Emission phases of implosion sources for x-ray absorption fine structure spectroscopy

Spherical implosions are a fundamental platform for studying inertially confined plasmas because the convergent geometry amplifies the achievable pressure.^1–3 Thin shell implosions have long been studied using simplified physics models providing intuition for high-performance applications such as inertial confinement fusion (ICF);⁴ however, their ability to act as bright, broadband x-ray sources make them a compelling probe for absorption spectroscopy.^5,6 This paper focuses on characterizing the x-ray emission phases of thin plastic shell implosions and the impact of these phases when using these shells as x-ray sources for studying high energy density (HED; pressures>100 GPa⁷) matter.

Materials under HED conditions are present in both astrophysical bodies and laboratory experiments, making a detailed understanding of the material's properties under these conditions critical to a wide range of topics from astrophysics and planetary science^8,9 to ICF.^10,11 Modern laser facilities provide platforms to study materials compressed to hundreds or thousands of GPa,^12–15 where innovative measurement techniques and diagnostics are continually developed^16,17 to improve the characterization of these materials.

X-ray absorption fine structure (XAFS) spectroscopy^18–20 is a diagnostic technique sensitive to the local atomic arrangement and chemistry of materials and has been extended to the HED regime to infer material temperature.^5,21–23 XAFS is commonly divided into two subcategories: extended x-ray absorption fine structure (EXAFS) spectroscopy, which measures the modulations in the absorption coefficient above an absorption edge to characterize the crystallographic structure, inter atomic distances, atomic vibrations and ultimately the ion temperature of the material,^5,20,24 and x-ray absorption near edge spectroscopy (XANES),²⁵ which provides information on the oxidation state,²⁶ available electron transitions,²⁷ electron temperature,^28,29 and melting.^30,31

XAFS spectroscopy requires a well-characterized x-ray radiation source to produce the absorption spectrum of the material under study. At large laser facilities, and in particular, at the Laboratory for Laser Energetics' (LLE's) OMEGA Laser System,³² spherically driven implosions are often used as x-ray sources for these studies.^{5,21–23,33,34} These spherical implosions must satisfy four primary criteria. First, the spectrum must be broadband and structureless because XAFS measurements cover ∼1 keV around the absorption edge.²⁰ Second, the source must be bright, on the order of 10¹² photons/eV/sr,³⁵ to perform single-shot transmission measurements, which are subject to attenuation through the measured material. Third, the source must be small, on the order of hundreds of micrometers, to allow for high spectral resolution, which is often governed by source-size broadening for flat crystal spectrometers.³⁶ Finally, the emission must have a short duration relative to the dynamics of the system to probe the sample at a uniform thermodynamic state. For capsule implosions, this duration is of the order of hundreds of picoseconds.^5,23

Previous work has characterized the performance of implosion backlighters for XAFS experiments on large laser facilities. Early XAFS experiments on OMEGA measured the x-ray fluence and emission duration for 16-μm-thick, 850-μm-outer-diam (OD), 0.1 atm-Ar–filled plastic shells.³³ Later work switched to 9-μm plastic shells as the x-ray source,^5,23 and similar work developing x-ray sources has been completed at the National Ignition Facility (NIF).^6,37 Capsule implosions are also of interest for experiments outside of XAFS, such as opacity measurements,³⁸ and doping of the plastic shells has been investigated to improve the x-ray output.³⁹ 

This work presents a comprehensive characterization of implosion GDP (glow-discharge polymerization) backlighters on the OMEGA laser, including a detailed measurement of the temporal, spatial, and spectral nature of the x-ray emission measured by a variety of diagnostics across multiple experimental campaigns. In addition, we will discuss improvements to the x-ray emission of GDP shells where the total x-ray fluence was doubled through changes to the laser drive on the shell.

Experiments were carried out in four different configurations on the OMEGA-60 Laser system. The target and laser details for each configuration are shown in Table I. The laser pulse shape for all experiments was a 1 ns square pulse. Configurations A, B, and C (in Table I) used SG5 distributed phase plates (DPP's)⁴⁰ and configuration D used SG5-650 DPP's. The beam profile from the DPP's can be approximated as a super-Gaussian,⁴¹ where, for the SG5 DPP's, the radius that encloses 95% of the energy is $r95=417$ μm and the exponent power is n = 4.7 and, for the smaller SG5–650 DPP's, $r95=337$ μm and n = 4.2.

A subset of the OMEGA-60 beams was used to drive the shell, which resulted in a nonuniform laser intensity. To increase the laser uniformity on the shell, the laser pointing was adjusted in configurations C and D. This beam pointing was calculated in SAGE,^42,43 a 1D or 2D hydrodynamics simulation coupled to a 3D ray-tracing code using an algorithm designed to compensate for missing beams.^44,45 Table I shows the standard deviation (⁠$σI$⁠) in the absorbed laser intensity normalized by the mean laser intensity for each of the four configurations, where σ_I was based on calculations made at 400 ps into the experiment. In configurations A and B, no laser repointing was conducted and the laser uniformity was determined by the available beams driving the shell.

The Rowland (Yaakobi) x-ray spectrometer (XRS)³⁶ measured the time-integrated spectrum for all four experimental configurations. A flat, 2-cm-wide Ge (111) crystal was used to measure the spectrum from 4.6 to 8.1 keV. A 101.6-μm beryllium blast shield was placed in the front of the spectrometer to protect the crystal from debris. Aluminum filtering 25–75 μm was also placed in the front of the XRS to attenuate the signal to below saturation levels, while iron, vanadium, and/or cobalt was placed on one third of the open aperture to allow for spectral calibration. The spectrum was recorded on BAS-MS image plate covered with a 12.7 or 25.4-μm beryllium light shield. The image plate was scanned at a sensitivity of 1000 with 50-μm pixels on a Typhoon FLA 7000 scanner as soon as possible after the experiment (typically 20–30 min after shot time).

A static pinhole camera array (SPCA) measured the time-integrated spatial profile for configurations B, C, and D. The SPCA had a set of 16 pinholes at a magnification of $12×$ that projected onto an image plate. Each pinhole was made up of a 10-μm-diameter hole in 50.8-μm-thick Ta supported by a 270-μm-diameter, 0.50-mm-thick Ta collimator. The 16 pinholes were filtered in pairs with eight different filter sets.⁴⁶ Three of the filter sets were Al[101.6]Fe[12.5], Al[101.6]Cu,¹⁰ and/or Al[50.8]Ti[25.4], where the filter thickness units were in μm. The Fe and Cu filters were used as an approximate ROSS filter pair,⁴⁷ allowing for an energy range of 7.1–9.0 keV to be isolated in the image, where the Fe and Cu foil thicknesses had an uncertainty of $±15%$⁠. The Al[50.8]Ti[25.4] pinholes were used to characterize the change in core stagnation size due to repointing the beams. For configurations C and D, the data were recorded on a BAS-SR image plate; BAS-MS was used in configuration B. The image plate was covered with 25.4 μm of Kapton and generally scanned at a sensitivity of 1000 and a pixel size of 25 or 50 μm on a Typhoon FLA 7000 scanner as soon as possible after scanning the XRS image plate (typically 25–35 min after shot time).

The time-resolved spatial profile was measured using a pinhole array coupled to a framing camera.⁴⁸ The pinhole array had a magnification of $6×$ and four rows of 10-μm-diam pinholes, where the first row had seven pinholes and each of the last three had 13 pinholes for a total of 46 pinholes. The four strips of the framing camera were aligned so that each row of pinholes illuminated one framing camera strip with the seven-pinhole row illuminating the earliest time strip. Each strip had an exposure duration of 200 ps and was adjusted in time and bias to map out all of the phases of the x-ray emission. The pinholes had a 254-μm beryllium blast shield, and the framing camera had a 25.4-μm aluminum rear filter. The framing camera was primarily sensitive to x rays between 4 and 7 keV and all images were recorded onto a charge-coupled-device (CCD) camera.

For configuration C only, the time-resolved spectrum was obtained using a streaked x-ray spectrometer (SXS) attached to an x-ray streak camera model A (SSCA).⁴⁹ A pentaerythritol (PET) (002) crystal was used to cover the energy range of 6.7 to 8.7 keV and a 127-μm beryllium blast shield protected the crystal from debris. Iron and aluminum filtering attenuated the signal and provided spectral calibration. The SSCA used a solid KBr photocathode with a 1000-μm slit to convert the spectrally dispersed x rays into electrons, which were then swept in time over a 4-ns window. The streak camera dwell time per pixel was calibrated using a timing laser fiducial, and the timing relative to the target laser was determined by correlating peak emission with the framing camera data with an uncertainty of ∼50 ps. The spectrum was recorded on T-Max 400 film with an LLE step wedge to convert the image to exposure, a unit proportional to photons^50,51 and scanned with $20 μ$m pixels. From the slit width, pixel size, and dwell time per pixel, SXS has an estimated temporal resolution of 130 ps.

Three experimental x-ray emission phases consisting of the corona, core stagnation, and afterglow are apparent both in the experiments and post-processing hydrodynamic simulations. During the corona phase, the laser illuminates the shell producing x-ray emission and driving a shock through the shell, causing the material to release inward. When the remaining material reaches the center, it stagnates, reaching Gbar pressures and producing a bright x-ray flash. After stagnating, the remaining material decompresses at Gbar pressures, remaining hot enough to emit x rays for a brief period of time. A schematic of each x-ray emission phase is shown in Fig. 1.

The time and spatially resolved x-ray diagnostics combine to demonstrate and characterize the three x-ray emission phases. The time-integrated spatial profile, shown on a log scale in Fig. 2, indicates three concentric regions of emission. The central bright spot is emission from the core flash. The diameter of the outer diffuse emission approximately agrees with the initial target diameter, shown as the dotted white line in Fig. 2, indicating that this emission is from the corona as the shell travels inwards. Although the corona emission is dim relative to the core stagnation, the large emission region makes it a non-negligible contribution to the total x-ray signal. The middle emission region with a diameter of ∼300 μm is primarily attributed to signal passing through the pinhole substrate, producing an image of the collimator.

The fraction of the signal from the core stagnation and corona emission phases was extracted from the time integrated image, shown in Fig. 2. In each image, the core emission was isolated along with the collimator emission. The remaining corona emission was assumed to be constant in the central region. By isolating the core and corona and taking the difference between the signals in the copper and iron filters, the signal was approximately isolated to the energy range of 7.1–9.0 keV. The ratio of the corona emission to the total signal from the corona and core emission was measured for two shots in configuration C and one shot in configuration D to be $13±3%$⁠.

Each of the three emission phases are shown in the time resolved spectrum. The raw streaked x-ray spectrum was converted to photons,^50,51 integrated in energy between 7 and 8 keV and plotted along with the normalized laser energy in Fig. 3(a) (red and blue curves, respectively). The data show that the corona emission begins just after 0 ns when the laser turns on, and a kink in the data at point I indicates when the core flash starts dominating the emission.

The time-resolved spatial profile of all three x-ray phases was measured using the framing camera data. Figures 3(b)–3(d) show images of the corona at 0.31 ns, core stagnation at 1.07 ns, and afterglow at 1.26 ns for a shot in configuration D, where the color scale on the all three images was adjusted for visibility. X rays from the core flash were bright enough to not be fully gated in time and were masked from the center of the corona and afterglow images [Figs. 3(b) and 3(d)]. Average radial lineouts were extracted from each of the images, adjusted for the framing camera strip bias, and normalized to the core stagnation signal. Finally, the radius of the shell as a function of time was extracted from the images and is shown in Fig. 3(a) (black circles, right axis). The peak x-ray emission was used as the radius for the corona, the 17% contour was used as the radius for the core stagnation, and afterglow radius was found by approximating a circle that encompassed the afterglow emission.

To estimate the duration of the core flash, the signal in the framing camera strips containing emission from the core was measured for each image. This signal was fit^3,52,53 assuming a Gaussian model with additional parameters to account for uncertainty in the bias conversion between framing camera strips. Using data from configurations A, B, and D, the average full width at half maximum (FWHM) of the emission was measured to be 84 ± 7 ps. An example of the core emission signal is shown as the red circles in Fig. 3(a).

The x-ray emission of the plastic shells was simulated by post-processing the output from the 1D hydrodynamics code LILAC.⁵⁴ The simulated plastic shell had an 865-μm OD and was 9 μm thick with a vacuum fill. The simulation was run in a spherical geometry with 24 kJ of laser energy symmetrically distributed on the surface and an experimental 1-ns square laser pulse, shown in Fig. 3(e). The simulation had 250 zones in the plastic shell and a maximum time step of 0.1 ps.

The bremsstrahlung emissivity (⁠$Jν$⁠) was calculated from the electron density (⁠$ne$⁠) and temperature (⁠$Te$⁠) using^3,55

where e is the electron charge, $ε0$ is the permittivity of free space, $me$ is the mass of the electron, $Z¯$ is the average ionization state, k is the Boltzmann constant, c is the speed of light, h is Planck's constant, and ν is the photon frequency.

Figure 3(e) shows the incident laser power on the shell, the normalized x-ray power, and the radius of peak x-ray emission as functions of time. The x-ray power was simulated through similar filters as SXS-SSCA and integrated between 7 and 8 keV. The x-ray power shows significant changes in the slope at points I and II, indicating the beginning and ending of the core dominated emission. The simulated x-ray power does not include a correction for the SXS-SSCA temporal resolution; therefore, the width of the simulated emission peak has a shorter time duration than in the experiment.

Figures 3(f)–3(h) show time slices of the electron temperature, shell density, and simulated framing camera images at the same three times as shown in Figs. 3(b)–3(d). The core reaches a maximum temperature of around 8.5 keV while the corona has a temperature of around 3 keV. The synthetic framing camera images were produced by assuming spherical symmetry, ignoring absorption, and Abel transforming the x-ray emission onto an image plane, taking into account the framing camera's instrument response. The color scales in the framing camera images were adjusted for visibility.

The hydrodynamic simulation helps verify the mechanisms behind the three different x-ray emission phases, which are in qualitative agreement with the experimental results. In the corona phase, there is a hot ablation plasma but the shell is still formed and dense, producing a ring of emission on the framing camera. The core stagnation emission occurs when the shell material reaches the center, and the afterglow is due to the remaining material expanding outward.

In order to quantify the signal in each emission phase from the time resolved spectrum, models of each phase were bench-marked using the hydrodynamic simulation. Each of the three emission phases can be seen in the calculated bremsstrahlung emission, shown as a function of position and time in Fig. 4(a). In this figure, the bremsstrahlung emissivity was calculated using Eq. (1), integrated between 7 and 8 keV, interpolated onto radial $1 μ$m zones and weighted by the volume of each $1 μ$m zone to obtain units of ph/s. The three emission phases were isolated in this image by dividing the image into regions of position and time. The core radial cutoff was assumed to be the radial distance corresponding to 25% of the peak signal. The separation between the corona and afterglow phases was determined by starting from the time of peak core emission and drawing a line to the critical surface corresponding to the time when the laser pulse, shown in Fig. 4(b), was at 25% of its maximum. At radial distances larger than this critical surface point, the separation between corona and afterglow was assumed to be at a constant time. The spatially integrated emission along with the contributions from each emission phase are plotted as functions of time in Fig. 4(b).

Each emission phase was modeled separately using semi-analytic models. The corona emission was assumed to be temperature dominated so that the emission due to the corona $Jcorona$ was given by

where p(t) was the laser power at time t, $rcrit(t)$ was the radius of the critical surface at time t, and τ was used as an approximate temperature taking the form for $Jcorona$ from Eq. (1). For the experimental data, $rcrit$ was taken from the framing camera radius as a function of time, shown in Fig. 3(a). The core flash was assumed to be a Gaussian distribution, confirmed by the measured framing camera data in Fig. 3(a),

Finally, the afterglow model was assumed to be density dominated, where the shell started with a radius of $50 μ$m and expanded self-similarly (⁠$r∝t3/2$⁠),

and

where η_e was used as an approximate density taking the form for $Jafterglow$ from Eq. (1). Therefore, the total emission model was given by $Jmodel=Jcorona+Jcore+Jafterglow$ with free parameters A₁, B₁, A₂, μ₂, σ₂, A₃, v₃, and t₃. A Bayesian inference routine^3,52 was used to fit the data. During the fitting routine, a constraint forced $t3>μ2$ so that the afterglow would not start until after the core flash. Using a Gaussian likelihood and a sequential Monte Carlo sampler,⁵³ the posterior distributions for each of the free parameters was determined. The results of the fit are shown in Fig. 4(c) and the fractions of each of the emission phases are shown in Table II. Good agreement between the initial fractions and the results from the fit indicate that our model replicated the system well.

The data were fit using the models verified with the simulation including a few adjustments to approximate diagnostic resolution and account for constraints from the imaging diagnostics. First, because the streaked spectrometer has a temporal resolution of $130$ ps, $Jmodel$ was convolved with a Gaussian whose FWHM corresponded to 130 ps. Second, the relationship between the core and corona signal, measured with SPCA in Sec. III A, was enforced in the fit. Third, the framing camera's constraint on the FWHM of the core emission was also incorporated into the prior on σ₂. Fourth, the critical surface in the corona model was approximated from the framing camera measurement of radius as a function of time, shown in Fig. 3(a), even though the peak emission radius is smaller than the critical surface late in time. Finally, similar to the simulation fit, $t3<μ2+σ2$ was enforced in the fit to prevent the afterglow from beginning too late in time.

To confirm that the addition of the streaked spectrometer's temporal resolution did not impact the ability to extract signal fractions, the simulation was post-processed assuming the instrument response. The initial fit underestimated the corona and afterglow signals; however, after incorporating constraints on the core emission duration and ratio between the corona and core, the fits recovered the fractions to within a few percent.

To fit the data, lineouts taken in the energy range between 7 and 8 keV from two shots in configuration C were fit to characterize the three emission phases. The normalized data were assumed to have a 5% error along with a constant error of 0.01. The fits were conducted with the same Gaussian likelihood function and sequential Monte Carlo sampler used in Sec. III C 1 and an example fit is shown in Fig. 5. The data are shown in black along with the fit, corona, core, and afterglow models. The fit and model were generated from the median of the posterior distributions of the fit parameters. As illustrated in the figure, the fit captures the behavior of the data over three orders of magnitude. The three modeled phases are shown prior to performing the convolution with the streaked spectrometer's temporal response.

From the fits, we can characterize the signal fraction in each of the emission phases as well as the time duration. The results are shown in Table III.

Different spatial profiles of the x-ray sources directly impact the spectral resolution for x-ray spectrometers. For flat crystal spectrometers, the source size often limits the spectral resolution of the instrument.³⁶ The spectral resolution due to source-size broadening is³⁶ 

where $dEdx$ is the spectrometer dispersion, α is the angle between the x ray and the detector plane, and a is the source size in the detector plane. By approximating the size of the corona, afterglow, and core stagnation as 850, 300, and 50 μm, respectively, the corona can degrade the spectral resolution by $17×$ and the afterglow can degrade the spectral resolution by $6×$ relative to the core stagnation spectral resolution.

Spectral resolution is important for XAFS measurements, which measure the modulations in the absorption coefficient [$μ(E)$],²⁰ 

where I₀ represents the incident intensity on the sample, $It$ represents the transmitted intensity through the sample, and t is the sample thickness. The EXAFS modulations are isolated to obtain²⁰ 

where μ₀ represents the absorption coefficient without neighboring atoms, $k=2meℏ2(E−E0), ℏ$ is Planck's constant divided by 2π, and E₀ is the energy of the absorption edge.

Using XRS as an example XAFS spectrometer, the impact of these three phases on the spectrometer spectral resolution for XAFS measurements can be estimated. The spectral resolution for XRS around the iron K edge was determined using a dispersion of 49 eV/mm³⁶ and $α=52°$ to be 4.0, 23.9, and 67.7 eV for the core stagnation, afterglow, and corona, respectively. When performing a complete XAFS analysis, other impacts to the spectral resolution, such as detector resolution and crystal rocking curve,³⁶ should also be considered. An iron synchrotron absorption spectrum⁵⁶ was assumed to be the spectrum for a point source. To simulate the XAFS spectrum for different source sizes, the point-source absorption spectrum was convolved with a Gaussian function⁵⁷ whose full width at half maximum corresponded to the spectral resolution of each emission phase. The total signal was estimated by adding the signals from all three sources in transmission space while including the fractional weights from Table III.

The XANES spectrum for each of the three phases along with the total signal is shown in Fig. 6(a). While the core spectrum is able to capture the majority of the features of the XANES spectrum, the corona and afterglow phases cannot. This is reflected in the total signal, which is not able to duplicate all of the features in the XANES spectrum. For example, the total spectrum loses the modulation, highlighted with the arrow [in the inset plot], which can be used to distinguish structural changes and melting in iron.³⁰ Furthermore, the slope of the total spectrum is decreased, which must be accounted for when extracting the electron temperature.⁵⁸ Figure 6(b) shows the degraded EXAFS spectra with each of the three phases and the total spectrum. Temperature can be extracted from the damping in the EXAFS modulations and, under the harmonic approximation,²⁴ this damping is given by $e−2k2DWF$⁠, where DWF represents the Debye–Waller factor.^5,20,24 Fitting⁵⁷ the point source and total signal spectra with this harmonic EXAFS approximation, the total signal spectrum has a DWF that is $16±6%$ larger. It should be noted that other spectrometers will have different spectral resolutions for each emission phase and will be impacted differently. Finally, these spectra represent a sample, that is, in a single thermodynamic state for the duration of the backlighter emission. If the material was not in a uniform thermodynamic state, each emission phase could potentially probe the material at a different density, temperature, or crystallographic structure resulting in shifting, amplifying, or decreasing XAFS modulations in unexpected ways.

The experimental setup was adjusted to improve the x-ray performance of the plastic shells. Increasing the laser intensity on the shells resulted in an increase in total x-ray emission. The time-integrated source spectrum was defined as S in units of photons/eV/sr, where^6,36

and $PSLpixel$ represents the measured XRS data, $SIP$ is the image-plate sensitivity in units of PSL/photon⁵⁹ including a correction for x-ray incident angle,^17,T(E) is the filter transmission,⁶⁰ and the spectrometer sensitivity G(E) is defined as

where $dΩdA$ is the solid angle per pixel, $dEdθ$ is the spectrometer dispersion, and R(E) is the crystal integrated reflectivity. During the calculation, a $±15%$ Gaussian uncertainty was assumed on the image-plate sensitivity,^17,59 a $±15%$ uniform uncertainty was assumed on the aluminum filtering thicknesses, and the integrated reflectivity of the XRS Ge(111) crystal was obtained as a function of energy by averaging over two references.^61,62 For configurations A, B, C, and D, 11, 10, 5, and 5 shots were averaged, respectively, and the resulting source spectra are shown in Fig. 7. For configuration D, a filter change was performed to reduce image-plate saturation, resulting in the gap in the data around 7 keV, where three shots were averaged below 7 keV and all five shots were averaged above. The error bars represent the variation of the x-ray signal for all shots and the systematic errors in converting the raw data. In this figure, x-ray spectra from previous measurements^6,63 are also shown as a reference. NIF opacity measurements use similar x-ray sources that are 20-μm-thick, 2-mm-OD polyalpha-methyl styrene capsules driven with 80 TW, which produce ∼$1.2×1012$ ph/eV/sr at 5 keV.³⁸ 

The results from configuration D show approximately a factor-of-2 increase relative to the other experiments conducted on OMEGA. The most significant difference between configuration D and the previous configurations was the change to smaller phase plates, SG5 to SG5-650, resulting in a decrease in the beam profile from $r95=417$ μm to $r95=337$ μm. The smaller phase plates reduce the fraction of laser light that passes the shell in the latter half of the laser pulse, ultimately increasing the laser energy absorbed by the shell. SAGE calculations show an increase in absorption of approximately 20% for configuration D relative to the three other configurations.

Optimizing the laser intensity's uniformity on the plastic capsules generated a more-symmetric implosion, resulting in a smaller core at stagnation. In configuration B, the beams were not repointed and SAGE simulations showed that $σI=21.8%$⁠. The result of the core stagnation, imaged with SPCA through 25.4 μm of titanium and 50.8 μm of aluminum is shown in Fig. 8(a). In configuration D, a beam repoint was performed and SAGE estimates $σI=5.0%$⁠, taking into account the change in phase plates. This improved intensity uniformity resulted in a more-symmetric spot size, as shown in Fig. 8(b). A smaller core stagnation size will improve the spectral resolution of XAFS measurements as discussed in Sec. III D.

The x-ray emission from thin imploding GDP shells was characterized and improved. The corona, core stagnation, and afterglow x-ray emission phases were experimentally identified and confirmed with hydrodynamic simulations, accounting for 12%, 76%, and 12%, respectively, of the total x-ray signal. The corona and afterglow phases are newly measured in this work and have not previously been taken into account. These two phases have different temporal profiles than the core emission, ultimately increasing the backlighter emission's duration. Furthermore, the increased size of these two phases degrades the spectrometer spectral resolution, limiting the ability to perform XANES measurements and impacting the quality of the EXAFS data. Future work includes time-gating the XAFS measurement to avoid these detrimental impacts from the corona and afterglow. Finally, increasing the laser intensity and uniformity on the shell increased the total x-ray emission by a factor of 2 while reducing the core stagnation size. While other x-ray sources based on laser-illumination of foils^63,64 have been considered for XAFS measurements and have been shown to be brighter than the capsule implosion above ∼10 keV, this work illustrates how XAFS measurements in the 7-keV band can be improved using the optimized capsule implosion configuration that we propose here.

This material was based upon work supported by the Department of Energy National Nuclear Security Administration under Award No. DE-NA0003856, the University of Rochester, and the New York State Energy Research and Development Authority. The support of DOE does not constitute an endorsement by DOE of the views expressed in this paper. D.A.C. acknowledges DOE NNSA SSGF support, which is provided under Cooperative Agreement No. DE-NA0003960.

This report was prepared as an account of work sponsored by an agency of the U.S. Government. Neither the U.S. Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the U.S. Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the U.S. Government or any agency thereof. This collaborative work was partially supported under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52–07NA27344.

The authors have no conflicts to disclose.

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