When stellar radiation interacts with a molecular cloud, the cloud's fate depends on the strength of the incident radiation and the radiation's mean-free-path within the cloud [F. Bertoldi, Astrophys. J. 346, 735–755 (1989)]. Under the right conditions, the radiation compresses the cloud and a star formation may occur. Where and when the stellar formation occurs in the cloud's collapse are open questions. Direct observation of the complete star–cloud lifecycle is nearly impossible due to the immense timescales and distances over which the interaction occurs. Laboratory astrophysics offers a way to investigate such a system by scaling the important astrophysical parameters to the laboratory. This work describes laboratory experiments to study the radiation-driven implosion of clouds, using x rays from a laser-irradiated, thin, gold foil as a surrogate star and a carbon-foam sphere as a surrogate cloud. An optically thick system, theoretically corresponding to a star-forming regime, was selected by choice of the foam density. Gold foil and sphere motions were imaged by x-ray radiography. Radiographic images show the formation of an interface between rarefied gold and carbon plasmas, a shock moving into the sphere, and a blunting of the initial sphere's shape. Measurements show that the shock moved linearly around 64 m/ns into the sphere, and the gold–carbon interface formed by 2 ns at the sphere edge remained stationary. The deformation of the sphere was driven by the incident radiation and not by mechanical pressures applied by gold plasma. The blunting of the sphere was likely due to the geometric reduction of flux near the sphere's poles. Higher x-ray flux near the sphere's equator caused high compression and a faster shock, which flattened the sphere. We will discuss the results and implications of our observations.
I. INTRODUCTION
Large stars, with their high ultraviolet spectral content, drive ionization fronts through surrounding neutral gases, known as HI regions, creating ionized plasmas, known as HII regions, behind the front. The motion of a simple photoionization front generated by a large star moving through a HI region is depicted in Fig. 1. The photoionization front can expand, for hundreds of parsecs,2 until the ultraviolet flux is geometrically diluted to the point where the ionization rate matches the recombination rate. This outer radius is known as the Strömgren radius. The creation and modeling of photoionization fronts is a topic of high-energy-density research today.3–5 The effect of high-energy photons traveling through an ionized medium to irradiate a curved object is of interest to both the astrophysical and inertially confined fusion (ICF) communities. At the heart of both applications is radiation transport.
A cartoon showing a photoionization front that has moved outward from its generating star and encompassed a nearby gas cloud. The gray, central region depicts the ionized HII region. Outside of the HII region is the un-ionized HI region. The cloud within the HII region and is being directly irradiated by the star, while the other is in the HI region and is not yet irradiated.
A cartoon showing a photoionization front that has moved outward from its generating star and encompassed a nearby gas cloud. The gray, central region depicts the ionized HII region. Outside of the HII region is the un-ionized HI region. The cloud within the HII region and is being directly irradiated by the star, while the other is in the HI region and is not yet irradiated.
Ultraviolet photons streaming through an HII region that encounter a cloud of gas can interact in diverse ways. Bertoldi's 1989 paper describes five potential outcomes of a gas cloud interacting with a nearby star.1 These five results can be simplified into a star-forming limit and a cloud-dissipation limit shown in Fig. 2.
Modified plot from Keiter 2017 that described the dimensionless parameter space that might lead to further star formation.6 Plot adapted from Bertoldi's 1989 paper.1 This figure was published in High Energy Density Physics, 22, P.A. Keiter, M. Trantham, G. Malamud, S.R. Klein, J. Davis, R. VanDervort, D. Shvarts, R.P. Drake, J.M. Stone, M. Fraenkel, Y. Frank, E. Raicher, Design of laboratory experiments to study radiation-driven implosions, 37–40, Copyright Elsevier (2017).
Modified plot from Keiter 2017 that described the dimensionless parameter space that might lead to further star formation.6 Plot adapted from Bertoldi's 1989 paper.1 This figure was published in High Energy Density Physics, 22, P.A. Keiter, M. Trantham, G. Malamud, S.R. Klein, J. Davis, R. VanDervort, D. Shvarts, R.P. Drake, J.M. Stone, M. Fraenkel, Y. Frank, E. Raicher, Design of laboratory experiments to study radiation-driven implosions, 37–40, Copyright Elsevier (2017).
A closeup, direct study of many astrophysical objects, such as protostar accretion disks, nebulae and the cores of planets, is impossible with modern spaceflight. The best that humanity can do is observe these features from afar using telescopes. While many details of these structures can be observed, observations are often limited to only one angle of observation, the objects under study are often too small to observe, and frequently the physics evolves on extreme timescales. For these reasons, it is advantageous to replicate the space environment in laboratories on Earth, where the limitations are less extreme. The hope with these types of experiments is to translate the key aspects of the astrophysics to the laboratory and thus arrive at new information that improves the astrophysical models and observations. Frequently, the scale length of the astrophysical phenomena is too large to study in the laboratory. In these cases, scaled experiments are the best way to study the phenomena, outside of observation and simulation. Scaled experiments attempt to match estimates of key dimensionless parameters of the astrophysics to make a representative experiment in the laboratory. For example, optical depth, Reynolds number, normalized mass density, and Mach number are dimensionless numbers frequently considered for scaling.
In the case of the star–cloud interaction, two dimensionless parameters are identified in Bertoldi's 1989 paper:1 dimensionless velocity (similar to a Mach number) and optical depth. Dimensionless velocity describes how fast the star–cloud system interacts. The optical depth describes how the radiation transports through the material. Initial experiments focused only on scaling the optical depth. A comparison between the laboratory experiment and the astrophysical phenomena is shown in Fig. 3.
A comparison of the simplified, laboratory-astrophysics experiment (left) with the astrophysical phenomena (right). The gold foil x-ray source mimics ultraviolet photons from the star and the carbon foam sphere mimics the gas cloud. Nominal experimental target dimensions are shown on the left. Astrophysical parameters are listed on the right.6
A comparison of the simplified, laboratory-astrophysics experiment (left) with the astrophysical phenomena (right). The gold foil x-ray source mimics ultraviolet photons from the star and the carbon foam sphere mimics the gas cloud. Nominal experimental target dimensions are shown on the left. Astrophysical parameters are listed on the right.6
The ultimate goal of this platform is to experimentally mimic a star–cloud system of nearly any optical depth so that all regions and boundaries of the Bertoldi plot are testable. The research, reported here, describes our initial experiments on a platform to explore the asymmetric irradiation of an optically thick sphere, which is relevant to potential star formation. Data from this platform can help improve radiation transport models for both high-energy-density and astrophysical models. Section II describes the experimental setup, targets, and diagnostics. Section III discusses HYADES simulations, which constrained our understanding of the bulk features. Section IV evaluates the experimental and simulation results. Section V draws final conclusions about the experiment.
II. EXPERIMENTAL SETUP
These experiments were conducted at the OMEGA Laser Facility located at the Laboratory for Laser Energetics (LLE) at the University of Rochester in Rochester, New York.7–12 OMEGA-60 features 60 laser beams (351-nm) that can, altogether, deliver up to 30 kJ of energy to many targets.8 The timing of each laser beam can be altered slightly using precise, path length delays. Additionally, individual laser beams are precisely pointable, which allows the irradiation of different surfaces or targets. Together, the beam delays and repointing capabilities allow for the setup of complex experiments, such as multi-target experiments. We use the repointing of laser beams to drive a physics target and two backlit pinholes. Timing delays are used to observe dynamics within the sphere at different experimental times. Each set of targets are precisely aligned within the target chamber, usually to within 25 m of positional uncertainty and of rotational uncertainty. Target geometry, laser beam selection, and alignment features were computed using the VISRAD program.13
Our laboratory-astrophysics experiment focuses on replicating the radiation transport of the astrophysical phenomena by scaling to a relevant optical depth. The optical depth ( ) is simply estimated as the product of the sphere mass density ( ) with the sphere diameter (D) and the mass-attenuation coefficient14,15 ( ). Figure 4 shows the estimated [optical depth] of a carbon sphere as a function of density and diameter. The temperature of the x-ray source, and thus the flux of x-ray photons, on the sphere directly impacts the hydrodynamic fate of the sphere. For example, hotter source temperatures produce higher energy photon fluxes, which generally lowers the optical depth of the sphere. These experiments occurred in the optically thick limit, , to simplify target construction and experimental diagnosis.
Estimate of the [optical depth] as a function of carbon foam sphere density and diameter. The dot is the estimated experimental optical depth. The line shows the density and diameters that make the optical depth .
Estimate of the [optical depth] as a function of carbon foam sphere density and diameter. The dot is the estimated experimental optical depth. The line shows the density and diameters that make the optical depth .
Quality results are enabled by precise characterization of distances between internal components, and the stalk angles for each target on an in-house metrology system. Diagnostics were used to infer shot performance, characterize the gold foil x-ray source, and radiograph dynamics within and around the sphere. Shot performance was monitored by laser beam diagnostics, diagnostic timings, hard x-ray detectors, fixed pinhole cameras around the experiment chamber, and long duration visible light camera exposures. The hard x-ray detectors (HXRD) revealed the number of hard x-rays produced within the experiment.16,17 Fixed pinhole cameras around the OMEGA-60 chamber captured a full length exposure of the experiment and were helpful in understanding the potential sources of background. Visible light cameras provided information, after the conclusion of the experiment, about the debris patterns produced by the targets. Additional experimental details are discussed in Keiter 20176 and VanDervort's thesis.18 Characteristics of the physics and backlighting targets are discussed.
A. Physics target
The experiment begins when lasers irradiate a thin, gold foil located in the “physics target,” shown in Fig. 5. The photon flux seen by the sphere from the planar gold foil has a strong dependence on the distance from the source. Thus strict control of the gold foil and sphere positioning is vital to obtaining comparable measurements. The foil and sphere were housed in a single target to mitigate positional uncertainties inherent in aligning two targets. Time dependent, flux emissions from the gold foil were measured using DANTE.19–22 The resulting gold foil flux measurements are contaminated by background x rays from the backlighter targets, since DANTE collects x rays from a wide area near target chamber center (TCC). A camera, sensitive to soft x rays, placed in TIM1 imaged the emission spot size. Laser beams heat the gold blow off, which produces an 80-eV quasi-thermal blackbody source for many nanoseconds when viewed through the gold foil.23,24 These measurements were made to characterize the x-ray source, if needed, as was done in prior calibration experiments.23,24 We assume that the x rays produced by the thin, gold foil are similar to those produced in the calibration experiments.
The left side of the above image is a VISRAD model of the experimental setup. The right side of the image is a picture from metrology of a target's shielding, sphere, stalk, and fiducial grids. Lasers enter the physics target from the left and irradiate a thin, gold foil embedded in the right side of the cone. View along a radiographic line-of-sight.
The left side of the above image is a VISRAD model of the experimental setup. The right side of the image is a picture from metrology of a target's shielding, sphere, stalk, and fiducial grids. Lasers enter the physics target from the left and irradiate a thin, gold foil embedded in the right side of the cone. View along a radiographic line-of-sight.
The physics target's central component is a machined acrylic cone, which forms the base to which most other components directly attach. The machined acrylic cone had a wall thickness of 1.2 mm, a height of 6 mm, and an entrance diameter of 33.76 mm. The rear surface of the acrylic cone, closest to the sphere, is counter-bored so that the foil and its supporting washer sit flush with the rear surface of the cone. The foil was attached to a gold washer with a thickness of 150 m, an inner diameter of 3.0 mm, and an outer diameter of 5.0 mm. A 0.5- m-thick foil covered the majority of the gold washer. Two circular bases are machined into the cone's exterior 180 degrees apart, which serve as mounting points for the back-support.
The cone's primary purpose is to support shielding to contain radiation from the hot gold plasma and prevent the irradiation of radiographic diagnostics. Most of the cone's exterior was covered by a laser-cut, 100- m-thick gold foil, which was attached in two pieces. The exterior foils formed a small gap in the shielding between their edges and around holes cut to allow the back-support to attach to the cone. The cone's large entrance was left uncovered by the thick shielding to provide a consistent positional alignment fiducial. The interior of the cone was lined with a 10- m-thick gold foil, so that if the target was slightly misaligned, then the laser beams would still irradiate gold and maintain a similar x-ray source.
A 100- m-thick gold foil washer with an inner diameter of 4.0 mm and an outer diameter of 8.04 mm covered the smaller rear face of the cone. This washer overlapped the edge of the foil on its supporting washer. The shield-covered rear face of cone made for another positional alignment fiducial. A concentric tungsten washer, known as a “block-washer" was attached to the rear surface of the gold washer. This washer was 125 m thick, with an inner diameter of 4.0 mm and an outer diameter of 5.0 mm. This washer geometrically constrained x rays, emitted by the hot gold plasma, from irradiating radiographic detectors. The physics target was aligned using a rotation flag and circular loops surrounding the small and large diameters of the cone, which was uncovered from the gold foil.
The physics target was mounted in Target Positioning System (TPS) 2 using an 800- m-diameter tungsten stalk. A back-support was made from a 3-D printed plastic and was glued to the acrylic cone through two holes cut in the exterior shielding. The back-support formed an arch to maximize the distance to the thin gold foil, which mitigated the ablation of the support materials and prevented the contamination of the experiment. An 80- m-diameter tungsten stalk was glued roughly into the center of the arch nominally over the gold foil's center. A 500- m-diameter sphere was carefully glued to the end of this stalk closest to the gold foil. The nominal distance between the sphere edge and the gold foil was 500 m (750 m from sphere center to gold foil edge). The sphere was made from a machined, 130-mg/cc, mostly carbon foam. Additionally, two orthogonally aligned gold grids were cut into 11-mm-edge-length squares and were attached to the stalk. Each grid25 had a pitch of 64 m (38- m hole and 26- m bar) and a uniquely cut grid pattern for simple identification of the radiographic view. These grids provided spatial scale and an absolute coordinate system when paired with metrology data for inter-shot comparisons. The distance of the bottom of the stalk to the gold foil and grid positions were set by a precision-machined alignment jig.
B. Backlighting target
Two backlit-pinhole targets imaged the sphere, an example target is depicted in Fig. 6. Each target provided an independent source of characteristic energy x rays along one of the orthogonal, radiographic axes. One backlighter was mounted in TIM4 and projected along the TIM4–TIM6 axis. The second backlighter was mounted in TIM2 and projected along the TIM2–TIM3-cranked axis. Backlighter targets consisted of an 800- m-diameter tungsten stalk glued to a 7-mm-edge-length, laser-cut, 50- m-thick, tungsten substrate. The pinhole substrate had a 50- m-diameter entrance hole with a 20- m-diameter exit hole. Smaller pinholes were attempted and did not work well due to the reduction in imaging photons. X rays from the backlighters were imaged by x-ray framing cameras (XRFC) mounted in TIM3 and TIM6 and recorded on a charge coupled device (CCD) medium. A step-wedge filter was machined into 50- m-, 150- m-, and 250- m-thick steps of acrylic and placed in the camera at the edge of the CCD. This step-wedge filter provided a means to convert pixel count to areal density and estimate the high-energy photon content included in the radiographic images. The pinholes were tilted at 30-degrees to the substrate normal to mitigate debris directed at the radiographic detectors.26 Additionally, the XRFCs were shielded from debris and stray x rays by Los Alamos National Laboratory's Close-In Ported Snout (CIPS) nosecone.27
Photograph of the laser-irradiated side of an example backlit-single-pinhole radiography source. The pink material that joins the pinhole substrate to the stalk is glue, which is convenient for evaluating glue locations. Image Credit: Sallee Klein.
Photograph of the laser-irradiated side of an example backlit-single-pinhole radiography source. The pink material that joins the pinhole substrate to the stalk is glue, which is convenient for evaluating glue locations. Image Credit: Sallee Klein.
A titanium or saran foil was glued to 500- m-edge-length, laser-cut, plastic cubes, which offset the foil from the pinhole substrate. Laser irradiation of these targets cause the generated plasma to emit a strong He- signal. The He- photon energy is 4750 eV for titanium and 2800 eV for chlorine in the saran foil.28 The backlighters were aligned using the corners of the pinhole substrate.
III. HYADES SIMULATIONS
The experiment's radiation hydrodynamics were largely modeled in the HYADES code, a one-dimensional, Lagrangian, radiation hydrodynamics code.29 HYADES provides a quick and simple means to simulate experiments with minimal simulation knowledge to compute experimental parameters that are either not directly estimable or measured. A three-dimensional experiment cannot be modeled in detail with one-dimensional simulations. Nonetheless, one-dimensional simulations can reveal qualitative features in the experiment. The code provides a self-consistent assessment of the interaction of the laser beam, the gold foil, the resulting radiation, and the sphere. Specifically, in this experiment, one-dimensional HYADES simulations have the most relevance to the axis formed by the center of the laser irradiation spot (nominally the gold foil center) and the sphere center. Initial pre-experiment simulations used a radiation boundary source to qualitatively evaluate how foam material, source temperature, and foam density affected the evolution of the sphere. An interface between the gold and carbon plasmas was not seen in these simulations due to the absence of the gold foil. After the presence of the interface was clearly observed in the experimental radiography, the radiation boundary source was replaced by a laser-irradiated gold foil of nominal experimental parameters. Even beyond the geometric limitations, one should not expect high accuracy from the simple treatment of the gold equation-of-state. Despite that, one does get a qualitative, self-consistent result as described above.
Once added to the simulation, rarefied carbon and gold plasmas formed an easily observed interface as seen in Fig. 7. In post-experiment simulations, a 0.5- m-thick gold slab is placed 500 m from a 500- m-thick slab of carbon. These slabs represent the thin, gold foil and carbon-foam sphere, respectively. A planar simulation geometry was used to maintain the asymmetric irradiation of the sphere found in the experiments. A low-density (<1 mg/cc), hydrogen gas was defined between these slabs to represent the vacuum that existed between the two experimental components.
Plot containing a density lineout from HYADES simulation at 1.9 ns. HYADES predicted qualitative features such as the various rarefactions and shocks of gold and carbon. Lasers irradiate the gold foil from the left. The gold begins rarefying toward the simulated irradiating lasers, on the left. The initial sphere edge is at −250 m, the sphere center is at 0 m, and the gold foil is at −750 m.
Plot containing a density lineout from HYADES simulation at 1.9 ns. HYADES predicted qualitative features such as the various rarefactions and shocks of gold and carbon. Lasers irradiate the gold foil from the left. The gold begins rarefying toward the simulated irradiating lasers, on the left. The initial sphere edge is at −250 m, the sphere center is at 0 m, and the gold foil is at −750 m.
All three slabs use an average-atom local thermodynamic equilibrium (LTE) ionization model and a polytropic equation-of-state ( ). The adiabatic index ( ) is estimated using each atomic species' estimated degrees-of-freedom. In this simulation, the adiabatic index used for gold was 1.2, the adiabatic index used for carbon was 1.67, and the adiabatic index used for the hydrogen vacuum gas was 1.67. The simulations were computed for up to 8 ns of experimental time. The estimated laser wavelength (351 nm) and intensity ( W/cm2) was incident on the foil using HYADES' laser source input. The shock generated in the gold slab transits the width of the slab in the time span of hundreds of picoseconds after laser irradiation begins. A shock in the sphere developed around 0.5 ns after the experiment began.
A multi-group, diffusive, radiation transport model was used with photons grouped into two logarithmically spaced bins, which were split about the carbon K-edge. The first set of twenty logarithmically spaced bins ranged from 1 to 284 eV. The second set of twenty logarithmically spaced bins ranged from 284 eV to 30 keV. Simulations displayed expected behavior, such as the rarefaction of the gold and carbon, the formation of the interface, and the shock of the sphere. Furthermore, the simulations showed that the rarefied gold and carbon plasmas that form the interface are both shocked by the collision. An example lineout is shown in Fig. 7.
The interface position is tracked by the positions of the last gold zone and the first carbon zone at each time step. Additionally, the shock position in the sphere was tracked throughout the simulation.
IV. RESULTS
Figure 8 depicts a post-processed radiograph with the initial sphere center and sphere edge, as computed from metrology data, denoted. Measurements of the shock in the sphere and interface positions were taken along a horizontal lineout through the initial sphere center. Frequently, the interface position along the shock in the sphere was hidden by the tungsten washer on the physics target. The gold–carbon interface position was determined by fitting a quadratic function to points selected along the edge of the interface leading up to the washer. Several images were corrupted by sources of background noise and were unable to be measured.
A sample processed radiograph, taken 4.2 ns after the lasers began irradiating the gold foil. The gold foil sits on the left side of the image and is hidden by shielding. The initial sphere position, denoted by the red-dashed line and asterisk, was determined using metrology measurements of gold-grid positions relative to the sphere center.
A sample processed radiograph, taken 4.2 ns after the lasers began irradiating the gold foil. The gold foil sits on the left side of the image and is hidden by shielding. The initial sphere position, denoted by the red-dashed line and asterisk, was determined using metrology measurements of gold-grid positions relative to the sphere center.
The radiographs feature the tungsten washer shield, gold–carbon interface, gold fiducial grid, shock in the sphere, and a step-wedge. Early-time measurements near the gold foil are blocked from view by the tungsten washer, so the interface could have formed earlier, but it is not visible. The gold–carbon interface forms a cap over the nearby sphere, which is an inherently three-dimensional structure. X ray radiography can only capture the two-dimensional projection of the mass structure, which is why the interface seems to have a large width and appears to penetrate the initial sphere position. Qualitatively, we define the interface as the edge furthest from the sphere center. The sphere did not show compression on the surface in shadow, which was predicted in pre-experimental, two-dimensional simulations. The horizontal axis through the sphere center is where the measurements of the positions shown in later figures are made. The locations of the gold–carbon interface and shock in the sphere were the primary measurements of interest to evaluate the structure of the gold and carbon plasmas.
The simulations paint a similar physical picture as was found in the experiments. Once laser-irradiated, the gold begins rarefying toward the simulated irradiating lasers and a shock forms. The shock in the gold transits through the foil rapidly and, upon breakout, creates a gold rarefaction toward the sphere. Once the x-ray intensity, from the laser-heated gold plasma, is sufficient, the carbon begins to rarefy to the left and a shock is launched into the sphere. The rarefied carbon collides with the gold and forms a second shock in the rarified plasmas for both species. Interpenetration between the carbon and gold occurs until small mean-free-path conditions are met, after which the gold piles up on the carbon. The mean-free-path is likely small (<1 μm) upon first contact due to the likely high ionization state of gold (a consequence of the weakly bound outer-shell electrons). Only at extremely low values of density and extremely high values of relative velocity is a carbon atom able to meaningfully penetrate into the gold plasma. The ram and thermal (total) pressures of the carbon pressure balance the total pressure of the gold. These counter-propagating plasma flows are similar to an indirectly driven inertial confinement system hohlraum interior. The experimental and simulated positions of the shock in the sphere, and gold–carbon interface are plotted in Fig. 9.
HYADES simulation results compared with experimental results. The experimental measurements are points plotted with error bars. The cyan line forms the approximate location of the shock in the sphere. The black line is the position of the first carbon zone. The red line is the position of the last gold zone. Along the central axis through the center of the initial sphere, the sphere edge is at 0 m, the sphere center is at 250 m, and the gold foil is at −500 m.
HYADES simulation results compared with experimental results. The experimental measurements are points plotted with error bars. The cyan line forms the approximate location of the shock in the sphere. The black line is the position of the first carbon zone. The red line is the position of the last gold zone. Along the central axis through the center of the initial sphere, the sphere edge is at 0 m, the sphere center is at 250 m, and the gold foil is at −500 m.
The qualitative shape that the features' positions take along the central axis as a function of time is similar between the experiment and simulation. However, the simulated shock in the sphere is faster than the experimentally measured value and the simulated interface position is offset from the sphere edge by hundreds of micrometers. The gold and carbon zones converge around 2 ns, which is consistent with experimental measurements. Differences between the simulation and experiment might be due to the one-dimensional nature of the simulations, which prevent energy from moving in directions transverse to the simulated axis. Consequently, more energy must escape along a single axis, which can lead to faster flow speeds, or larger x-ray fluxes than are found in an experiment. In our experiment, a result of constraining the energy to one-dimension, is that the carbon slab is illuminated by a higher flux of x rays from the gold slab, which drives a stronger (faster) shock into the sphere, and increases the ablation rate (carbon ram pressure) that moves the pressure balance (interface position) further from the sphere. The interface forms around the same time and, though offset by a few hundred micrometers, has a similar trajectory as in the experiment. In the simulations, the tracked gold and carbon zones do not touch due to the presence of a hydrogen “vacuum” gas used to mock up the initial vacuum between the gold and the carbon slabs. As the simulation evolves, the initially low-density gas is compressed to high pressures and acts to separate the gold and carbon tracked zones.
Experimentally, the shock in the sphere begins around 1.5 ns and appears to move linearly into the sphere as time increases. A linear fit to the experimental data suggests a - m/ns shock speed. Measurements show that the gold–carbon interface forms at the initial sphere edge and the interface does not move much over the span of the experiment.
The carbon sphere experiences x-ray ablation, gold ram pressure, and gold thermal pressures. The total pressure from the gold is estimated as many orders of magnitude lower than the ablation due to x rays, which is of the megabar scale. This suggests that the sphere is driven solely by the x-ray radiation, which is important because there is no interface in the astrophysical phenomena.
V. CONCLUSIONS
In this paper, we described a scaled experiment relevant to an astrophysical phenomena where a large star might collapse a nearby gas cloud, which might create another star. This laboratory-astrophysics experiment platform is important to probe the radiation transport boundaries of star-forming conditions as described in the Bertoldi's 1989 paper. This platform uses x rays from a previously characterized, laser-irradiated, thin gold foil to drive the optical depth-scaled experiment. Different radiation transport regimes (optical depths) are possible by altering the size, density, and material of the sphere.
In this optically thick experiment, an 80-eV quasi-thermal x-ray source drove a shock into the illuminated side of the sphere at a rate of m/ns. The shock developed in the sphere around 1.5 ns. An interface formed between the rarefying gold and carbon plasmas, which was not astrophysically relevant. However, this feature likely did not impact the astrophysical analog, since the total pressure of the gold was much smaller than the x-ray ablation pressure. The creation and study of this interface maybe of interest to the inertial confinement fusion community.
One-dimensional HYADES simulations qualitatively agreed with the experimental measurements and physics intuitions. However, HYADES did not capture the measured location of the interface as a function of time. While the shape of the interface trajectory was consistent, the offset of the interface location was likely due to the one-dimensional nature of the simulation. These experiments have shown that this experimental platform is an interesting testbed to study the potential for stars to form other stars by radiation-driven implosions.
ACKNOWLEDGMENTS
The authors thank the Omega Laser Facility staff, scientists, and engineers for supporting this work. This work was funded by the U.S. DOE NNSA Center of Excellence under Cooperative Agreement No. DE-NA0003869, the NLUF Program, Grant No. DE-NA0002719, and through the LLE, University of Rochester by the NNSA/OICF under Cooperative Agreement No. DE-NA0003856.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
R. W. VanDervort: Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Project administration (supporting); Software (supporting); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Sallee Klein: Investigation (supporting); Project administration (equal); Resources (lead). M. Trantham: Resources (supporting); Software (equal); Validation (lead); Visualization (equal). Pawel M. Kozlowski: Writing – review & editing (equal). Paul A. Keiter: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Project administration (equal); Supervision (equal). R. Paul Drake: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Project administration (equal); Supervision (equal). Carolyn Kuranz: Funding acquisition (equal); Resources (equal); Supervision (equal).
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.