The colliding planar shocks platform to study warm dense matter at the National Ignition Facility

The equation of state (EOS) defines the relationship between thermodynamic state variables. Accurate EOS models are essential to understand material properties and perform high-fidelity simulations. However, such data are notoriously difficult to model in the warm dense matter (WDM) regime. Indeed, complex models are required to describe its properties as this particularly interesting state of matter exhibits partial ionization, significant ion–ion coupling, and comparable thermal, Coulomb, and Fermi energies. For such a state with many competing and interconnected effects, high-quality experimental benchmarks are essential to guide models, but only a few experimental data exist.

WDM exists in the interiors of astrophysical bodies and is produced as a transient state in many high energy density (HED) physics experiments in the laboratory,^1–6 including inertial confinement fusion (ICF) implosions.^7–9 As such, accurate EOS models in the WDM regime are required to predict the interior structure and evolution of astrophysical bodies^10,11 and are critical in the design of ICF implosions.¹² Two specific quantities have been previously identified to strongly constrain existing EOS models in the WDM regime: ionization measurements to improve models for ionization potential depression (IPD)^13–16 and accurate temperature measurements.¹⁷ 

A key difficulty in many experimental investigations is producing a large volume of WDM at uniform conditions that can be accurately determined. Previous measurements of carbon ionization, for example, used x-ray Thomson scattering (XRTS)¹⁸ to probe spherical implosions.^19–21 Spherical implosions enable extremely high pressures to be reached at peak compression; however, the imploded material consists of a wide range of plasma conditions. Such experiments create highly compressed material in the core of the implosion (typically >10 g/cm³), moderately compressed material moving inward behind the shock front (typically 2–6 times compressed), and low-density ablation plasma far below solid density, and all regions contribute to the measured XRTS signal.

In this paper, we describe the colliding planar shocks (CPS) platform at the National Ignition Facility (NIF), designed specifically to reduce the distribution of plasma conditions in the probed volume to make high-precision EOS measurements in the WDM regime. Furthermore, the CPS platform uses both x-ray radiography and XRTS as complementary diagnostics, minimizing the uncertainties arising from relying on a single measurement to constrain the inferred plasma conditions.²² The high-precision data obtained using this platform will help resolve the discrepancies in EOS models and ionization in WDM at a well-defined temperature.

Many material properties, such as energy transport or compressibility, are strongly temperature dependent. Thus, it is extremely important that the temperature is well constrained when comparing theoretical predictions and experimental data, in particular, when the theory benchmarked by the experiment is further employed to model systems such as planetary interiors and for ICF designs. Shock wave experiments, where the EOS is investigated along the Hugoniot, highlight this requirement. Here, different EOS models may result in the same curve in pressure-compression space as the measurements while predicting largely different temperatures for these states. Thus, additional temperature measurements can be extremely useful in discriminating these EOS models.¹⁷ Despite its critical role in determining material properties, very few diagnostics exist that can accurately measure temperature in the WDM regime, and new platforms and diagnostic techniques to fill this need are high priorities for the field.

For pressures where reliable cold curve (isotherm) data exist from static compression experiments, below approximately 10 Mbar, the temperature along the Hugoniot can be constrained by comparing cold curve and shock compression data. At higher pressures where this relation cannot be made, temperature diagnostics become particularly important to inform EOS models. Additionally, more complex loading paths resulting in off-Hugoniot states are not constrained by the Rankine–Hugoniot relation, and precise temperature measurements are required to determine the states created in phase space.

Probing WDM conditions requires penetrating x-rays, which can escape the dense plasma conditions and reach the detector. In the recent decades, a number of diagnostic techniques has been developed: x-ray fluorescence spectroscopy,^23–25 x-ray absorption spectroscopy,^26–28 extended x-ray absorption fine structure (EXAFS),^29,30 x-ray absorption near-edge spectroscopy (XANES),³¹ x-ray diffraction,³² and x-ray scattering.^33–36 All of these approaches require considerable effort to field and have their own advantages and shortcomings, in particular, when used as a temperature diagnostics. The CPS platform uses XRTS in the non-collective scattering geometry, where the scattering is sensitive to the motion of individual electrons. For this platform, the width of the inelastic scattering (Compton) spectrum is influenced by changes in both the Fermi and thermal energy and can be used to infer both the electron density and the temperature of the system.

Ionization is a crucial parameter in plasma physics that affects many important properties of the plasma, such as the EOS, transport properties, and heat capacity. For most conditions, ionization is primarily determined by the plasma temperature. In dense plasmas, the bound states, and accordingly the ionization balance, are further modified by the interaction with the surrounding medium. In general, the electron binding is weakened, which can thus be described by a lowering of the effective ionization energies. For matter at pressures beyond one Mbar, valence and conduction bands become distorted causing significant changes in the typical materials chemistry. At several tens of Mbar, the thermal motion of the ions has a greater impact than chemical bonds. At extreme pressure (e.g., 100 Mbar for CH³⁹), continuum lowering and pressure-induced ionization begin to play a role in the EOS and transport properties of the material.

Ionization models for dense plasmas can be divided into two classes: those that assume a continuous spectrum of states (orbital free) and those that include shell effects, i.e., the discrete bound state energies of ions. The most widely used examples of each case are the orbital free Thomas–Fermi model and the Stewart–Pyatt model.⁴⁰ The latter interpolates between high-density limits and the classical Debye limit for hot, dilute plasmas.

Ionization strongly influences the compressibility and heat capacity of WDM. For example, ionization directly affects the shape of the shock Hugoniot for a given material.^41,42 At shock pressures sufficient to ionize the material, the creation of additional free electrons absorbs energy from the system that would otherwise increase the temperature. Thus, the shock Hugoniot is relatively soft while ionizing due to the reduced temperature of the shocked material, increasing the compressibility of the material.³⁹ 

Carbon is an ideal candidate for a systematic study of shell structure and ionization effects at extreme pressures and temperatures.⁴¹ As one of the most abundant elements in the universe, carbon under extreme conditions is highly relevant for astrophysical objects. For example, many of the recently discovered extra-solar planets have been found to exist in extremely carbon-rich solar systems, despite oxygen being the slightly more dominant mid-Z element in our solar system. As methane and higher order hydrocarbons are thought to dissociate under extreme pressures,⁴³ giant planets in carbon-rich solar systems can have an extremely high concentration of carbon close to the core, while hydrogen is released to the surface (e.g., the supposed “diamond-planet” Cancri 55e⁴⁴ or the very recently discovered 51 Eridani b⁴⁵). Predictively modeling the composition and internal structure of these planets requires accurate EOS models in the WDM regime, and recent theoretical work has shown that ionization models disagree significantly extreme pressures.⁴⁶ 

Several experiments measuring the carbon ionization in CH plasmas have identified significant shortcomings in current ionization models in the WDM regime. Figure 1 shows the experimental results compared to carbon ionization predicted by OPAL,^37,38 the opacity code that is commonly used in modeling ICF capsule implosions. The colors of the experimental data points correspond to the measured ionization state of carbon, which do not agree with the OPAL predictions. Fletcher et al.¹⁹ used an imploding CH shell to show that the charge state of carbon was significantly underestimated at pressures approaching 50 Mbar and temperatures of 5–10 eV, reporting that carbon was stripped to the He-like state at these conditions (Z_C = 4), while OPAL predicts $Z C = 2.0$⁠. Kraus et al.²⁰ spherically compressed a solid CH sphere and measured significantly higher ionization states of carbon than predicted by either the Thomas–Fermi or Stewart–Pyatt models at electron temperatures near 100 eV, measuring an average carbon charge state of $⟨ Z C ⟩ = 4.92 ± 0.15$ compared to $Z C = 4.0$ predicted by OPAL.

Due to the spherical symmetry in these platforms, it was not possible to restrict the x-ray scattering volume to a homogenous region at peak compression. Although significant effort was put in to account for spatial gradients in these experiments,^20,49 this method relies on the accuracy of hydrodynamic models to fit the integrated x-ray scattering signal. The sparse data available in this regime is the primary motivation for the development of the CPS platform at the NIF. The CPS platform aims to provide experimental data to benchmark theoretical models. It is designed to minimize gradients in the plasma conditions to improve measurement precision for the conditions indicated by the red box in Fig. 1.

The primary goal of the CPS platform at the NIF is to create a large, uniform volume of WDM at pressures approaching 100 Mbar that can be accurately characterized using x-ray diagnostics. In the CPS platform, two counter-propagating planar shocks, produced using an indirect drive, collide in a cylindrical shock tube. The experimental platform was designed using a combination of several previously successful platforms at the NIF. The physics package, laser drive, and radiography setup use the fundamental design of the Shock/Shear platform,⁵⁰ and the design of the XRTS shielding was developed for x-ray scattering measurements on the NIF Gbar platform.^20,21,51 The initial design described in this paper uses simultaneous XRTS and x-ray radiography to measure warm dense CH for conditions where ionization models do not agree with existing experimental data. Future iterations of the CPS platform can make similar measurements on other materials of interest and use additional x-ray diagnostic techniques (e.g., x-ray spectroscopy) to interrogate other properties of WDM.

The target, shown schematically in Fig. 2(a), consists of two Hohlraums, a central physics package, and the backlighter assembly. The physics package contains the cylindrical target material with iodine-doped CH (CHI) ablators on each end, placed inside a Be tube with a wall thickness of 250 μm to minimize lateral expansion of the target material during the experiment. Each Hohlraum is driven by 145–260 kJ provided by 56 beams of the NIF using a 4 ns pulse shape. For the first experiments studying CH at solid density, each gold Hohlraum is 4.0 mm in diameter and 3.0 mm in length, with a 2.6 mm diameter laser entrance hole and 50 μm wall thickness. The solid CH cylinder is 1 mm in diameter and 2 mm in length with an initial density of 1.05 g/cm³. The diameter was chosen to optimize the x-ray radiography measurement and the length to ensure that the ablator material does not enter the probe volume of the XRTS measurements but can also be optimized for other target materials.

The 200-μm-thick CHI ablator contains 3 at. % iodine (C₅₀H₄₇I₃) with an initial density of 1.48 g/cm³ to strongly absorb x-rays from the Hohlraum, reducing preheat of the sample material, and to clearly identify the position of the ablator interface in x-ray radiography measurements. The CHI ablators are countersunk into the Hohlraum radiation exit hole (REH) and machined to press directly against the sample material and the Be casing. This design is intended to minimize the propagation of hot, streaming plasma from the Hohlraum interior into the probe volume.

The laser drive for the CPS platform uses a truncated form of the drive developed for the Shock/Shear platform⁵⁰ as shown in Fig. 3. The CPS platform uses the Big Area BackLighter (BABL)⁵² as the x-ray source for both x-ray radiography and XRTS. The backlighter foil stack consists of a 10-μm-thick Zn foil that is directly irradiated by the backlighter beams and a 100-μm-thick CH foil to reduce preheating of the target due to backlighter emission, significantly attenuating soft thermal x-rays while attenuating 9 keV Zn Heα emission by less than 3%. The Zn foil is driven by 16 beams of the NIF with a total of 134 kJ. The backlighter provides both a large area backlighter for x-ray radiography and the source for XRTS measurements. The backlighter beams are tiled over the surface of the backlighter foil to produce a uniform intensity profile over an area of approximately 1 × 1 mm². The backlighter pulse shape is designed to maximize x-ray emission from the backlighter over a 5 ns window to observe the incoming shock wave, the collision of the shocks, and the evolution of the doubly shocked region. The 5 ns backlighter also provides timing flexibility for the XRTS probe.

The backlighter structure consists of a backlighter foil stack, a 3D printed scaffolding, and gold shielding to contain the expanding Zn plasma and prevent background on the XRTS measurements from the direct line-of-sight view of the plasma and secondary scattering from other target components. The design of the radiography aperture between the backlighter and the sample material is shown in Fig. 2(b), restricting the incoming x-rays to a 700-μm-wide region along the axis of the sample and includes four 100 × 100 μm² fiducials to provide spatial calibration of the radiography data.

An additional gold shield blocks the view of the target from the XRTS spectrometer, which has a 700 × 150 μm² aperture to limit the scattering to doubly shocked material. Using both the radiography and XRTS apertures, the scattering volume is restricted to a volume of approximately $700 × 700 × 150$ μm³ in the center of the sample material, significantly reducing the gradients in the plasma conditions due to edge effects in the probed volume. The XRTS spectra are measured by the Mono Angle Crystal Spectrometer (MACS),^47,48 fielded with two cylindrically curved HOPG (highly oriented pyrolytic graphite) crystals coupled to an x-ray framing camera to record scattering spectra at two times per experiment.

We model the system using xRAGE,⁵³ an Eulerian radiation-hydrodynamics code with adaptive mesh refinement, maintained by Los Alamos National Laboratory. The simulation uses a 2D mesh resolved to 1 μm in the ablator and target cylinder, and dezoned as appropriate elsewhere. The EOS is modeled using SESAME^54,55 tabular data for Be and Au, with all plastic components approximated as polystyrene. The simulation further uses SESAME data for heat conduction, and a multigroup diffusion model for the radiation transport.

The simulation is driven using a frequency-dependent radiation source (FDS) at the boundaries of the domain to mimic the x-ray drive from the Hohlraum in the experiment. Since the iodine-doped ablator prevents virtually all x-ray energy for reaching the CH cylinder, the spectral details of the FDS are not particularly important to the compression physics as long as the FDS drives a shock of the correct strength. Therefore, we choose a Planckian profile for simplicity. Benchmarking of the simulation against experimental data are described in further detail in Sec. IV A.

Figure 4 shows results from the xRAGE simulation. In Fig. 4(a), a density map just prior to shock collision is shown. In this frame, the target is oriented in the same direction as the schematic in Fig. 2(a), with the shocks propagating in the vertical direction. Meanwhile, Fig. 4(b) shows the density just after the shocks have collided, and a dense, uniform plasma has been created around z = 0. The volume of plasma probed by XRTS, defined by the overlap of the in-coming radiography aperture and outgoing XRTS apertures, is depicted by the dashed red box in Fig. 4(b). Indeed, the simulations show that we can expect quite homogeneous conditions in the space probed.

Modeling XRTS spectra from a distribution of conditions requires the proper weighting of each condition to be known, typically using the results of hydrodynamic simulations. Although it is possible to extract plasma conditions from integrated measurements,⁵⁶ doing so inevitably requires a model for the distribution of plasma conditions, increasing the uncertainty in the measurement. To avoid relying on the accuracy of hydrodynamic codes and opacity models to account for spatial gradients, the primary goal of the CPS platform is to minimize the range of plasma conditions in the probed volume by creating a uniform plasma.

Figure 4(c) highlights the ability to make high-precision measurements of WDM conditions using the CPS platform, where the distribution of mass densities probed by this setup is given by the red curve in Fig. 4(c). The distribution of densities is significantly narrower using the CPS platform than the corresponding curve for the NIF Gbar x-ray scattering experiment²⁰ that measured warm dense CH, thus improving the precision of the inferred plasma parameters. In this example, the compressed CH has a density of 4.3 $− 0.6 + 1.0$ g/cm³, corresponding to a range of less than ±25% of the average density. Furthermore, the platform uses simultaneous XRTS and radiography to determine the density distribution in the probe volume. By narrowing the distribution of states probed by scattering, the precision of the inferred plasma parameters is significantly improved, providing the resolution required to distinguish between EOS models.

The primary diagnostics for the CPS platform are x-ray radiography and XRTS. X-ray radiography provides both imaging to determine the shock positions as a function of time and a transmission measurement to determine material density and opacity. Although both density and opacity affect the transmission measured by x-ray radiography, both quantities can be constrained when combined with XRTS to measure the electron density, temperature, and ionization state of the compressed material. Additional x-ray diagnostics will be considered in the future, such as x-ray spectroscopy to expand the scope of measurements of the CPS platform.

There are two possible configurations for the x-ray radiography diagnostic on the CPS platform, either 2D imaging using a pinhole imaging system and a gated x-ray detector (GXD) or 1D streaked radiography using an x-ray streak camera. Streaked x-ray radiography provides an absolute EOS measurement for the incoming planar shocks by measuring the shock velocity and density at the shock front using the technique developed in the NIF Gbar campaign,⁵⁷ where the spatial imaging direction would be aligned with the cylindrical axis of the CPS platform. In order to make an accurate EOS measurement using the streaked x-ray radiography setup, the slit width would need to be small enough to only probe the planar region of the system including any uncertainty due to diagnostic pointing.

Simulated data for both gated and streaked x-ray radiography using xRAGE simulations are shown in Fig. 5. The three cases shown are for (a) after shock collision with no radiography aperture to measure the structure of the planar shocks and determine the width of the planar region after the shocks have collided, (b) the same radiograph with the radiography aperture included to restrict the probe x-rays to the axial region of the target, and (c) the streaked x-ray radiograph imaging along the axial position of the cylinder. The experimental data presented in Fig. 6 show that the simulated shock curvature is larger than predicted by xRAGE.

The transmission, T, measured by x-ray radiography can be modeled using the path integral of the absorption along the ray from the source to the detector, $T = I / I 0 = ∫ exp ( − μ ρ ) d x$⁠, where $I / I 0$ is the ratio of initial to measured intensity, μ is the mass attenuation coefficient of the material, and ρ is material density. This integral is calculated along the line of sight through the entire sample, including both the CH sample and Be tube, although the opacity of Be at the probe energy of 9 keV is significantly smaller than the opacity of CH. The mass attenuation coefficient, typically given in cm²/g, contains the opacity information of the materials and depends on the plasma conditions. At 9 keV, photoelectric absorption from the carbon K-shell (1s orbital) dominates the total opacity of the CH. It follows that the opacity of the compressed CH material will be relatively unaffected until the carbon K-shell begins to ionize.

The first experiments on the CPS platform used 2D imaging with no radiography aperture to measure the curvature of the converging shock waves to define the aperture design for future experiments, as seen in the top and middle rows of Fig. 6. X-ray radiography data from shots N190911-002 (top row) and N190911-003 (middle row) are shown in Fig. 6, with four times per shot using a four-strip GXD. Over this time sequence, the shocks travel toward the center of the CH cylinder and collide at approximately 22.2 ns, and a large volume of doubly shocked material is formed at 25.0 ns. The top Hohlraum on the target used in shot N190911–003 (20.8–25.0 ns) was slightly tilted, resulting in a tilted shock front clearly seen in the radiograph at 25.0 ns. The radiography data shown in Fig. 6 were used to define the width of the incoming and outgoing aperture widths, both of which are 700-μm-wide, corresponding to the planar region of the shocks of the measured data. The bottom row of Fig. 6 shows radiography data from shot N200716-001 taken with the incoming radiography aperture, demonstrating that the aperture restricts the probe x-rays to the planar region of the system.

The positions of the ablator interfaces and shock fronts were measured at each time using the x-ray radiography data from Fig. 6 to calibrate the drive in the xRAGE simulations band benchmark the predictive capability for subsequent experiments. A lineout was taken over the central portion of each image along the axis of the cylinder where the shock is planar, as shown in Fig. 7(a), to determine the positions of the counter-propagating shock fronts (orange) and ablators (blue). The resulting time histories of the position of each interface are plotted in Fig. 7(b), showing a shock collision time just after 22 ns, followed by a rebounding shock. The asymmetry in the transmission profile is due to nonuniformities in the area backlighter, which have been reduced by improving the pointing scheme of the backlighter beams. The updated pointing spreads beams from each backlighter quad over the entire backlighter area to reduce the impact of energy fluctuations between laser quads.

Knowledge of both the shock front and ablator interface is required to constrain the simulated hydrodynamic state of the CH. This is because the final, doubly shocked state depends not only on the initial compression provided by the shocks (governed by the drive temperature at early times, when the laser is irradiating the Hohlraum) but also on the decompression profile behind the shock (governed by the drive temperature at later times; i.e., shock support by the slowly cooling Hohlraum). The positions of the simulated interfaces as a function of time are shown as dashed lines in Fig. 7(b). Since the simulation is able to reproduce both the trajectories of the leading shock front and the trailing CH-ablator interface well, we have confidence that the simulation satisfactorily describes the overall evolution within the CH cylinder. The benchmarked simulations predict the incoming shock pressure of 13 Mbar and a peak pressure in the doubly shocked region of 70 Mbar.

XRTS is a powerful diagnostic tool to measure plasma conditions in the HED regime.^18,60 As shown in Fig. 8, a typical XRTS spectrum fundamentally consists of two components, elastic and inelastic scattering. The spectrum of the x-ray source determines the elastic scattering spectrum as elastic scattering events do not change the energy of the scattered photon. Elastic scattering primarily comes from the tightly bound, inner-shell electrons; thus, the strength of the elastic feature can be used to constrain and monitor the K-shell ionization of carbon. The inelastic scattering component, in the non-collective scattering geometry, consists of free–free and bound–free scattering contributions, where free–free scattering comes from free and delocalized electrons, making the inelastic feature sensitive to the electron distribution in the plasma. The bound–free scattering results from bound electrons being liberated by probe x-rays, reducing the energy of the scattered photon by the binding energy of the electron.

The effect of plasma temperature and carbon ionization state on the non-collective XRTS spectra for the conditions created by the CPS platform is illustrated in Fig. 9. Panel (a) shows non-collective XRTS spectra at $ρ = 4.0$ g/cm³, a carbon charge state of Z_C = 4, for electron temperatures of $T e =$ 10–30 eV at a scattering angle of 113°. The plasma temperature determines the velocity distribution of the free electrons in the plasma, which is reflected in the shape of the inelastic scattering feature, broadening with increased temperature.

Figure 9(b) shows the strong effect of the carbon ionization state of the non-collective XRTS spectra at conditions of $ρ = 4.0$ g/cm³ and T_e = 20 eV. A carbon ionization state of $Z C = 4.0$ corresponds to two remaining electrons, and thus a full K-shell (1s orbital), and $Z C > 4$ indicates ionization of the carbon K-shell. The K-shell contains the tightly bound electrons, and any reduction in the K-shell population results in a significant decrease in the intensity of the elastic scattering peak. Thus, by measuring the non-collective XRTS spectra from the highly compressed material created in these experiments, we can accurately measure both the plasma temperature and carbon ionization state.

The MACS spectrometer at the NIF allows two to four XRTS spectra to be obtained per shot depending on the spectrometer configuration. Using a flat crystal allows a four-strip GXD to capture XRTS spectra at four times. For the curved crystal configuration, only two times can be collected per shot because the two curved crystals each focus onto a single GXD strip, although the signal is significantly brighter due to the collecting geometry of the crystals. Additionally, the curved crystals provide spatial discrimination, allowing other x-ray sources to be separated from the XRTS signal. To limit the scattering volume to the uniform plasma in the doubly shocked region, a collimating aperture restricts the XRTS field of view to 200–300 μm along the tube axis as well as blocks scattering from the edges of the sample as depicted in Fig. 2(c). The size of the XRTS aperture in the radial direction can be adjusted to optimize the balance between signal level and source size broadening, where a larger aperture width increases the signal while reducing the spectral resolution due to the increased source size. The resolution of the XRTS measurement can be improved further by reducing the spectral bandwidth of the x-ray backlighter.⁶¹ 

After stagnation, extracting a density measurement from the radiography is complicated by opacity effects resulting from K-shell ionization of carbon. At 9 keV, the bound–free component of the CH opacity is dominated by the K-shell electrons, which are expected to be partially ionized after stagnation. We can account for this effect by directly measuring the ionization state of carbon using XRTS. Additionally, we will be able to accurately measure the density profile of the CH outside the stagnation region (where K-shell is intact) to constrain the mass in the stagnation region. The scope of this publication is limited to the development of the CPS platform, and XRTS spectra from these experiments will be presented and analyzed in a separate publication.

We have developed a platform to make high-precision EOS measurements of WDM with minimal spatial gradients. Initial experiments demonstrated that the CPS platform can produce high-quality experimental data, and future experiments will focus on probing the uniform conditions created by the colliding shocks. Upcoming experiments using the CPS platform will provide EOS measurements of CH in a regime where previous experimental data have shown that models are not predictive. Future experiments will use CH foam instead of solid CH to reach higher shock temperatures, and thus higher carbon ionization states, to probe the physics of carbon K-shell ionization. The long-term goal of the CPS platform is to provide a reliable experimental platform to make high-precision measurements of material properties and atomic physics in the WDM regime.

The authors would like to thank the NIF operations team for successful experimental campaigns and the NIF target fabrication team for their support target design and assembly. These shots were supported through the Discovery Science Program at the National Ignition Facility. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 and supported by Laboratory Directed Research and Development (LDRD) Grant No. 18-ERD-033. This material is based on work supported by the Department of Energy, National Nuclear Security Administration (NNSA) under Award No. DE-NA0003842 and by the Department of Energy, Fusion Energy Sciences under FWP100182. R.W.F. acknowledges support by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, Award No. DE-AC02–05CH11231.

The authors have no conflicts to disclose.

Michael J. MacDonald: Conceptualization (lead); Data curation (lead); Formal analysis (equal); Investigation (lead); Methodology (lead); Project administration (lead); Writing – original draft (lead); Writing – review & editing (equal). Rick Heredia: Conceptualization (equal); Methodology (equal). Scott Vonhof: Conceptualization (equal). Gilbert Collins: Investigation (equal); Methodology (equal); Writing – review & editing (equal). Jim A. Gaffney: Conceptualization (equal); Investigation (equal); Methodology (equal). D. O. Gericke: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). Siegfried Glenzer: Conceptualization (equal); Investigation (equal); Methodology (equal). Dominik Kraus: Conceptualization (equal); Investigation (equal); Methodology (equal). Alison M. Saunders: Conceptualization (equal); Investigation (equal); Methodology (equal). Derek W. Schmidt: Conceptualization (equal). Christopher T. Wilson: Conceptualization (equal). Carlos Alex Di Stefano: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). R. Zacharias: Conceptualization (equal); Methodology (equal). Roger W. Falcone: Conceptualization (equal); Investigation (equal); Methodology (equal). Tilo Doeppner: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). Luke Bennett Fletcher: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). Kirk A. Flippo: Conceptualization (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). Daniel Kalantar: Investigation (equal); Methodology (equal); Writing – review & editing (equal). Elizabeth C. Merritt: Investigation (equal); Methodology (equal). Suzanne Jihad Ali: Investigation (equal); Methodology (equal); Writing – review & editing (equal). Peter M. Celliers: Investigation (equal); Methodology (equal).

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