Experimental methods to test photoionized plasma models in emission Open Access

The expanding foil photoionized plasma platform was developed on the Z-machine at Sandia National Laboratories to produce terrestrial photoionized plasmas at some of the same conditions as those observed in astrophysical black hole accretion disks. The platform uses the intense x-ray drive produced by a Z-pinch dynamic Hohlraum generated using a double nested tungsten wire array to drive a sample of relevant material into the actual astrophysical plasma temperature and density regimes of accretion disk photoionized plasmas.

Although previous attempts have been made, this is only the second instance in which high quality emission data with high resolution from a laboratory photoionized plasma have ever been collected.^1,2 A laboratory photoionized plasma was created with the GEKKO-XII laser facility; however, that experiment was conducted with a much shorter (<160 ps) radiation drive compared to the 3.5 ns duration of this experiment, and significant source size broadening limited the spectral resolution of those measurements.¹ A separate effort attempted to measure emission spectra from photoionized plasmas using an earlier version of the Z-pinch dynamic Hohlraum, as is used in the current platform; however, insufficient diagnostic capabilities proved to be the main obstacle to collecting high quality emission data in that case.² The platform described in this paper overcomes all of these physics challenges and represents a significant advancement in experimental capabilities. The specific goal of the current iteration of the platform is to inform the supersolar Fe abundance problem (described below). However, the fact that only limited experimental tests have ever been conducted of photoionized plasma models in emission provides broad motivation for these experiments that extends even beyond the astrophysical context.

The strategy to robustly test the model predictions is simple in principle but difficult to achieve in practice. It requires three main components: 1) successfully producing and collecting spectral data from a laboratory photoionized plasma, 2) measurements of the supporting model inputs, and 3) performing detailed comparisons of the absolute measured spectral irradiance in emission against model calculations performed using the model inputs collected in step 2. The supporting model inputs include the radiation drive spectrum used to create the photoionized plasma, the density, and the temperature. In this paper, we focus on components 1 and 2—the experimental platform and the model inputs. Specifically, we focus on detailing the methodology used to measure the plasma conditions. Component 3 will be provided in a future publication.

The supersolar Fe abundance problem refers to a long-standing unresolved puzzle in x-ray astrophysics. The inferred Fe abundance in a preponderance of accreting black hole systems exceeds the Fe abundance observed in our Sun.^3–10 A particularly dramatic example is the Seyfert galaxy 1H0707–495, for which the Fe abundance was inferred to be 10–20 times the solar value.^11,12 Recent model improvements incorporating more accurate physics at higher plasma densities than that have been considered in the past revise inferred Fe abundances for many objects to lower values. However, the values remain supersolar for others, and the emission models used to fit Fe abundances have never been tested against high quality laboratory data.

Fe abundances are inferred using reflection spectroscopy. The physics in question is that embedded in the synthetic so-called reflection spectrum model calculations.^13–15 The model spectra are used in fits for the various parameters of interest including the accretion disk inner radius or inner most stable circular orbit, black hole spin, the inclination angle of the system, Fe abundance, coronal emission power law photon index, and others.^4,9,10,16 The term “reflection” is used to refer to the collection of processes that take place as the photoionized plasma at the surface of the accretion disk absorbs, reprocesses, and re-radiates the driving continuum radiation emitted by a hot diffuse plasma localized to a small region at the center of the system. This includes, for example, the many fluorescent features produced at lower energies by L-shell ions and the relativistically broadened Fe-K feature, which refers to the handful of lines produced by n = 2 to 1 transitions in K-shell ions that become blended into a distinct single feature at $∼$6.4 keV, among others. The reflection spectrum often refer to the total observed emission spectrum, which is a superposition of the coronal emission (driving radiation), the “reflected” emission, and thermal disk emission.

Recently, the arbitrary imposition of a maximum electron density of $ne=1015 cm−3$ has come under scrutiny as a possible culprit for the supersolar Fe abundance inferences. This maximum density of reflection spectrum model calculations has been implemented in most reflection spectrum codes.^{13–15,17–19} New analysis suggests that the supersolar iron abundance problem would be at least partly resolved by using higher electron densities in the spectral model calculations. Using higher electron density values for the accretion disk plasma is plausible. It has long been recognized that even the standard Shakura & Sunyaev (1973)²⁰  $α$-disk model prescription predicts that the density is likely to be orders of magnitude higher in many cases.²¹ 

The XSTAR photoionized plasma code was recently updated to more accurately capture the effects of high density in an attempt to better understand and inform the supersolar Fe abundance problem. The changes include appropriate suppression of dielectronic recombination,²² a more detailed treatment of continuum lowering, and updated atomic data.^19,23 Given the plasma composition, density, and driving radiation flux, XSTAR solves for the plasma temperature profile, emissivities, opacities, and level and ion populations. XSTAR also uses escape factor approximations to perform radiative transfer and outputs predicted spectral emission and absorption.

When incorporated into XILLVER, a full accretion disk reflection spectrum code, the newer high density version of XSTAR produces synthetic reflection spectra that exhibit significant modifications to those of the older version. One particularly consequential difference was the enhancement in the intensity of the thermal continuum attributed to increased free-free heating associated with higher disk temperatures at the newly available higher densities.^5,7 Reflection spectrum models calculated at different disk densities using the newer high density version of XSTAR are plotted in Fig. 1. In some cases, these modifications result in lower, more reasonable Fe abundance determinations. However, in others, the fits continue to return supersolar Fe abundances.

Alternative explanations have been proposed. For example, more complicated models that consider the effect of strong winds succeed in fitting the strong Fe K- $α$ feature without requiring supersolar Fe abundances.^24,25 However, these models do not necessarily address the issue of the “soft excess” or the observed enhancement in flux at soft x-ray energies that ab initio models have had difficulty reproducing. Though key progress has been made, the supersolar iron abundance problem persists.^8–10,16 Even in the face of notable improvements to the models, a key question is whether the revised treatment of the physics itself is accurate, since photoionized plasma spectral model tests are rare even at the lower assumed densities.

Therefore, while the supersolar Fe abundance problem is itself an interesting phenomenon, the deeper motivation and urgency to understand the problem stems from the possible systematic model inaccuracies, which could also affect other black hole determinations including spin, not to mention non-local thermodynamic equilibrium calculations in general. If the assumptions and/or approximations used in the reflection spectrum models are inaccurate or inappropriate, then the results for other inferred black hole parameters may be affected as well.

Experimental measurements of the Fe L-shell region have the potential to provide a useful test of the model predictions.

Figure 2 shows a clear change in the predicted shape and intensity of the reflection spectrum in the Fe K-shell region (right) at different disk densities. However, zooming into the Fe L-shell emission region (left) shows that the reflection spectra exhibit even greater sensitivity to changes in the disk density in this energy range. Furthermore, the Fe L-shell spectral lines fall at lower energies than the K-shell lines and are superposed on the thermal continuum emission. An experimental measurement of Fe L-shell spectral radiance emitted from a well-characterized photoionized plasma compared with model predictions would simultaneously test whether the predicted enhancement of continuum, and the line intensities across the spectral region, are accurate. If the synthetic spectra are found to significantly underpredict emission intensity compared to the absolutely calibrated laboratory spectra, then the result would show that the fits require artificially high Fe abundance to compensate for the missing emission. The core set of experiments described in this paper are intended to perform precisely this test.

The spectral emission measured in the experiments described here is produced by the sample absorbing, reprocessing, and re-radiating the Z-pinch drive spectrum. Therefore, the platform represents a direct analog of the astrophysical system not just in plasma parameters but also in the way in which the primary spectral component of interest (the “reflection”) is produced. As such, there is no need to apply any scaling and the laboratory data can robustly test the relevant astrophysical codes in the actual regime and geometric configuration they were intended to be used for.

For a photoionized plasma, the synthetic spectral emission depends sensitively on the predicted ion and level populations. However, unlike in plasmas that are in thermodynamic equilibrium, these do not approach an analytic statistical distribution. Rather, they depend sensitively, in turn, on the radiation drive spectrum. As such, the key question is whether photoionized plasma models can accurately predict these populations given a known radiation drive spectrum. Comparison against high quality benchmark laboratory data is perhaps the only way to answer this question.

The laboratory platform described in this paper has been used to collect high quality emission spectra analogous to astrophysical “reflection” spectra from Fe targets. Thus, the sample composition is also of direct astrophysical relevance. The key data product of interest is the self-emission of the target. This self-emission is driven by the independently diagnosed Z-pinch radiation drive. Ultimately, the goal is to generate model-to-data comparisons that can be used to identify detailed model-to-data discrepancies. In particular, differences in the intensities of specific lines between synthetic vs actual spectra, if observed, can be used to interrogate inaccurately predicted level populations and, by extension, inaccuracies in the detailed collection of excitation pathways for the upper states of the corresponding transitions.

This paper focuses on the methodology used to establish these model input quantities. The temperature is diagnosed using population ratios obtained from the analysis of spectral absorption lines.²⁶ The density is diagnosed with a well established technique that uses the height of the spatially resolved spectral lines to measure the sample expansion size.^2,27 Therefore, all of the necessary model inputs are independently diagnosed, verify that the data are of benchmark quality, and enable robust model tests.

An expanding foil photoionized plasma experiment was first fielded on the Z-machine over two decades ago.² While those efforts produced interesting analyses of the absorption spectra to extract charge state distributions,^28,29 the quality of the data that could be obtained using the available emission diagnostics at the time did not allow for quantitative spectroscopic analysis. Since then, new diagnostics have been developed that enable high signal-to-noise spectroscopy of the faint mJ-energy self-emission. Renewed efforts to continue development of the expanding foil experiment have been successful.³⁰ 

The platform uses a thin (⁠ $∼$900–1000 Å) foil tamped on both sides with thicker layers of (⁠ $∼$700–2000 Å) CH plastic, which promote uniform expansion and hence a uniform plasma. The samples are irradiated using the quasi-blackbody radiation drive spectrum emitted by the Z-pinch dynamic Hohlraum³¹ with the foil arranged to accept the radiation face-on. The foil sample is placed $∼$29 mm away from the center of the pinch. The final location of the target plasma is $∼$35 mm away from the center of the pinch due to expansion and translation of the material. The initial pre-heat phase vaporizes and expands the foil sample to produce a plasma. The subsequent higher-energy radiation drive associated with the Z-pinch stagnation photoionizes the plasma driving it into the requisite high charge states. Past experiments have focused on silicon, an astrophysically relevant element, and showed that the assumption of Resonant Auger Destruction in astrophysical black hole accretion disk spectral models is inaccurate.³⁰ The current set of experiments described here focuses on iron to investigate the accuracy of predicted intensities obtained using the new high density version of astrophysical models in the context of the supersolar Fe abundance problem.

To provide some perspective on the difficulty of producing a terrestrial photoionized plasma, the tick lines at the bottom of Fig. 3 show the energy required to ionize into each subsequent charge state of Fe. At the n = 3 (M-shell) to n = 2 (L-shell) boundary, the amount of energy required to ionize from the Na-like to Ne-like charge state dramatically increases from 0.48 keV to 1.26 keV. Additionally, because the pinch spectrum is a quasi-blackbody, the number of photons quickly dwindles toward higher energy, in particular, at energies high enough to ionize into the Ne-like charge state and beyond. This situation, along with the challenge of producing a sufficiently powerful x-ray drive while contending with the problem of geometrical dilution, makes it difficult to produce a macroscopic photoionized plasma.

Figure 3 plots the pinch drive spectrum along with the ionization energies of the relevant charge states that dominate the target plasma. The total power and energy of the drive spectrum is constrained using diagnostics fielded independently and simultaneously on every shot. The drive spectrum is taken to be the superposition of three Planckians that represent the major components of driving radiation produced by the central load hardware: the pinch itself and re-radiation from metal components. While some minimal shot-to-shot variation is inescapable, the drive spectrum does not vary significantly and the observed shot-to-shot variation in the final spectral data from the target plasma is minimal.

In this paper, we focus on the plasma conditions and the experimental platform. Accurate determination of the plasma conditions is essential to establishing the data as benchmark quality. To address this issue, the rest of this paper is dedicated to a detailed description of the diagnostics and experimental methods used to extract the plasma conditions.

The suite of diagnostics used on this platform in its current iteration includes four instruments: the x-ray Scattering Spherical Spectrometer (XRS³),^32,33 two Time-Integrated conveX crysTaL spectrometers (TIXTL),^34,35 and the newly available Multi-Optic Novel Spherical-crystal Spectrometer with Time Resolution. We focus here on the time-integrated instruments used to measure the plasma density and temperature. The XRS³ and two TIXTLs are both time-integrating spectrometers fielded with Kodak 2492 RAR X-ray film as the primary detector.^36,37 The XRS³ uses concave spherical crystal geometry, and the TIXTLs use convex cylindrical crystals and slits to achieve simultaneous spatial and spectral resolution in the data images.

The XRS³ observes the foil samples on an edge-on line of sight (LOS) to isolate the self-emission signal from the plasma (see Fig. 4 for a schematic). This setup also has the added benefit of achieving spatial resolution along the direction of the plasma expansion. The nominal distance between the center of the XRS³ crystal surface and the center of the foil sample is 80 cm. By contrast, the TIXTLs observe the foil sample in absorption along a LOS roughly normal to the plane described by the flat face of the foil with the Z-pinch as a backlighter from a distance of approximately 5 m. Both emission diagnostics are fielded “in-chamber” in the center section. The TIXTLs are mounted on diagnostic arms in a dedicated “boat” outside of the central chamber where they are largely shielded from debris.

Each diagnostic and foil is located according to its LOS number, which indicates how many degrees away from north it sits. The TIXTL diagnostic boat is at LOS 130, and the XRS³ is fielded at LOS 220. Because the foil samples need to be oriented such that the emission diagnostics observe them edge-on, the foil sample observed by the XRS³ is installed at LOS 130. The TIXTLs also achieve space resolution but with the use of slits rather than crystal geometry. However, because the TIXTLs observe the foil sample face-on, a limiting aperture restricts the field of view to the central portion of the sample where the pinch and therefore the foil plasma is expected to be fairly uniform.

Although the detectors are time-integrating film, the data are heavily weighted by the peak of the backlighter. The data are largely insensitive to early or late time emission relative to the pinch peak emission at stagnation. Emission spectra are effectively only observed when the intensity of the photoionizing radiation from the pinch is high enough at the energies required to produce K-shell and L-shell holes that electrons can occupy following radiative de-excitation to produce the emission signatures. Similarly, absorption spectra are only recorded when the backlight from the Z-pinch is bright enough to produce the relevant lines from high charge states in transmission.

The plasma density analysis proceeds in two steps: measuring 1) the expansion size and 2) the areal density. This technique has been used successfully in the past.^2,27 The film data image is used to infer the size of the plasma in the direction of radial spatial expansion induced by the pre-heat phase (see Fig. 5). The height of the spectral lines observed on the film image are converted to actual plasma spatial extent using the magnification in the sagittal plane of the crystal.

The expansion size is obtained by fitting the vertical height of the emission lines. The lineouts are simultaneously fit with a variable number of Gaussians to obtain the most accurate value for the expansion size of the main plasma component of emission. The full width half maximum (FWHM) of the main component from the spectral lines, converted to actual distance units and averaged across all of the lineouts (using the appropriate magnification value at the central wavelength of the section), is taken to be the expansion size of the plasma. As indicated by the value in the legend in Fig. 6, the main component of intensity corresponding to the Fe L-shell emission lines has a FWHM of $∼$7.4 mm. This means that the originally 800 Å thick foil sample undergoes expansion of almost 10 000 times its original thickness.

The final density estimate relies on independent Rutherford backscattering measurements (RBS) performed on witness samples produced from the same bulk material that the foil samples are manufactured from. The RBS measurements provide the areal (or column) density of the specific compositional makeup of the sample. This RBS analysis is necessary because thin sample production yields atom densities that are different from typical solid densities, and there is also some unavoidable oxidation. The final composition of the material must be independently measured. Division of the areal density values by the measured expansion size (based on the height of the spectral lines) yields the volumetric density. Because the RBS densities provide areal densities of the atomic composition, the inferred volumetric density is a measurement of the Fe ions/cm³, not the electron density. The final Fe ion density estimated using this method for the three lowest density plasma shots is $1.12x1018$ ions/cm³ $±1.63x1017$⁠.

To estimate the electron density, we multiply the measured ion density by the mean charge predicted by four sets of model calculations (XSTAR, ATOMIC, SCRAM, and PrismSPECT) and take the uncertainty to be the standard deviation among the various predictions: $Z¯=16.74±0.37$⁠. The electron density is too low to be able to use Stark broadening as a diagnostic. The inferred electron density is therefore $1.87x1019$ e⁻/cm³  $±2.76x1018$⁠, where the individual uncertainties associated with the fit to the height of the spectral lines and the standard deviation in the predicted mean charge have been added in quadrature to give the total uncertainty. The total uncertainty is dominated by the fit to the heights of the spectral lines. The final uncertainty on the electron density is $∼$15%, which is reasonable for a high energy density (HED) experiment.

Complementary density diagnostics are desirable since the density is a key parameter. In the future, other measurements, such as interferometry, can be deployed to test these assumptions and obtain a direct measurement of the electron density. The fact that there are, to date, only limited laboratory tests of photoionized emission models makes it difficult to determine the minimum required accuracy. Nevertheless, we can still test whether the models agree with the laboratory data to within the reported uncertainty. Should the codes turn out to be so accurate that they match the observed emission, we will implement an improved measurement of electron density to refine the model-to-data comparisons. Stark broadening and interferometry are unlikely to be any more accurate than the current methods.

Transmission line ratios are used to extract the plasma electron temperature using the technique described in Mancini et al.²⁶ Electron temperatures in photoionized plasmas are moderate (low tens of eV). The distribution of electron kinetic energies quickly reaches equilibrium to form a Maxwellian (on the order of 100 picoseconds). However, the kinetic energies are not high enough to collisionally ionize a sufficient number of atoms to produce the charge state populations observed. Nevertheless, electron collisions can still produce excited states if there exist low lying states that are energetically allowed via collisional excitation. So, if there are two absorption lines arising from two lower states that are close enough in energy, the populations of the atomic states that produce those lines should be in local thermodynamic equilibrium (LTE) and hence, governed by Boltzmann statistics. This reasoning provides us with a way to measure the plasma electron temperature.

The numerical integrals of the lines $∫(ln(Ti))$ in the transmission spectrum provide the total lower state population participating in the absorption transition. The level energies and oscillator strengths are taken from the database in the Prism computational software suite. The values can be obtained using the “show transitions table” GUI within “spectra viewer” in the PrismSPECT code.³⁸ 

The absorption spectral data obtained using samples that consisted of a single layer of Fe were not useful for obtaining a temperature estimate. The Fe L-shell absorption spectrum turned out to be too complex and the line blending too severe to apply this technique. Relatedly, the severity of the line blending obscures the location of the continuum. Without being able to identify where the continuum, is, it is impossible to accurately convert an absorption spectrum into transmission. An accurately converted transmission spectrum is necessary to obtain an accurate measurement of the level populations.

This required a redesign of the sample and a spectrometer configuration capable of observing a different spectral regime. A 3-layer sample design as pictured in Fig. 7 provided the solution. Instead of a single layer of iron, in the 3-layer sample, the iron layer is sandwiched between a layer of silicon and another layer of aluminum. All three layers are then sandwiched between the normal CH tamper material. The relatively simpler Al and Si spectra from their respective Li-like charge states provide reliable temperature estimates. This new sample design was implemented successfully on three shots z3829, z3831, and z3836 in April 2023. Up to three slit spectra were obtained on each shot, yielding a total of eight absorption spectra that were used in this analysis (see Fig. 8).

Figure 9 plots the theoretical population ratios as a function of electron temperature (in eV) for the four pairs of silicon and aluminum lines observed in the Z transmission spectrum data. It is evident that the LTE populations vary sensitively as a function of electron temperature, making these transmission line ratios a suitable diagnostic. At higher temperatures (low population ratios), the temperature range inferred by the measured population ratio is too large and hence too uncertain to be useful.

The final temperature determination obtained using this method is $kTe=$ 41 eV $±$ 15 eV. The analysis was performed using all possible combinations of lower state populations (see Fig. 10). The final value is an average of all values, and the uncertainty is taken to be the standard deviation. The lower state population is calculated by simultaneously fitting all of the individual transition features with Gaussians and taking the numerical integral of the Gaussian curve corresponding to the relevant transition. This final temperature agrees with the 33 eV $±$ 7 eV temperature obtained using the same approach for the silicon-only foil examined in earlier experiments.³⁰ Those Si foils consisted of a single $∼$800 Å layer of silicon tamped with $∼$1000 Å of CH, which is considerably less material than these triple layer samples and similar to the single $∼$800 Å layer Fe samples.

While the expansion size of the three-layer sample is less than that of the single-layer sample type, we do not observe a drastic difference in the measured temperature. This result validates the use of a similar range of temperatures in model calculations to compare against the final emission spectra. The final model-to-data comparisons should accommodate a reasonable range of temperatures given these measurements. While it is important to establish a temperature measurement, it is not vital to obtain an extremely accurate electron temperature for this target plasma. The main goal is to test the ability of various codes to accurately predict the spectra given the input radiation field. This is because the dominance of photoionization and photoexcitation in producing the charge states and level populations responsible for the L-shell emission spectrum means that there is only a modest dependence on electron temperature and a much stronger dependence on the driving radiation spectrum. Importantly, the measured temperature is well within the range relevant for astrophysical black hole accretion disks and simultaneously confirms that the plasma is dominated by photon driven processes.

This paper describes the platform used to collect Fe L-shell emission spectral data, the methods establishing the plasma conditions, and the plasma condition results. The key emission spectra are produced by Fe atoms ionized into the L-shell. The discrete emission features arise mostly from n = 3 to n = 2 transitions. To date, this platform has successfully collected high signal to noise self-emission data at three electron densities and, therefore, three different photoionization parameters. The careful analysis of plasma conditions, the newly available and successfully deployed time-resolved emission diagnostic, and demonstrated reproducibility verify that the data are benchmark quality and mark significant progress in laboratory astrophysics capabilities.

Definitive tests of photoionization emission models require crystal reflectivity measurements. Reflectivity characterizes the crystal reflection efficiency and is required to establish the absolute intensity of the target plasma emission. Therefore, this is the final piece required to fully satisfy the claim of benchmark quality data. We have collected independent Manson source x-ray calibration data with an identical spectrometer configuration as that used in the XRS³ on the actual Z experiments and performed an absolute intensity calibration of the scanner used to read in the data. This work validates the parameters used to calculate the reflectivity curves and establishes appropriate uncertainty bounds for the absolute emission intensity of the data obtained on Z.

Ongoing work is also extending the measured spectral range of the photoionizing drive spectrum to higher photon energies. The present drive spectrum measurements employ absolute time-resolved x-ray power, time-resolved spatial distribution in three monochromatic photon energies, and view factor calculations to infer the large majority of the driving x-rays at the sample. However, the pinch does produce some emission at photon energies above approximately 2 keV that are not accurately characterized by these measurements. Additional measurements using dedicated crystal spectrometers to refine knowledge of this portion of the drive spectrum are in progress.

Finally, a complete analysis of the spectral data will ultimately benefit from a detailed set of high fidelity radiation hydrodynamic simulations. The simulation work is already under way and will be provided in future publications as the work matures and the results become available.

The measurements of the plasma conditions presented here have adequately small uncertainties, given that absolute emission intensities of photoionized model predictions have never been benchmarked until now. Establishing absolute intensity of the measured data is particularly challenging. These data and the substantial supportive work set robust uncertainties on the absolute emission intensities and establish these data as first-of-its-kind laboratory measurements of absolutely calibrated spectral emission from Fe photoionized plasmas produced in terrestrial laboratories. As such, they enable, for the first time, a direct test of model calculations, both in terms of absolute predicted emission intensities and relative line strengths across the observed spectral range, allowing us to evaluate model calculations in detail and interrogate the supersolar Fe abundance problem.

This work was performed at Sandia National Laboratories. We thank the Z-facility teams and in particular R. Harmon, L. Molina, B. Ritter, J. Mignon, M. McCall, J. Swalby, A. Edens, and R. Speas for their support. We wish to acknowledge the support of the Z Astrophysical Plasma Properties (ZAPP) collaboration and the Fundamental Science Program at Z. P.B.C. thanks Tim Kallman, Javier Garcia, Thomas Gomez, Don Winget, and Mike Montgomerey for guidance and helpful discussion.

Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under Contract No. DE-NA-0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. P.B.C. and D.C.M. acknowledge support from the Wootton Center for Astrophysical Plasma Properties under U.S. Department of Energy Cooperative Agreement No. DE-NA0003843 and DE-NA0004149.

P.B.C acknowledges support from the DOE NNSA Laboratory Residence Graduate Fellowship (LRGF) under U.S. Department of Energy Cooperative Agreement No. DE-NA0003960.

This manuscript has been authored in part at Lawrence Livermore National Security, LLC under Contract No. DE-AC52-07NA2 7344 with the US. Department of Energy. The United States Government retains, and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.

The authors have no conflicts to disclose.

P. B. Cho: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). G. P. Loisel: Conceptualization (equal); Investigation (equal); Methodology (equal); Supervision (equal); Writing – review & editing (equal). J. E. Bailey: Conceptualization (equal); Methodology (equal); Supervision (equal); Writing – review & editing (equal). G. S. Dunham: Investigation (supporting); Writing – review & editing (supporting). D. C. Mayes: Investigation (supporting); Methodology (supporting). T. Nagayama: Conceptualization (equal); Investigation (supporting); Methodology (supporting). C. J. Fontes: Investigation (supporting); Software (equal); Writing – review & editing (equal).

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