRV configuration was used for the measurements. Velocity maps from two cryogenic shots, Figs. 6(a) and 6(b), show significant discrepancy between these nominally identical shots. One warm shot, Fig. 6(c), shows similar ∼50 μm ring features as the cryogenic shots, but an overall lower level of velocity roughness. These ∼50–100 μm features seen in the lower left in Fig. 6(a), the top and bottom of (b), and throughout (c) are perturbations resulting from dust or particulates on the hohlraum side of the ablator. The warm targets require additional handling during preparation and therefore have a higher incidence of dust or particulate contamination than the cryogenic samples.

Simulations of the seeding and propagation of perturbations in beryllium because of the measured surface roughness were done to determine whether the observed level of velocity nonuniformity could be attributed to surface roughness alone. The resulting simulated velocity maps using the target metrology and drive conditions for the experiment velocity map, shown in Fig. 6(a), are shown in Fig. 7. Some similar features are seen in the simulations, including the 50 μm features discussed above; however, simulated amplitudes were considerably lower than measured amplitudes. This indicates that there is most likely an additional source of heterogeneity in the beryllium and with the current surface roughness achievable on NIF capsules, this internal heterogeneity may now be the most significant seed for perturbations. Experiments to understand the exact source of the perturbations are ongoing in order to determine which of the potential seeds, acoustic or chemical, is predominant.

The velocity spectral density measured on the Be shots is shown in Fig. 8. The previous Be OHRV experiments, as shown in Fig. 1 of Ref. 36, were a factor of 4–16 times lower, depending on dopant. This could be because of differences in foil fabrication details, as rolled foils were used for the previous experiments. The previous experiments also only released Be into PMMA, with no cryogenic shots releasing into D2. In simulations, the release into D₂ vs PMMA has little effect on the expected velocity modulations, which is supported by the relatively small difference between the measured velocity spectral density in the cryogenic shots and the warm PMMA shots shown in Fig. 8. On the other hand, current fabrication technology introduces Ar into the Be, and the best available estimates of the Ar inhomogeneity can result in velocity modulations similar to those currently being measured. This is discussed further in Sec. VI.

Tungsten-doped HDC is currently the leading ablator material in terms of neutron yield,¹⁰ has a higher density than GDP, allowing for thinner ablators and shorter drive durations,^36,43 and can be reproducibly fabricated within the capsule specifications outlined by Haan et al.¹⁴ As discussed in the Introduction, however, the polycrystalline nature of this material does potentially seed perturbations during the implosion and the high melting point of HDC on the Hugoniot (>12 Mbar for fully melted) places the fuel on an adiabat that is potentially too high to achieve ignition with the current laser platform. To better understand the intrinsic seeds for perturbations in HDC in the melt region, we have measured velocity nonuniformity following the release from HDC into liquid D₂. As with the beryllium, samples were fabricated as closely as possible to the NIF ICF capsule fabrication process. There is evidence for some potentially significant differences in the microstructure for deposition on a flat as opposed to a sphere, and for future experiments, the use of large-diameter capsule segments is planned. While the >12 Mbar fully melted state in HDC has not yet been achieved in these experiments, the data have been collected at 7 Mbar and 10 Mbar, in the coexistence region. The resulting velocity maps for two cryogenic shots are shown in Figs. 9(a) and 9(b), and for one warm shot with the release into PMMA in Fig. 9(c). Due to the smaller difference in shock impedance between HDC and PMMA, as compared to HDC and D₂, there is less perturbation growth on the release for the warm shot. As would be expected, with the increase in the pressure into the melt region, velocity nonuniformity decreases; however, the degree of roughness remains high and as with the beryllium, simulations were done to determine whether this level of roughness would be expected based on the measured surface roughness. The surface-roughness-only simulated velocity map for the 10 Mbar cryogenic shot shown in Fig. 9(a) is shown in Fig. 10, and results in a velocity rms of 19 m/s, more than four times lower than the measured velocity rms of 86 m/s. This again suggests that with the currently achievable level of surface roughness, the predominant source of hydrodynamic perturbation seeds may be a feature of the material and the shock dynamics that is different from conventional seeding by surface roughness. Possible implications of this are discussed in Sec. VI.

The velocity spectral density for the HDC experiments is shown in Fig. 11. Compared to the previously published results,³⁶ we see that the release into D₂ at both 7 and 10 Mbar is considerably worse than into PMMA. Only one case from Ref. 36, showing 4.5 Mbar releasing into PMMA, is comparable to the new results for release into D₂. The new results for release into PMMA are comparable to the previous experiments. Simulations based on surface roughness alone give much smaller perturbations, especially at shorter wavelengths. This is evident in Figs. 10 and 11.

The 12–14 Mbar first shock pressure used in current NIF ICF designs fully melts the HDC, unlike the shock pressures discussed here. These pressures should be achievable on Omega and plans for future experiments include collecting velocity maps in the fully melted regime.

An understanding of the origin and impact of the observed velocity modulations is vital to improve the designs and develop the next generation of ignition experiments. The significance of the observed velocity modulations to progress in inertial fusion depends on their origin. This varies between the three ablators, because the inhomogeneities likely to be seeding these modulations vary from case to case. For all three ablators, performance of current NIF implosions is believed to be limited by three other sources of asymmetry: radiation asymmetry, the capsule support, and the fill tube.^1,15,44 These current experiments are also at higher adiabat than may ultimately be needed for full gain conditions of >10 MJ of yield, although it should still be possible to achieve ignition conditions on NIF. Progress towards >10 MJ of gain will ultimately require both reducing the currently dominant asymmetries and moving towards lower adiabat implosions. These future implosions will have more growth at the 10–200 μm scale lengths (modes of 30–600), and we expect them to be affected by these results as follows:

For GDP, these experiments have established that the variations in oxygen content generally dominate the surface roughness as seeds for hydrodynamic modulations. Work on characterization of the oxygen inhomogeneity, and its photo-induced origin, has established a fairly mature understanding of the perturbations seen in these experiments and of their impact on NIF implosions. If the oxygen modulations are eliminated, either with careful control of exposure to light and oxygen or with a protective layer such as alumina, then the observed modulations are consistent with surface roughness and seeds for hydrodynamic instability in an implosion can be assumed to be merely surface roughness as is generally assumed.¹⁵ 

For Be, the sputter coated ablators are known to contain somewhat inhomogeneous argon and oxygen impurities. The best estimates that these inhomogeneities are consistent with the observed velocity modulations are described in this work. For Ar, this corresponds to ∼0.1 at. % peak-to-valley variations on an average level of ∼0.1 at. % Ar, with characteristic modulation scale that is 15–100 μm laterally and 10–30 μm in the transverse direction (radial or depth of burial). This level of Ar modulation, in simulations, can seed velocity modulations of several 100 m/s as seen in these experiments and is equivalent to 50–100 nm of initial surface roughness as a seed to RM/RT instabilities in implosions. This is to be compared to 15 nm of allowed initial surface roughness on the Be outer surface. These projections depend on the depth-of-burial of the Ar, both as a seed to the velocity modulations in these experiments and as a seed to instability growth in an implosion. Because the details of the Ar inhomogeneity are not available, it is impossible to extrapolate quantitatively from the observed velocity modulations to a meaningful estimate of the impact on NIF implosions. Since the velocity modulations are consistent with the observed Ar inhomogeneity, and the Ar inhomogeneity causes instability growth that is several times larger than that caused by surface roughness, it seems very likely that it will be important to reduce the Ar modulations by a factor of several. This can be tested experimentally with instability growth experiments on NIF and with Omega OHRV experiments testing new Be fabrication technology. Similarly, oxygen modulations of ∼1 at. % are believed to be present in the sputtered Be with the lateral scale length of 10–50 μm, which causes ∼10 m/s modulations in the shock front measured here. This is accordingly a factor of a few less important than the Ar inhomogeneity. A third possibility for Be is that there is some seed to the perturbations that arises dynamically from shock propagation in this sputtered material and would remain even if the fabrication technology were changed to eliminate Ar and O. In that case, the observed velocity modulations could be less well-coupled to RM/RT growth, and the current NIF Be implosion campaigns might not be strongly affected these modulations. At this time, it is not possible to predict with confidence the ultimate significance of these perturbations for Be on NIF. However, these results strongly indicate that better characterization of the Ar and O inhomogeneity is important and that it probably needs to be reduced by a factor of several for Be to function well as a NIF ablator.

For HDC, we see very large velocity modulations whose size depends on the shock strength. The only known contaminant seed is Mo, and the best characterization available suggests that it is not likely to be the source of these velocity modulations. (There is also hydrogen captured in the HDC, but it is very unlikely to be a problem because of its low opacity.) The issue that has generally been thought to be a possible problem for HDC is inhomogeneity introduced by incomplete melt, either behind the shock or following some amount of refreeze during release. At solid-solid shock strengths, below ∼5 Mbar, the acoustic anisotropy considered in Ref. 40 for Be is also likely to be an issue. The Omega experiments discussed here were at shock pressures that could be expected to be possibly problematic for these processes. Future experiments with the same platform will address stronger shocks at 12 Mbar, for which these effects should be considerably diminished. Past experiments by one of us (P. M. C., including those published in Ref. 36) showed ∼100 m/s modulations for shock strengths of 4–7 Mbar, comparable to that seen in our cryo experiments. The new cryo experiments show velocity modulations that are several times larger than a similar shock strength releasing into PMMA. There are several scenarios for how the melt/refreeze could seed velocity modulations on the shock front and then subsequent RM/RT instability growth. There are probably associated density and pressure modulations that are not measured in these experiments. Simulations of these processes and the resulting velocity modulations are sensitive to the details of where and how the shock front modulations are generated. Applying similar modeling to NIF implosions also shows high sensitivity to the details of the modeling, but the resulting hydrodynamic instability growth in a NIF implosion is not directly related to the shock front velocity modulation as measured here. Thus, as was concluded above for Be, it is not possible to meaningfully extrapolate these results to a quantitative impact on NIF implosions. We can conclude from the experiments that there are hydrodynamic irregularities that are several times larger than expected from surface roughness and that generally decrease with the strength of the first shock. As currently observed, it is very likely that these processes will be important for future NIF implosion below full-melt at 12 Mbar.

It is interesting to note that some NIF experiments were done around 2013 with a 4-shock pulse shape, with first shock strength ∼6 Mbar. One notable example is an undoped HDC single-shell noncryogenic implosion N130628, which performed very well and for a time was the NIF neutron yield record holder.⁴⁵ There was no evidence in these shots of problems arising from hydrodynamic irregularities of the type discussed here. The shots did show significant perturbations from the tent and the fill tube. Simulations indicate that this implosion had growth factors up to about 300, and a nominal HDC surface roughness would have caused ∼3 μm rms features on the DT/HDC interface at burn time. If things were, for some reason, an order of magnitude worse than this, this would have been very evident in the experimental results. We can conclude then that, at 6 Mbar first shock level, the perturbations seeded in the HDC as it was fabricated for N130628 were at most about five times larger than surface roughness. Since that time, the HDC program on NIF has concentrated on two and three-shock implosions, with initial shock level 12 Mbar and above, which would be expected to be less sensitive to the issues discussed here.⁴⁶ A few two-shock implosions were done with 9 Mbar first shocks,⁴⁷ but these were also very low growth factor and are probably not a tighter constraint than N130628.

Another option for HDC to function at lower shock pressures is to alter the fabrication technique, possibly by moving to nanocrystalline grain sizes. The previous work by Dawedeit suggests that nanocrystalline HDC has a significantly lower Young's modulus and therefore potentially a lower melting temperature.⁴⁸ Experiments on NIF and Omega to explore differently fabricated HDC will be an important part of that development.

In this article, we have presented spatially resolved two-dimensional measurements of shock front velocity nonuniformities accumulated after propagating through samples of the ablator materials used in current NIF implosion experiments. The observed shock front variations provide a unique probe of the effects of inhomogeneities generated in the bulk regions of the ablator samples which are otherwise difficult to model or characterize. Our investigation into perturbation seeds in beryllium and HDC is still ongoing. While we have determined that the measured velocity nonuniformity is greater than would be expected from surface roughness alone, identifying the specific microstructural or chemical variations in the material requires additional metrology, experiments, and simulations. The future work using this platform includes moving from the planar foil samples to large diameter shell segments to remove any remaining differences in the fabrication process. While we are limited in peak pressure at the Omega-60 laser facility, relative to NIF, future experiments will measure velocity nonuniformity at the ICF second shock level in beryllium and GDP.

We thank Carol Ann Davis, Russel Wallace, and Christoph Wild for the target preparation and the staff of OMEGA operations for their invaluable assistance in fielding the experiments. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 and by General Atomics under Contract No. DE-NA0001808.