The interface between the capsule ablator and fuel ice layer is susceptible to hydrodynamic instabilities. The subsequent mixing of hot ablator material into the ice reduces fuel compression at stagnation and is a candidate for reduced capsule performance. The ability to diagnose ice–ablator mix is critical to understanding and improving stability at this interface. Combining the crystal backlighter imager with the single line of sight camera on the National Ignition Facility (NIF) allows direct measurement of ice–ablator mix by providing multiple quasi-monochromatic radiographs of layered capsule implosions per experiment with high spatial (∼12 μm) and temporal (∼35 ps) resolution. The narrow bandwidth of this diagnostic platform allows radiography of the inner edge of the capsule limb close to stagnation without capsule self-emission contaminating the data and removes opacity uncertainties typically associated with the spectral content of the radiograph. Analysis of radiographic data via a parameterized forward-fitting Abel inversion technique provides measurements of the distribution of mix mass inwards from the ice–ablator interface. The sensitivity of this mix measurement technique was demonstrated by applying it to layered experiments in which the stability of the ice–ablator interface was expected to vary significantly. Additional experiments suggest that high-density carbon capsules that employ a buried-layer dopant profile suffer from mixing at the innermost doped–undoped interface. Data from these experiments suggest that opacity models used in hydrodynamic simulations of NIF experiments can potentially over-predict the opacity of doped capsules. LLNL-JRNL-850535-DRAFT.
I. INTRODUCTION
In the indirect-drive approach to inertial confinement fusion1 (ICF), soft x-rays ablate the surface of the capsule, driving an implosion and compressing it to 30–40× its initial radius. At the National Ignition Facility2 (NIF), this soft x-ray drive is generated using 192 laser beams to deliver up to ∼2.1 MJ of ultraviolet light to the interior of a high-Z Hohlraum which contains the capsule. The fuel is present initially as a layer of solid deuterium-tritium (DT) ice coated onto the inner surface of the ablator, as illustrated in Fig. 1(a). To achieve ignition, the implosion of the capsule must compress the DT ice layer from its initial solid density of 0.23 g/cc to final densities approaching ∼500 g/cc.3 This extreme density is required so that alpha particles produced by fusion reactions initiated in the hotspot at the center of the capsule deposit their energy within the ice layer, heating the fuel to conditions where a cycle of self-sustaining fusion reactions can occur.
Hydrodynamic instabilities are well known to be detrimental to the performance of ICF capsule implosions.1,4–6 If the interface between the ablator and the DT ice becomes unstable then ablator material can mix into the fuel and severely reduce capsule performance by limiting fuel compression and final convergence. The stability of the ice–ablator interface can be characterized by the Atwood number, defined here as A = ( − )/( + ) where and are the densities of the fuel and ablator, respectively, and A <0 represents a stable ice–ablator interface. Figure 1(b) shows a 2D simulation using the radiation hydrodynamics code HYDRA7 of a stable (A < 0) ice–ablator interface. In this case, the ablator and ice are clearly separated at the interface (left) and the fuel is uniformly compressed to high density (right). However, if during the implosion the fuel density at the interface exceeds that of the ablator then A > 0 and the interface becomes unstable to the classic Rayleigh–Taylor instability.8 In this case, hydrodynamic mixing of ablator material into the ice will occur, as shown in Fig. 1(c): Interpenetration of the ablator and ice occurs (left) and the average density of the ice is significantly reduced (right).
Experimentally, the areal density of the stagnated fuel (ρR) is inferred by measurement of the down-scatter ratio (DSR), defined as the ratio of 10–12 MeV scattered neutrons to the primary 13–15 MeV neutrons,9 where ρR(g/ ) ∼20×DSR. Experiments on the NIF consistently observe that the measured DSR is 10%–25% lower than predicted by 1D HYDRA simulations7,10 (which do not include hydrodynamic mix or alpha heating). The potential impact of reduced DSR on fusion performance can be quantified using the experimental ignition threshold factor11,12 (ITFX), which may be interpreted as a metric of the likelihood of ignition. This is defined as , where Y is the neuron yield and Yc, DSRc refers to yield and DSR from 1D “clean” simulations at ignition. The strong sensitivity to DSR means that a measured value 10%–25% lower than the clean value represents a significant 20%–45% reduction in the ITFX. Therefore, in ICF platforms where ice–ablator mix is the likely cause for lower than expected DSR, increasing the stability of the interface is key to improving fusion performance.
The disagreement between the observed and expected areal density could arise from multiple processes that are not modeled with full fidelity: In addition to ice–ablator mix, the areal density can be reduced by non-ideal shock timing and the value of the ablation pressure and time over which the shell decelerates near stagnation. Therefore, while a lower than expected areal density can indeed indicate the presence of mix, it is an indirect indicator, i.e., it is a measure of a symptom with multiple potential causes rather than a direct measurement of mixing. For example, experiments have explored whether areal density can be increased through the doping of the ablator, which is intended to stabilize the ice–ablator interface by reducing pre-heat. One set of experiments used CH (plastic) capsules and varied the concentration of dopant in the ablator significantly, but did not observe a correlation with areal density.10 This suggests that x-ray pre-heat (resulting in an unstable Atwood number and therefore ice–ablator mix) may not be the primary reason for lower than expected fuel compression in this particular platform. This is likely because CH is an amorphous material13 and so does not exhibit any significant internal structure variations, which might seed ice–ablator mix. Another set of experiments used high-density-carbon (HDC) capsules and showed that the addition of dopant did result in an increase in areal density compared to an undoped capsule,14 suggesting that ice–ablator mix may be more relevant in this platform. This is consistent with HDC being a crystalline material with a granular structure15 that is expected to seed ice–ablator mix.16 However, without a direct measurement, the extent to which ice–ablator mix was responsible for the areal density trends observed in these experiments cannot be confirmed. Furthermore, strategies to reduce mix such as creating more stable Atwood numbers and raising the adiabat work well in simulations but at present there is only indirect experimental evidence of their effectiveness, further motivating the development of a direct mix measurement capability. This paper describes the development of a radiography platform, which can make direct measurements of mix at the ice–ablator interface on the NIF.
The first direct measurements of instability growth at the ice–ablator interface17 used the hydro-growth radiography (HGR) platform18 to study the evolution of well-characterized, pre-imposed perturbations. The HGR platform uses a cone-mounted capsule to perform face-on radiography and is therefore restricted to fairly modest capsule convergence ratios18 (CR ∼ 2–3). Side-on radiography using a full capsule is required to make measurements at late time, when the capsule is at peak velocity just prior to stagnation and ice–ablator mix has developed to its full extent. This type of measurement provides the closest surrogate to a fully integrated ignition-effort experiment and provides data that are better suited for inferring the distance over which mixing occurs. However, such measurements are extremely challenging: At peak velocity the capsule is moving at 300–400 μm/ns and the region experiencing mix is expected to be only a few tens of micrometers wide located on the inside of a spherical surface. Therefore, the diagnostic platform must be capable of spatial resolution on the order of ∼10 μm, high enough temporal resolution to reduce motion blur to ∼10 μm, and must provide data of sufficient quality that Abel inversion can be reliably performed. Additionally, the diagnostic must be capable of providing data that is largely unaffected by the self-emission from the capsule hotspot, which begins to emit strongly as the capsule approaches stagnation.
On the NIF, the stringent diagnostic requirements for making a side-on radiographic measurement of mix have been met via the coupling of the crystal backlighter imager19 (CBI) to the single line of sight (SLOS) camera.20,21 CBI is a narrowband imager with 10× magnification based on near-normal-incidence Bragg reflection from a spherically bent crystal x-ray optic.22–27 This instrument simultaneously provides the required high spatial resolution while rejecting the continuum self-emission from the capsule hotspot. This paper provides a brief description of the CBI instrument, while a detailed description of the diagnostic can be found in Ref. 19. The SLOS camera provides the required high temporal resolution and allows multiple radiographs to be captured from CBI's single x-ray optic on a single NIF shot. The coupling of these instruments is described in Sec. II, which discusses the experimental configuration and measurement technique. Section III describes the procedure by which a radiograph is analyzed to measure ice–ablator mix. The sensitivity of this mix measurement technique was demonstrated by applying it to layered experiments in which the stability of the ice–ablator interface was expected to vary significantly. Results from these experiments are presented in Sec. IV. Further experiments were then performed with HDC capsules to assess the effectiveness of two strategies designed to reduce ice–ablator mix: the addition of high-Z dopant to the ablator and an increase in adiabat. These results are presented in Sec. V. Finally, Sec. VI discusses the observation that hydrodynamic simulations of these experiments appear to over-predict opacity in some situations.
II. EXPERIMENTAL CONFIGURATION AND MEASUREMENT TECHNIQUE
The experimental configuration for the diagnostic platform is illustrated in Fig. 2(a): The backlighter is positioned 35 mm from the capsule along an equatorial line of sight and is driven by 8 NIF outer beams (one upper quad and one lower quad). The remaining 184 NIF beams drive the Hohlraum. A pair of 800 × 800 μm HDC windows on opposing sides of the Hohlraum provides access for radiography. Backlighter x-rays passing through the Hohlraum are incident onto the CBI19 crystal, which reflects a narrow range of x-ray energies at near-normal incidence and images a radiograph of the capsule onto the SLOS20,21 x-ray framing camera.
When indirect drive ICF experiments do not require a backlighter, two groups of 16 outer quads (i.e., 128 beams) drive the upper and lower ends of the Hohlraum. Removing a quad from each of these groups to drive the backlighter impacts the energetics and symmetry of the drive, but these effects can be mitigated: To maintain the same laser energetics as an equivalent experiment conducted with all 128 outer beams driving the Hohlraum, the power of the remaining 120 outer beams is increased by a factor 128/120 = 1.067. In some cases, the asymmetry introduced by removing an upper and lower quad from the Hohlraum can also be mitigated by modifying the outer beam pointing from 16-fold symmetry to 15-fold symmetry. This modified pointing reduces the amplitude of the largest asymmetry mode, M1, from M1/M0 ∼ 2.5% to M1/M0 < 0.3%.29 However, this strategy requires a sufficiently large laser entrance hole to avoid clipping the beams and so cannot be implemented on all experiments.
The CBI configuration for these experiments uses a Si 6 2 0 crystal at a Bragg angle of to perform radiography with the 7.242 keV cobalt He-α resonance line (1s 2 1s2 ), a combination proposed in Ref. 30. This x-ray energy was chosen as it provides good contrast for the experiments described here. The bandwidth of this configuration to the backlighter source is ∼2.2 eV. This extremely narrow bandwidth aids with the analysis of the radiographs, as it eliminates any uncertainty that the data might be affected by opacity varying with x-ray energy.
In some of these experiments, the radius of the capsule limb can be as small as ∼100 μm when the radiographs are captured. This close to stagnation self-emission from the capsule is often present. This means that pinhole area-backlighting techniques31 are unsuitable for these measurements as the broadband response of pinholes can result in capsule self-emission impinging upon the radiograph, and close to stagnation this prevents accurate measurement of the limb profile. The narrow bandwidth of the CBI diagnostic (∼18.6 eV to a source located at the center of the capsule in the configuration presented here) is required, as it significantly mitigates the effect of capsule self-emission such that radiographic measurement of the limb profile can be performed close to stagnation.
ICF experiments on NIF produce extremely bright hotspot emission, and even with its narrow bandwidth, this can be visible in CBI radiographs. Therefore, it is important that the backlighter be bright enough so that it dominates any self-emission close to the capsule limb on the radiograph, minimizing its effect upon the data in the region of interest. The radiography platform for these experiments therefore used a high efficiency “cavity” backlighter source. A brief description of this source and its coupling to CBI is provided here, while a detailed description will be published separately. The cavity source consists of a solid cobalt cylinder, 1 mm long, with a 1 mm internal diameter and a 50 μm thick wall. The beams from two NIF quads are tiled over the inner surface of the cavity, as shown in Fig. 2(b). The continuous phase plates (CPPs) are removed from these beams to minimize the diameter of the beams, allowing them to pass through the entrance of the cavity without clipping. Ablation from the cavity walls produces a stagnating plasma on the axis which exhibits a peak laser-to-x-ray conversion efficiency into the He-α lines several times higher than flat foil backlighters. The cavity backlighter is aligned so that its axis is collinear with the CBI line of sight. Since the backlighter plasma motion is predominantly perpendicular to the cavity axis, the He-α emission from these cavity sources does not exhibit any Doppler shift, simplifying the coupling to the CBI's narrow bandwidth and allowing operation at the Bragg angle corresponding to a stationary emitter. Figure 2(c) is an x-ray image of the cavity source at the time of peak emission, when the radiographs are captured. This image is predominantly Co He-α emission viewed from an angle close to CBI's line of sight, showing that the source is close to circular and has a ∼700 μm FWHM. Using this source, the spatial resolution of CBI coupled to SLOS has been measured as 10.6 and 13.5 μm in the horizontal and vertical directions, respectively (12.1 μm mean). Note that the resolution of the NIF pinhole area-backlighter platform31 is limited by the relatively large diameter pinholes required to ensure sufficient fluence at the detector. A pinhole diameter of 25 μm is typically required, which, using the same x-ray energy and magnification as CBI, would limit spatial resolution to ∼28 μm before any detector contribution is included.
For these experiments, the radiographs are captured during the period when the capsule is at peak velocity (300–400 μm/ns), and therefore, it is vital for the framing camera to have a short integration time in order to minimize motion blur: When the radiograph is analyzed to measure ice–ablator mix, the analysis procedure (see Sec. III) can correct for the effect of instrument resolution if this resolution is not too poor. Testing of the analysis procedure with synthetic data suggests that the effect of instrument resolution can be accurately removed when the total resolution (combination of spatial resolution and motion blur) is 20 μm. The SLOS x-ray camera20,21 uses pulse dilation technology32,33 combined with an ultra-fast hybrid-CMOS sensor34,35 to achieve an integration time of 35 ps. For capsules imploding at peak velocity of 300–400 μm/ns, this limits motion blur to 10.5–14.0 μm. Combined in quadrature with the mean ∼12 μm spatial resolution of CBI coupled to SLOS, this gives a total resolution of ∼16.0–18.5 μm.
In contrast, the ∼100 ps integration time of NIF's micro-channel-plate x-ray framing cameras36 would result in unacceptably high motion blur (∼30–40 μm), making these instruments unsuitable for these experiments.
The SLOS hybrid-CMOS sensor uses in-pixel storage to allow four frames of data to be captured per NIF shot. Coupled to CBI, this allows four separate radiographs to be captured from a single backlighter and x-ray optic, dramatically improving the quantity of data that can be obtained compared to micro-channel-plate x-ray framing cameras which can only capture a single image per experiment. Figure 3 shows four sequences of radiographs obtained from the experiments discussed in this paper. For these experiments, the frame-to-frame separation of SLOS was set to ∼77 or ∼93 ps, giving a total record length of 235 or 280 ps: This is ideal for capturing several peak-velocity radiographs over the 400 μm radial field of view while simultaneously accommodating typical NIF timing jitter and uncertainties in the predicted implosion trajectory. However, the pulse dilation technique used in the SLOS camera involves the acceleration of electrons along a drift tube and care must be taken to ensure space-charge effects do not significantly affect the image. The x-ray flux onto the SLOS camera must therefore be limited (using filtering) to a level that reduces space-charge effects to acceptable levels, and this limits the signal-to-noise ratio (SNR) that can be achieved.
When high neutron yield is desired, e.g., when the goal of an experiment is fusion ignition, the ice layer consists of equal parts deuterium and tritium (DT). However, for many focused experiments in which a specific aspect of the implosion is being studied, high neutron yield is undesirable as some diagnostics can suffer damage or be overwhelmed by noise. The SLOS camera electronics are not hardened against neutrons, and therefore, the yield on the experiments presented here was maintained below 1E13 to reduce risk of damage to the instrument. To achieve this, the fuel ice layer used a tritium, hydrogen, and deuterium (THD) mixture37 of 75%T:24.9%H:0.1%D for the CH capsule experiment and 74.7%T:24.9%H:0.4%D for the HDC capsule experiments. The use of a THD (instead of DT) ice layer does not affect the hydrodynamics of ice–ablator mix as the density of the ice is essentially equivalent at the aforementioned fractions.
III. RADIOGRAPH ANALYSIS PROCEDURE
The radiographs shown in Fig. 3 and elsewhere in this paper have been processed from the raw data. First, hot pixels resulting from neutron noise are identified and disregarded, i.e., the values of these pixels are set to NaN so that they do not contribute further. Pixels that are affected by neutrons are easy to identify in the data since these events create large, predominantly single-pixel, peaks in the signal that are much brighter than the surrounding data by many standard deviations above the local signal-to-noise ratio. To ensure that all neutron-affected pixels are removed, a conservative approach is taken in which a pixel is removed if the signal is more than 3.5 sigma above the mean (using a local sample not including the pixel itself). This gives high confidence that all pixels affected by neutrons are removed, while only ∼0.3% of “good” pixels are discarded, assuming that the noise distribution is approximately Poisson.
The SLOS camera drift tube contains several acceleration grids which can cause shadowing on the radiographs, and pixels that have been affected by these grids are identified and disregarded. Affected pixels are identified by fitting the position of each grid line on the radiograph with a high-order polynomial, fitting a Gaussian profile to the grid cross section (i.e., the dip in signal caused by the shadowing) at each location where the polynomial intersects a pixel, then disregarding all shadowed pixels within the FWHM of this profile. Depending on the neutron yield and SLOS timing, the fraction of pixels that are disregarded from a particular radiograph due to neutron noise and grid shadowing ranges from ∼3% to ∼35% with a mean of ∼22% for the data discussed here.
Additional steps include the removal of the SLOS sensor background.38 This background is a low-mode pedestal that is easily identified and removed via analysis of the large sensor area not occupied by the data (radiographs occupy ∼8 × 8 mm2 of the 25 × 12.5 mm2 sensor). Finally, the radiographs are flat-fielded to account for non-uniformity in the brightness due to any misalignment between the crystal and the backlighter perpendicular to the line of sight. Raytracing shows that over the region used for analysis (typically ±350 μm vertically and horizontally from the capsule center) the radiograph uniformity is expected to be flat to within ±1.6% if the crystal and backlighter are perfectly aligned. Raytracing shows that misalignment in a direction perpendicular to the line of sight causes intensity to vary linearly across the radiograph, and therefore flat-fielded is performed by fitting a plane to the overall radiograph brightness profile. This flat-fielding method produces radiographs that are well-balanced left/right and top/bottom (see Fig. 3).
When the processed radiographs are analyzed to produce the radial profiles that will be discussed in Secs. IV–VI, disregarded pixels are not included in the analysis: these pixels are set to NaN and do not contribute to the measured radial profile. However, to make the radiographic data easier to visualize the radiographs shown in figures in this paper have had disregarded pixels replaced using interpolation. Note that this interpolation is for display purpose only, and no interpolation is applied to the data that is actually analyzed.
Radiography provides a spatially resolved measurement of the transmission of an object. Transmission at a specific photon energy is defined by , where κ is the opacity of the material at that energy, ρ is the density of the material, and is the path length of the backlighter rays through the object. It is convenient to express the radiograph in terms of optical depth (OD) which is defined as OD = such that OD = −ln( ). For these experiments, it is reasonable to assume spherical symmetry, and so the contribution of path length to the optical depth is known. However, for an object as complex as an imploding ICF capsule it is extremely difficult to separate the individual contribution of opacity κ and density ρ to their product. Therefore, for the experiments discussed here, the goal of the radiography measurement is to obtain radial profiles of the product of density and opacity, .
The principal of the ice–ablator mix measurement is illustrated schematically in Fig. 4. When the ice–ablator interface is stable and no mixing occurs, the radial density profile of the ice and the ablator do not overlap, and the density of each material should drop sharply to zero as the interface is crossed. However, when mixing occurs the density profiles might be expected to resemble Fig. 4(a): The interface is spread out over a finite range of radii as ablator material penetrates into the ice (shown inset) and the density profile of the two materials overlap each other, dropping gradually to zero over the mix width.
The opacity of the THD ice layer, , is much less than the opacity of the carbon in the ablator, . Assuming that, at the time the radiographs are captured, the photoelectric cross section of carbon is ∼50%–75% of the cold value at 7.242 keV and the THD is fully ionized, then . Therefore, while the density of the ice and ablator may be comparable, the product of density and opacity renders the ice layer essentially invisible relative to the ablator. This is illustrated (albeit in an exaggerated sense) by Fig. 4(b), in which the red line shows the profile that might be expected given the density profiles in Fig. 4(a). If there were no mixing (mix width = 0), the inner section of the profile might be expected to drop immediately to zero (rather than falling off gradually) as illustrated by the black line in Fig. 4(b).
For a spherically symmetric capsule, the optical depth measured by the radiograph is the forward Abel transform of the profile. Figure 4(c) illustrates the radial OD profiles that would result from path integrating the profiles in Fig. 4(b) assuming spherical geometry. From OD profiles, mix is most readily observed as a shallower inner limb profile.
The goal of the analysis procedure is to take a measured OD profile and recover the profile using Abel inversion so that the mix width can be inferred. Within the 800 × 800 μm2 field of view provided by the Hohlraum windows, there is no part of the radiograph where the field of view is empty of opaque material, i.e., there is no point at which OD = 0. Without this (or some other) reference point the measured radiograph represents relative OD. The Abel inversion requires absolute OD and so a uniform offset is added to each measured OD profile so that it matches the OD predicted by a 1D HYDRA simulation at r = 400 μm, i.e., at the edge of the field of view where the backlighter rays have passed through the least amount of material. For radii larger than 400 μm, the OD is extrapolated using the HYDRA simulation until OD = 0. At these large radii, d(OD)/dr is small and therefore, any inaccuracies in the simulations will not contribute significantly to the Abel inversion.
The presence of large windows in the Hohlraum along the radiography line of sight results in the capsule becoming prolate (elongated) in this direction due to the reduced drive. This effect is usually ignored in experiments which use radiography to tune the in-flight capsule shape since the effect on the capsule shape in the direction perpendicular to the diagnostic line of sight (i.e., in the plane of the radiograph) is small. For the mix measurement, not accounting for the prolate shape of the capsule along the line of sight will make the mix region appear smaller than it actually is and will lead to an underestimate of the mix width. This effect is small, but to obtain the most accurate measurement of mix width it is included in the analysis: For all the experiments described here, pinholes are used to image x-ray self-emission from the pole (along the axis of the Hohlraum) which allows measurement of the shape of the hotspot perpendicular to the radiography line of sight. For the experiments discussed here, fitting of the hotspot shape using Legendre polynomials gives the absolute size of the M2 (the amount by which the hotspot is prolate) as between 7.6 and 19.0 μm, with the size of the M2 for a given experiment remaining approximately constant throughout the burn width. It is reasonable to assume that the hotspot and ablator have the same absolute size of M2, i.e., that they are concentric. Therefore, in all instances where an Abel transformation is applied to the data discussed here, the transformation is modified from the usual assumption of axial symmetry to include the measured M2. For the definition of mix width described later in the paper, including the effect of the M2 results in a mix width increase in ∼1–2 μm compared to analysis, which does not account for the M2.
Abel inversion of real experimental data is made more difficult by noise. Reverse Abel inversion methods, i.e., direct processing of OD(r) to obtain (r), amplify any noise in the data significantly. For the experiments presented here, Abel excribed laterinversion is performed via parameterized forward-fitting to minimize the impact of noise. A combination of mathematical functions is used to represent ; then, the variables defining these functions are optimized until the Abel transform of the parameterized matches the measured OD. Another advantage of forward-fitting is that the effect of the instrument response function on the data can be accounted for during the fitting procedure so that the result best represents the underlying profile. In this case, the spatial and temporal resolution of the CBI+SLOS radiography platform (plus any additional smoothing used) is applied to the Abel transform of the parameterized form for before it is compared to the data, allowing the assessment of features smaller than the resolution of the instrument. As discussed in Sec. II, testing with synthetic data showed that the high resolution of the CBI+SLOS radiography platform allows the instrument response to be accurately removed using this analysis procedure.
Comparison to modeling and data led to the adoption of the parameterized form for shown in Fig. 5(a), which uses different functions to represent the ablation and mix regions, and can also accommodate the presence of capsule self-emission. The ablation region is represented by the sum of three super-Gaussians, aligned such that each peak is at the same radius, and joined to the mix region via a flat top. The mix region is comprised of two linear sections, since this can represent a situation where there is no mix (i.e., a sudden drop from peak to zero over zero mix width) or a situation in which there is significant mix and decreases gradually over a large mix width. Using a single linear function to represent the mix region of (as used in the illustrations in Fig. 4) does not produce a satisfactory fit to the OD data, but two linear sections allows all the data to be fit well. Finally, if capsule self-emission is present it is represented by a single negative super-Gaussian, since self-emission acts in the opposite manner to actual opacity by increasing the brightness at the center of the radiograph. This feature was included for the final radiographs in the three HDC experiments, where inspection of the data concluded that self-emission was responsible for reduced OD at small radii. The presence of self-emission is especially obvious in the final radiographs of the two doped HDC experiments and is labeled in Figs. 3(c) and 3(d). This parameterized form for , comprising of 14 independent variables (17 when self-emission is included), produces a good fit to the experimental data: The example profile shown in Fig. 5(a) produces the OD profile shown in red in Fig. 5(b), which is a good fit for the measured OD shown in black. With regard to this parametric fitting approach, the range of options for parametrized fits is extremely broad, and there is no limit to how many could be tried. The choice described here was adopted as the simplest option that fit the data well while simultaneously allowing zero mix and a high mix to be represented. As long as the parametrized function used is the same for every experiment and the data can be fit well, it is reasonable to use this to infer mix widths, but for analysis of future experiments, the intention is to use a fully generalized (i.e., non-parametric) forward-fitting method.
It should be noted that the presence of self-emission is not expected to impact the shape of the mix region since measurements show that the radius at which self-emission occurs is significantly smaller than the inner region of the capsule limb. For the final radiographs in the three HDC experiments where self-emission was present, polar pinhole imaging showed that the radius of the self-emission (defined by the 17% contour) projected along the radiograph line-of-sight was ∼29, ∼37, and ∼37 μm whereas analysis suggests the mix region ends at a lower radius of ∼65, ∼65, and ∼100 μm, respectively.
The measured OD is obtained by performing an azimuthal average over some range of angles, as illustrated by the inset in Fig. 4(c). Some amount of averaging and smoothing is necessary to produce a radial OD profile with sufficient SNR for the forward-fitting Abel inversion to produce a good fit to the data. This is because x-ray fluence onto the camera is limited by the requirement that space charge effects inside the SLOS drift tube not distort the data, and this in turn limits the SNR of the radiograph. For the first three experiments discussed here (N190714, N190902, N190929) a very conservative approach was taken to limiting space charge effects and the fluence was reduced such that the mean SNR (local mean/σ of pixel values) of the radiographs was ∼3.6. With the limited SNRs achieved in these first three experiments, all the analysis in this paper uses averaging around the full azimuth. After azimuthal averaging, 10 μm of Gaussian smoothing is applied to the OD profile to further improve the SNR before the Abel inversion is performed—this additional smoothing is minor compared to the combined spatial and motion blur within the radiographs, and is removed along with the instrument response function during the forward fitting procedure. After smoothing and full azimuthal averaging, the mean SNR of pixel values over a region between (the radius of maximum OD) and – 25 μm (the region of interest for the mix measurement) was ∼26 for these first three experiments. For the final experiment (N200712) modeling of the electron dynamics inside the drift tube39 determined that the x-ray flux onto the camera could be increased with negligible impact of space-charge on the data. This resulted in the mean SNR of the radiographs increasing to ∼5.6. After smoothing and azimuthal averaging, the SNR in the same region of the OD profile described above increased to ∼42. In future, the use of higher x-ray fluences in addition to potential camera and analysis improvements is expected to allow averaging over smaller azimuthal regions, although it is unlikely that the SNR of radiographs with SLOS can be increased above ∼8–10 without space charge effects becoming non-negligible.
The use of azimuthal averaging requires that deviations from roundness must be corrected to prevent the capsule shape artificially broadening the limb profile. This correction is applied by fitting the capsule limb (minimum transmission) using Legendre polynomials (up to order 4) then applying a radial shift to each section of the data to align the limb to the radius given by the P0 term of the Legendre fit. This typically results in a radial shift of up to m for sections where the limb deviates most from roundness, which is important for preventing broadening of the OD profile but insufficient for the shifting process itself to significantly affect the Abel inversion.
The mix width is calculated using the two linear sections of the parameterized profile. First, this section is normalized as shown in Fig. 6(a). Assuming that the peak density of the unmixed ice and ablator are comparable [i.e., the situation illustrated in Fig. 4(a)], the of the unmixed ice is expected to be 3%–5% of the peak (discussed above). Defining rf as the radius at which is 10% of the maximum, the region r is ignored in order to avoid any contribution from the unmixed ice. The interface of the mix region, ri, is defined as 90% of the peak , and so the region considered as representing mix is r , shown as the red shaded area in Fig. 6(a).
The mix width W(m) is defined as the distance from the interface containing a certain fraction m of the total mix mass. Figure 6(b) shows the relation between W and m for the profile shown in Fig. 6(a).
The uncertainty in the mix width measurement introduced both by the experiment and the analysis procedure was assessed via the creation and analysis of a large set of synthetic data: After the parametrized fitting has concluded, the calculated optical depth produced by the Abel transform of is used to create a synthetic version of each original radiograph. The Legendre fit obtained during the initial analysis is applied so that the synthetic radiograph has the same shape (deviations from roundness) as the original data.
Next, the noise modeling technique described in Ref. 40 is used to apply noise to the synthetic radiograph based on the specifications of the SLOS camera. For each synthetic radiograph, the noise model is tuned so that the SNR of the synthetic images matches that of the original data, and is run hundreds of times to produce a large set of noisy synthetic images. The location of pixels affected by neutron noise is random. The location of pixels affected by shadowing by the SLOS grids can also be considered as random, since the position on the detector surface where the image falls (and therefore the location of the grids relative to the radiograph) is determined by random variations in the alignment of the instrument. So, to account for the pixels that are disregarded (set to NaN) in each original radiograph due to neutron noise and shadowing by the SLOS grids, an equal number of pixels are chosen at random in the synthetic image and are also disregarded.
Finally, uncertainties during instrument alignment can affect the crystal-to-object distance, which in turn affects the magnification and resolution of the radiograph. The CBI alignment procedure allows the crystal-to-object distance to be set to an accuracy of 200 μm (1 σ). To account for this uncertainty, each synthetic image is assigned an error in crystal-to-object distance, which is randomly sampled from a Gaussian distribution with σ = 200 μm and raytracing is used to calculate the expected resolution and magnification resulting from each specific misalignment. Assuming this calculated magnification and resolution at each step, each synthetic radiograph is then run through the same analysis procedure as the original data.
The result is that each experimental radiograph is accompanied by a large set of potential solutions for , which represent the uncertainty introduced by the disregarding of pixels due to neutron noise and grid shadowing, the removal of capsule shape via Legendre fitting of noisy data, the overall effect of the noise and limited SNR on the OD profiles, and the effect of unknown instrument misalignment. For each potential solution for the mix width W as a function of mix mass fraction m is calculated in the manner described above and shown in Fig. 6. When considering a specific fraction of the mix mass m, the value of the mix width and the uncertainty in this value are given as the mean and standard deviation of W(m) from the set of solutions.
Flat-fielding of the radiograph and subtraction of the SLOS sensor background are not considered during the uncertainty analysis, as these involve the correction of small changes in brightness which vary slowly on the scale of the image width, i.e., long modes. Since the inverse Abel transform depends on the differentiation of the OD profile extracted from the radiograph, slow changes in signal such as these are not expected to have a significant impact on .
IV. TESTING THE MIX MEASUREMENT PLATFORM
For this measurement technique to be useful for developing methods to mitigate ice–ablator mix, it must be sensitive enough to detect significant differences in the level of mix. To demonstrate this, the measurement technique was tested on two “subscale” (∼1 MJ of laser energy) experiments.
The first of these experiments (N190714) used the subscale “CH(Si) 2-shock” platform in a THD repeat of N161004, described in Ref. 41, and was expected to be stable to ice–ablator mix. This platform is not designed to be ignition relevant and instead trades away performance in return for a high stability implosion, useful for testing the predictions of hydrodynamic codes. Nuclear measurements of the CH(Si) 2-shock platform41 showed a DSR in very close agreement with 1D simulations, suggesting that mixing at the ice–ablator interface is minimal. This experiment used a gold Hohlraum, 5.75 mm inner diameter, 9.43 mm long, and a 3.1 mm diameter laser entrance hole (LEH). The capsule was CH (∼1 g/cc) uniformly doped with 1% silicon (atomic fraction), an inner radius of 564 μm with a total shell thickness of ∼120.6 μm, and a 40 μm thick THD layer.
The second experiment (N190929) used the subscale “HDC 3-shock” platform and was expected to be significantly more unstable. This experiment was a THD repeat of N160120 described in Ref. 14. This experiment used a bare (linerless) depleted uranium Hohlraum, 5.75 mm inner diameter, 10.13 mm long, and a 3.37 mm diameter LEH. The capsule was undoped HDC (∼3.5 g/cc) with an inner radius of 844 μm, a total shell thickness of ∼65.6 μm, and a 53 μm thick THD layer.
There are several key design differences between these two platforms that affect stability at the ice–ablator interface. The first of these is the drive adiabat. The hydrodynamically stable CH(Si) 2-shock platform uses a high adiabat (∼5) 2-shock drive to reduce the growth of ablation front instabilities and maintain a high degree of stability at the ice–ablator interface. By comparison, the unstable HDC 3-shock platform uses a low (∼2.5) adiabat 3-shock drive.
The second difference is the ablator material. The internal structure of the ablator is suspected to play a significant role in susceptibility to ice–ablator mix, as fine scale features within the bulk material of the ablator can seed growth of the Richtmyer–Meshkov instability.42 The stable platform uses a plastic ablator which, being an amorphous material, does not exhibit any internal structure from which mix might be seeded. Conversely, the unstable platform uses an HDC ablator. This is a crystalline material consisting of grains ranging from nanometer to micrometer scale, and exhibits an average density that decreases as the average grain size decreases.15 This is interpreted as a result of reduced density at the grain boundaries. 2D simulations of capsule implosions which incorporate this grain structure predict that the crystalline structure of HDC induces significantly more ice–ablator mix than would be expected from surface roughness alone.16,43 Additionally, experiments have measured spatial variations in the velocity of shock propagation through samples of HDC that suggest the grain structure may be a seed for ice–ablator mix.44 Indeed, this grain structure has been suggested as the dominant cause of lower-than-expected performance in platforms which use HDC ablators.
The third difference is the susceptibility to “pre-heat.” The ice–ablator interface is initially stable to the Rayleigh–Taylor instability, but stability can be reduced if high-energy components of the Hohlraum x-ray drive are able to penetrate to the region of the ablator immediately adjacent to the ice and deposit energy there. This pre-heats the ablator at the interface, reducing the density relative to the ice, and results in a more unstable Atwood number. The addition of a mid-Z or high-Z dopant to the ablator is used to stabilize the interface by shielding the innermost region of ablator from x-ray pre-heat. In the case of the stable CH(Si) 2-shock experiment, the ablator was doped with silicon. For HDC ablators, the dopant is usually tungsten, but for the unstable HDC 3-shock experiment, the capsule was intentionally undoped and therefore vulnerable to instabilities caused by pre-heat.
1D HYDRA7 simulations were used to calculate the Atwood number vs capsule radius for these experiments, shown in Fig. 7(a). For the CH(Si) 2-shock experiment, a stable Atwood number (A < 0) is expected at the ice–ablator interface for the entirety of the implosion, while for the HDC 3-shock experiment the Atwood number becomes unstable (A > 0) early in the implosion, when R ∼580 μm. The circular markers on each line represent the radii at which radiographs were captured during each experiment.
The sequence of radiographs obtained for the CH(Si) 2-shock experiment is shown in Fig. 3(a). The first three radiographs have limb-min radii of 171, 143, and 120 μm and cover the period over which the capsule is close to peak velocity ( 330 μm/ns). The final radiograph has a limb-min radius of 92 μm; HYDRA simulations suggest that the capsule is undergoing stagnation at this time, and an outgoing shock is transiting the limb. Radiographs for the HDC 3-shock experiment are shown in Fig. 3(b) and were captured at limb min radii of 247, 214, 189, and 160 μm.
Azimuthally averaged OD profiles for the CH(Si) 2-shock and HDC 3-shock experiments, together with 1D HYDRA simulations, are shown in Figs. 8(a) and 8(d), respectively. The differences/similarities between measured and simulated and peak OD in these experiments are striking and will be discussed in Sec. VI. Broadening of the inner edge of the capsule limb, indicative of mixing, is better observed using normalized OD profiles, shown in Figs. 8(b) and 8(e). Even before analysis to quantify mix width, the difference in stability between the two experiments is apparent from comparing the normalized profiles: For the CH(Si) 2-shock, the measured profiles at the inside of the limb (at times prior to stagnation) are steep and of comparable width to the 1D simulations, consistent with the expectation that little mixing occurs in this platform. Conversely, the measured profiles at the inside of the limb for the last 3 frames of the HDC 3-shock are noticeably more broadened and less steep than the 1D simulations, implying that significant mixing has occurred.
The parameterized Abel inversion was applied to the measured OD profiles shown in Figs. 8(a) and 8(d), producing the profiles shown in Figs. 8(c) and 8(f). These profiles further demonstrate the difference in stability between the two experiments: The lower gradient of the HDC 3-shock mix region and greater contribution from the innermost linear sections is a clear indication that this experiment experienced more mix than the CH(Si) 2-shock experiment.
The profiles were then analyzed in the manner described in Sec. III to calculate the mix width W as a function of the fraction of mix mass m. The mix width containing 50% and 75% of the total mix mass (m = 0.5 and 0.75) is then plotted as a function of limb radius in Figs. 9(a) and 9(b), respectively. This shows that the mix widths for the stable CH(Si) 2-shock are indeed small, with half the mix mass within a width W 5 μm at peak velocity. However, it does suggest there is some small amount of mix even for this very stable platform. Further modeling of the stable CH implosions using HYDRA combined with a fall-line mix model45 demonstrated that this platform can undergo a small amount of ice–ablator mix and yet still produce a 1D-like DSR, i.e., the small (but non-zero) mix widths shown here are compatible with the 1D-like nuclear measurements discussed in Ref. 41. Another interpretation for the finite width of the mix region is a density gradient resulting from pressure equilibration across the interface.
As expected, the mix widths for the unstable HDC 3-shock are significantly larger and are ∼2–3× larger than the CH(Si) 2-shock (disregarding the stagnation-time radiograph) for both m = 0.5 and 0.75.
V. STRATEGIES TO REDUCE MIX IN HDC CAPSULES
As discussed in previously, dopants are typically added to the capsule to reduce pre-heat at the ice–ablator interface. For HDC capsules on NIF the dopant is tungsten at atomic fractions between ∼0.2%–0.4% and has typically been added as a buried layer14,46,47 set back from the ice–ablator interface. This design leaves an undoped layer of ablator in contact with the ice with the intent that this layer remains dense having been shielded from hard x-rays.
The HDC 3-shock experiment discussed in Sec. IV used an undoped capsule to intentionally decrease stability. This was a THD repeat of an experiment discussed in Ref. 14, in which a doped (N160313)/undoped (N160120) pair of experiments were conducted to explore the effect of dopant on compression. The radiographic mix measurement technique was applied to a THD repeat of N160313, the doped experiment in Ref. 14, to investigate the effect of this dopant strategy on stability at the ice–ablator interface. This HDC(W) 3-shock experiment (N190902) used the same drive and Hohlraum design as the undoped HDC 3-shock experiment, the capsule had the same inner and outer radii, and the THD layer was the same thickness. The inner ∼5.5 μm of HDC ablator was undoped, followed by a ∼21 μm thick layer doped with tungsten at 0.25% (atomic fraction). The outer ∼39.5 μm of the capsule was undoped.
Increasing the adiabat is another strategy to improve stability. While the 3-shock platform has an adiabat of ∼2.5 and aims to achieve high convergence, the “Bigfoot” platform46 uses an adiabat of ∼4, which compromises convergence for increased stability. To understand how increasing the drive adiabat builds upon the stabilizing effect of doping the capsule, the radiographic mix measurement technique was applied to an experiment that used a Bigfoot drive. The capsule was the same design as the HDC(W) 3-shock experiment described above, with a 40 μm THD layer. This subscale “HDC(W) Bigfoot” experiment also maintained the same Hohlraum dimensions as the HDC(W) 3-shock, but used gold instead of uranium.
Figure 7 shows that as dopant is added to the capsule the HDC(W) 3-shock maintains a stable Atwood number for a significantly longer period of the implosion than the undoped HDC 3-shock. Maintaining the same dopant profile, the higher adiabat of the HDC(W) Bigfoot experiment extends the period of stability further still. The sequence of radiographs obtained for the HDC(W) 3-shock and HDC(W) Bigfoot experiments are shown in Figs. 3(c) and 3(d), respectively.
Azimuthally averaged OD profiles for the HDC(W) 3-shock and HDC(W) Bigfoot experiments, together with 1D HYDRA simulations, are shown in Figs. 10(a) and 10(c), while normalized profiles are shown in Figs. 10(b) and 10(d). From broadening of the inner limb region, it appears that both shots underwent considerable mixing.
These OD profiles were analyzed in the same manner as the previous experiments and the results included in Figs. 9(a) and 9(b), showing the mix width containing 50% and 75% of the total mix mass (m = 0.5 and 0.75) plotted as a function of limb radius.
The first impression of these results is concerning, as the mix widths for the HDC(W) 3-shock and HDC(W) Bigfoot appear no different, on average, than for the undoped HDC 3-shock, which is not expected from modeling. However, this result highlights a limitation of using a radiographic method to measure the inner limb profile of capsules that use a buried layer dopant profile: The mix measurement is only accurate when it is reasonable to assume that the opacity κ of the ablator does not change significantly across the inner region of the limb profile. When this assumption holds, the inner region of the profile represents a change in ρ alone, and the profile represents how ablator is mixing into the ice. However, when there is an inner layer of undoped ablator followed by a doped layer, the assumption that opacity is constant in this region is no longer reasonable. Any mixing of the doped ablator inwards into the undoped ablator means that there will be a strong opacity gradient across the inner region of the limb, and in this case the is dependent upon both κ and ρ rather than just ρ. This means that it is no longer possible to isolate how much the ablator has mixed into the ice, and any doped–undoped opacity gradient will dominate the gradient resulting from actual ice–ablator mix. A simple way to frame this problem is that, with a buried layer dopant profile, at the time the radiograph is captured the actual distribution of the dopant is unknown.
There is direct evidence for mixing between the inner undoped and doped layers in the OD profiles for the HDC(W) Bigfoot experiment shown in Figs. 10(c) and 10(d), since the data do not contain a second, outer OD peak predicted by the simulation: In the simulation, this second peak (e.g., at ∼265 μm in the simulation of the first radiograph) occurs because the radius at which there remains unablated material extends past the inner undoped layer and into the doped layer, resulting in increased opacity. That this feature does not appear in the data suggests that the inner undoped and doped layers are no longer separated, and that doped material has mixed inwards. The higher drive in the HDC(W) 3-shock experiment means that at the time the radiographs are captured all the material from the doped layer should have been ablated, hence the absence of the second OD peak in the simulation for this experiment. However, since the HDC(W) 3-shock is predicted to be less stable than the HDC(W) Bigfoot it should be expected that the inwards mixing of doped material into the inner undoped layer also occurs in this experiment. This is supported by the plots in Figs. 10(a) and 10(c), which show that in both experiments the measured peak OD is higher than in the simulations, consistent with the presence of higher opacity doped material present at smaller radii than in the unmixed case.
This issue means that the data shown for the HDC(W) 3-shock and HDC(W) Bigfoot does not accurately represent mix at the ice–ablator interface. This problem is not present when the ablator is either undoped or uniformly doped and so does not apply to the CH(Si) 2-shock or HDC 3-shock experiments. This likely means that the HDC(W) 3-shock and HDC(W) Bigfoot data cannot be compared directly to the data for the CH(Si) 2-shock or HDC 3-shock experiments. However, the data are still an indicator of how stable the HDC(W) 3-shock and HDC(W) Bigfoot are relative to each other in terms of mixing across the inner doped–undoped interface: While the buried layer of dopant will act to stabilize the ice–ablator interface by keeping the innermost undoped layer cold and dense, the dopant layer itself will undergo pre-heat and experience a density decrease. This creates an unstable interface between the innermost undoped layer and the doped layer, causing mix between the two layers. The high opacity of the doped material relative to the undoped material means that the mix region in the profiles better represent mix at the doped–undoped interface rather than at the ice–ablator interface. On the whole, there appears to be little difference between the stability of these two W-doped experiments, although the HDC(W) Bigfoot does appear to have a lower mix width compared to the HDC(W) 3-shock at radii >200 μm. This could suggest that the Bigfoot drive improves stability over the 3-shock drive earlier in time, but that the higher adiabat is not effective at maintaining stability later in the implosion.
Essentially, the effectiveness of a buried layer dopant profile to reduce ice–ablator mix cannot be determined accurately via radiographic measurement. The addition of a doped layer might reduce mix at the ice–ablator interface, and the improved DSR of the doped vs the undoped experiments in Ref. 14 is consistent with this. However, as discussed in Sec. I, changes in DSR can occur from causes unrelated to mix. A measurement of the effectiveness of a buried layer dopant could potentially be made using a version of the separated-reactants mix-measurement platform presented in Ref. 48 if it could be adapted to use in HDC capsules.
Recently, capsule designs have begun to incorporate a dopant profile in which the tungsten dopant extends all the way to the ice–ablator interface.49 This “W-inner” dopant profile is expected to reduce mix since it eradicates the potentially unstable innermost doped–undoped interface present in the buried layer design. At peak velocity, the capsule material present at radii smaller than the ablation front (the remaining mass) will be uniformly doped, and therefore, the radiographic mix measurement technique can be applied without the uncertainty associated with the mixing of doped and undoped material described above.
Extending the dopant inwards to the ice–ablator interface increases the integrated path length through doped material for the backlighter. Additionally, some designs require W-inner dopant concentrations of 0.4% and possibly higher. This will significantly increase the OD of the capsule. In order to maintain contrast on the inner edge of the limb, radiography of these experiments will require use of a 9.0 keV backlighter since this energy has significantly better transmission through tungsten than the 7.2 keV platform described here. The design and characterization of this 9.0 keV CBI platform, which uses a Zinc cavity backlighter source, will be described in a future publication.
VI. DISAGREEMENT BETWEEN MEASURED AND SIMULATED LIMB OPACITIES
The narrow bandwidth of CBI allows the opacity of the capsule to be compared to simulations without uncertainty regarding the spectral content of the radiograph.
When the OD predicted by 1D HYDRA simulations are compared to the CH(Si) 2-shock experimental data in in Fig. 8(a), it can be seen that the simulation significantly over-predicts the opacity of the limb. As discussed in Sec. III, the OD of the experiment is matched to the simulation at R = 400 μm, but the CH(Si) 2-shock profiles in Fig. 8(a) show that regardless of whether the experiment is matched to the simulation at R = 400 μm or R = 0 μm the peak OD would still be overestimated in the simulation. With the match performed at R = 400 μm, the peak OD of the pre-stagnation CH(Si) 2-shock measurements is overestimated by the simulation by ∼34%–66%.
This is unlikely to be the result of an error in the analysis procedure or some instrumentation effect, as it was verified that the radiography platform and analysis methods measured the correct OD to within ∼10% when applied to static (undriven) test objects.
Reference 50 reports on x-ray scattering measurements that found the average carbon ionization state for ICF relevant conditions on the NIF was higher by ∼1 than widely used models, a significant amount. The implication is that the population of carbon with remaining K-shell electrons is lower than models predict, which would result in reduced opacity. This could explain the disagreement between measurement and simulation observed in the experiments presented here.
Figure 8(c) shows that this phenomenon does not appear to be as pronounced for the HDC 3-shock experiment: the simulation overestimates the peak OD by only ∼12%–17% for the four radiographs. This mild discrepancy is complicated by the large amount of mixing in this experiment: mixing potentially reduces peak OD by broadening the capsule limb, but mixing can also increase peak OD if the ablator material cools as it mixes into the ice layer and the carbon ionization state is lowered. In this regard, the CH(Si) 2-shock experiment is a clearer indication of a potential opacity issue, as the stable implosion should be well represented by the 1D simulation. That said, the presence of dopant in the CH(Si) 2-shock experiment again complicates the interpretation: at first glance the fact that the over-prediction of OD is much larger for the doped CH(Si) 2-shock than the undoped HDC 3-shock suggests that the dominant issue may be the opacity model for the Si dopant, and not for carbon. However, the significantly higher Z of silicon (compared to carbon) means that differences in the ionization state on the order of those observed in Ref. 50 are unlikely to produce the changes in opacity required to explain the disagreement observed between the CH(Si) 2-shock data and simulation. A potential mechanism that may contribute here is the silicon dopant becoming heated by absorbing high-energy components of the Hohlraum drive, in turn causing the carbon to become heated, increasing its ionization state and reducing its opacity.
The drive for the CH(Si) 2-shock was investigated as a potential reason for reduced opacity, as the laser remains on all the way until stagnation. This means that at the time the radiographs are captured the laser is at full power, which in gold Hohlraums results in significant emission of non-thermal M-band emission (2–3 keV). Absorption of this high-energy component of the drive by the remaining ablator material and/or dopant could potentially drive ionization, reducing opacity. By comparison, the laser drive for the HDC 3-shock ended ∼1.2 ns before the first radiograph was captured, allowing plenty of time for the Hohlraum plasma to cool and cease emitting M-band. Additionally, the HDC 3-shock experiment used a bare depleted uranium Hohlraum, which have been shown to significantly reduce M-band emission compared to gold Hohlraums.51 While HYDRA simulations do attempt to model M-band, if this is not accurately reproduced then it might explain the opacity disagreement for the CH(Si) 2-shock experiment and also why there is less disagreement for the HDC 3-shock experiment.
To test whether opacity in the CH(Si) 2-shock experiment is affected by the presence of M-band, the experiment was repeated with the laser pulse truncated 300ps before the first radiograph was captured, providing time for the gold plasma to cool enough to cease emitting M-band x-rays. Radiographs of the truncated-pulse experiment (N210228) were captured at the same time and range of radii as for the original experiment (N190714). However, the limb OD was observed to be approximately the same between the two experiments over the full range of measured radii. This suggests that the presence of M-band during the original CH(Si) 2-shock experiment does not affect opacity significantly, and does not explain the disagreement between the simulation and the experiment. Note that the radiographs from the truncated-pulse CH(Si) 2-shock experiment (N210228) were not analyzed to measure mix, since an issue with the SLOS camera resulted in an uncertain, extended integration time. This renders the mix analysis too uncertain to be useful. However, the effect of this diagnostic issue on the peak OD is sufficiently minimal that comparison of OD with the original CH(Si) 2-shock experiment (N190714) is still valid.
The complicated interplay of competing effects in the CH(Si) 2-shock and HDC 3-shock experiments makes it difficult to definitively rule out any particular reason for the observed opacity disagreement: This requires dedicated experiments to investigate opacity effects, which was not the original goal of the experiments described here. For example, to eliminate potential temperature and density gradients resulting from ice–ablator mix, experiments to investigate carbon opacity should not feature an ice layer.
VII. CONCLUSIONS
The interface between the capsule ablator and fuel ice layer is susceptible to hydrodynamic instabilities. The subsequent mixing of hot ablator material into the ice reduces fuel compression at stagnation and is a candidate for reduced capsule performance. While DSR is used to infer the areal density of the fuel, reduced DSR can have underlying causes unrelated to ice–ablator mix, and therefore it is important to develop a method by which mix can be measured directly. Combining the Crystal Backlighter Imager with the single line of sight camera and a novel high-efficiency backlighter source provides the National Ignition Facility with a narrowband, high spatial, and temporal resolution 7.2 keV radiography system that can be used to directly measure ice–ablator mix.
Analysis of radiographic data via a parameterized forward-fitting Abel inversion technique provides measurements of how far a given fraction of the mix mass penetrates inwards into the fuel from the ice–ablator interface. The sensitivity of this mix measurement technique was demonstrated by applying it to a pair of layered experiments in which the stability of the ice–ablator interface was expected to vary significantly. In these experiments the stability was controlled by varying the ablator material, the capsule dopant (to control pre-heat at the ice–ablator interface), and the adiabat of the drive. The results indicate that the radiographic mix measurement platform has the sensitivity to readily distinguish between these two cases.
Comparison of the data from these experiments with 1D HYDRA simulations suggests that the peak opacity of doped capsule implosions is sometimes significantly over-predicted. It was hypothesized that the amount of M-band present at the time of the radiographic measurement might affect the degree of ionization of K-shell electrons, thereby affecting opacity. Additional experiments tested this by reducing the M-band present during the measurement, but no effect on opacity was observed.
Experiments were conducted with HDC capsules employing a buried-layer dopant profile. This dopant design leaves an undoped layer of ablator in contact with the ice. It was found that radiographic techniques are unsuitable for measuring ice–ablator mix with buried-layer dopants, as any opacity gradient resulting from mix across the innermost doped–undoped ablator interface will dominate the gradient resulting from actual ice–ablator mix. However, these measurements were able to demonstrate that there appears to be significant mix at the innermost doped–undoped ablator interface, which may feedthrough to exacerbate mix at the ice–ablator interface.
ACKNOWLEDGMENTS
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Gareth Neville Hall: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Project administration (supporting); Resources (equal); Software (equal); Supervision (supporting); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). David Kenneth Bradley: Conceptualization (equal); Project administration (supporting); Supervision (supporting); Validation (supporting); Writing – review & editing (equal). W. W. Hsing: Conceptualization (equal); Project administration (supporting); Supervision (supporting). Riccardo Tommasini: Investigation (supporting). Nobuhiko Izumi: Investigation (supporting). S. Le-Pape: Investigation (supporting). Laurent Divol: Investigation (supporting); Validation (supporting). Christine Krauland: Formal analysis (supporting); Investigation (equal); Resources (equal). Nathaniel Thompson: Investigation (supporting); Resources (equal); Writing – review & editing (equal). Edwin Casco: Investigation (supporting); Resources (equal). M. J. Ayers: Investigation (supporting); Project administration (supporting); Resources (supporting). Christopher Weber: Conceptualization (equal); Data curation (equal); Formal analysis (lead); Investigation (supporting); Methodology (equal); Project administration (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Sabrina Nagel: Investigation (supporting); Resources (supporting). Arthur Carpenter: Investigation (supporting); Project administration (supporting); Resources (equal). Emily Hurd: Formal analysis (supporting); Investigation (supporting); Project administration (supporting); Resources (equal). Matthew Dayton: Formal analysis (supporting); Investigation (supporting); Resources (equal). K. Engelhorn: Formal analysis (supporting); Investigation (supporting); Resources (equal). Joe Pierce Holder: Formal analysis (supporting); Investigation (supporting); Resources (equal); Writing – review & editing (equal). V. A. Smalyuk: Conceptualization (equal); Investigation (supporting); Methodology (equal); Project administration (lead); Supervision (lead); Validation (supporting); Writing – review & editing (equal). Otto L. Landen: Conceptualization (equal); Investigation (supporting); Methodology (equal); Project administration (equal); Supervision (equal); Validation (supporting); Writing – review & editing (equal). Clement Trosseille: Data curation (supporting); Formal analysis (equal); Investigation (supporting); Methodology (supporting); Resources (equal); Software (equal); Validation (equal). Arthur Pak: Conceptualization (equal); Investigation (supporting); Methodology (lead); Project administration (equal); Supervision (equal); Validation (supporting); Writing – review & editing (equal). Edward Paul Hartouni: Formal analysis (supporting); Supervision (supporting). Edward Marley: Formal analysis (supporting); Resources (supporting). Tina Ebert: Data curation (supporting); Formal analysis (supporting); Software (supporting); Writing – review & editing (equal).
DATA AVAILABILITY
Raw data were generated at The National Ignition Facility. The data that support the findings of this study are available from the corresponding author upon reasonable request.