Open Access
Add to BibSonomy
Abstract
Bright x-ray sources play a key role in high-energy density physics experiments. Such sources, when acting as backlighting sources, may shed more light on the dynamics of various high-energy time depended processes. This work describes a shadowgraphy experiment of a dynamic shock-wave propagating inside a silica foam using a Ti foil as a backlighter source, that supports the theoretical simulations. This was carried out using a relatively low (38 J) laser beam for backlighting, providing a 50 µm spot size, a 94 ps pulse duration, and 0.01-0.05 conversion efficiency from laser energy to 4.7 keV x-ray photons. The lateral resolution values of a Ti foil and a narrow Ti wire were measured to be 50 µm and 12 µm, accordingly. The shock front was observed about 200 µm from initial reference point, with a good agreement to theory. Its detection throughout an opaque halfraum was possible using dedicated viewing slits. This work describes the preliminary experiments of the backlighting implementation for future experiments.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Sufficient high-energy x-ray sources (> several keV's) are an important diagnostic tool for radiography of high-energy density physics experiments [1–8]. These sources act as backlighters usually in laser-driven experiments such as shock propagation [9], moving interfaces [10], opacity [5], among others. The backlighter spectral energy and source brightness are the most significant parameters for optimizing backlighting sources. The first determines the radiography spectrum necessary for the experiment, and the latter is necessary for a quality phenomenon observation. A backlighting diagnostic capability for shock wave experiments could expand the diagnostic tools and provide additional useful time-based data. Moreover, in order to implement a backlighting technique, the x-ray source should be distinguished energetically from the radiating environment. By choosing a rather high-energy spectrum emitter, distinctive x-ray source, a well-defined signal could be achieved and analyzed. However, acquiring a sufficient x-ray source for adequate data analysis could be a challenging task, due to the limited laser energy available in the diagnostic beam of the national laser facility (NLF), at Soreq, Israel. The generated spectrum and the conversion efficiency [11] are the most relevant properties for choosing the backlighter material, when tailored to the backlighted optical properties and thickness. There are several obvious candidates for backlighter materials, such as Ti (4.7 keV), V (5.2 keV), and Fe (6.7 keV).
There are several configurations to construct such a diagnostic tool. These are backlighting using large area illumination (i.e. using a large laser spot size), point projection backlighting using pinholes, and point projection backlighting using small area targets such as wires [12,13], without any pinholes [6]. The first approach uses pinholes for imaging, as the pinholes are located between the backlit sample and the detector. The efficiency for backlighting using a large laser spot-size (>hundreds of µm) requires sufficient laser energy. The first set-up is usually applicable for laser systems producing tens of kJ energy for backlighting. The second approach uses a pinhole to generate a point source, as the pinhole is located close to the backlighter target [13–15]. A typical target-pinhole distance and pinhole diameter are 50 mm and 15 µm accordingly. This setup reduces backlighter efficiency by ∼10−7. The last method uses a point source of x-rays that casts a shadow of the sample at the detector as no pinhole is necessary [2,16]. Here, due to a lack of energy available for backlighting (∼40J), the point-projection backlighting configuration was chosen, where a small x-ray source was achieved using a tight-focused laser beam.
In a typical shock-wave experiments, the main laser beams heat a cylindrical hollow element (halfraum). The stored energy is partially converted to x-rays that initiates a shock wave in a foam located inside the halfraum (Fig. 1). Various foams could be used, as the varying densities alter the shockwave propagation velocities. In these experiments, the foam density is tailored to achieve highest experimentally noticeable effect using simulations (elaborated in the theoretical design chapter). The x-ray shadowgraphy of the foam, which is perpendicular to the propagating shock-wave, may provide important analysis of dynamics in the experiment.
Fig. 1. Schematic illustration of the experimental setup. Four heating beams are focused into a halfraum that is partially filled with silica foam. A generated shock wave could be imaged using a backlighter source by the foam transparency variation as the wave propagates.
2. Theoretical design
The experiment conditions were chosen using two-dimensional radiation hydrodynamics simulations based on an arbitrary Lagrangian Eulerian scheme on a fixed Eulerian grid. The grid is based on axial symmetry (R, Z) where Z is the symmetry axis, which is the axis of the wave propagation, and R denotes the radius.
The foam dimensions where 1000 µm in diameter and 300 µm in length. The nominal cell size in the foam was 1.7 × 4.2 µm (in Z and R axes). The radiation transport was calculated using the implicit Monte Carlo (IMC) method with a multigroup (336) scheme. The simulation was based on a measured chemical composition of the foam using an element analysis measurement. The stoichiometric rations were Si1O1.89C0.32H0.065. The foam opacity and equation-of-state were calculated using this composition by the CRSTA [17] and QEOS [18] methods. The electronic heat conduction is modeled as flux-limited diffusion. The laser energy propagation and absorption were modeled using a ray-tracing method. The laser hits the inner halfraum walls at 45° incidence. Since the experiment is driven by four laser beams (a configuration that lacks cylindrical symmetry), it is simulated by a ring having the same laser flux. The halfraum is heated up to 140eV (radiation temperature), initiating a subsonic heatwave in the foam [1]. The subsonic heat wave is accompanied by a shock wave, that generates a jump in the foam density along its propagation [2,19]. The velocity and density jumps depend on the foam's initial density. The evolution of the maximal density variations versus the shock wave propagation length in the foam is shown in Fig. 2. From this analysis, it is clear that the compression increases as the wave propagates deeper into the foam. The circles denote the location of the shock just before the laser power is turned off (∼2.1ns). After the laser termination, the temperature declines, which makes the flow more subsonic, and enables a higher density variation. After the peak, there is a steep decline in density, which is a result of the shock arrival to the foam edge. It is worth mentioning that this regime and dynamics is irrelevant for the experiment demonstrated in this work. In the experiment, a 200 µm backlighting viewing slits are located in a 300 µm thick foam, as 50 µm from each side of the foam are opaque for backlighting (Fig. 4 left). Hence, viewing the shockwave is applicable around 200 µm, as the shock wave velocity is more distinguishable due to the varying velocities for different foam density.
Fig. 2. Simulation results showing the obtained density variations upon shock-wave propagation inside the foam, for several initial densities. The circles denote the shock location, as the laser is turned off, after 2.1 ns for each foam density.
These considerations dictated the foam density value to be 140 mg/cc (see Fig. 2). Generally, this calculation illustrates that decreasing the foam density also minimizes the density change due to the shock wave, and accelerates its velocity inside the foam. The density variations are manifested and measured by the foam transparency. Hence, higher density changes exhibit increased contrasts on the detector. This sets the foam initial density, and its desired temporal location. The timing of the backlighter was set to start at the end of the 2 ns main laser pulse. Few realizations were simulated to estimate the expected backlighter radiation transmission through the foam as could be seen in Fig. 3.
Fig. 3. Calculated transmission function of the backlighted halfraum, filled by the silica foam, along the wave propagation. The nominal conditions are accompanied by additional curves that describe ±20% laser variations and ±5% density changes in the foam.
Here, variations of ±5% and ±20% in the foam density, and in the laser power are investigated, respectively. The nominal simulation predicts a shock wave location at Z = 195 µm. Increasing the laser energy by 20% will shift the wave-front location forward (to the right), in respect to the nominal value.
3. Experimental design
3.1 Backlighter source and targets
The objective experiment in which the backlighter ability is required, involves generation and identification of a wave-front, propagating through the halfraum. This phenomenon affects the silica density and hence, its transparency, that could be analyzed using radiography. This interference is achieved by sending four 3rd harmonic laser beams (1800 J in total) with pulse duration of 2 ns into the inner part of the halfraum as already mentioned. Such interaction would initiate a wave into the silica foam that changes its properties (density and temperature). In addition, the halfraum radiates photons in a wide spectral range.
The laser system is equipped with four beams of 400-500 J each, characterized by a tunable 1-3 ns pulse duration at 355 nm operating wavelength. In the backlighting experiment a 2 ns pulse was chosen with 450 J per beam.
The beams hit the inner part of a 1 mm in diameter and 1.3 mm long gold halfraum [20]. The beams enter from one side, while the last 0.3 mm of the halfraum is filled with silica foam. An additional fifth beam, capable of 40 J at 94 ps, is used to produce the x-ray backlighter source (see Fig. 1). Thus, the intensity of the backlighting beam is ∼1 × 1016 W/cm2. The backlighter x–ray pulse duration is expected to be ∼150 ps according to our simulations
In this work a Ti source was chosen, as it can penetrates through the foam diameter, using a relatively narrow spectrum around 4.7 keV [3,21,22], providing 10% transmission through the undisturbed foam [5,8,23–26].
A small source size is required in order to detect this phenomenon with sufficient accuracy. Here, we demonstrate two backlighter sources, using (i) a 5 µm thick Ti foil and (ii) a Ti wire. The wire thickness and width are 5 µm and 12 µm, respectively. A custom targets design was carried out to allow the required precision for this experiment, as one unified holder contained the backlighter target and the halfraum. The halfraum target holder and the Ti backlighter wire target are presented in Fig. 4.
Fig. 4. Left: A picture of the halfraums placed on a tungsten holder. The heating beams enter from the left side, as the shock wave propagates to the right side, through the silica foam. Variations on the foam opacity are designed to be detected by backlighting using a Ti x-ray source through the slits. Right: Microscope image of a Ti wire backlighting source. The four holes are used for alignment purposes.
3.2 Spatial resolution evaluation
In order to determine the spatial resolution that could be achieved in such an experiment, a resolution target was placed at the foam location. In such configuration, a single beam is focused on the Ti backlighter target located 26.8 mm away. The heated target emits radiation that passes through the resolution target towards the detector, at distance of 462 mm apart. The obtained image on the detector is magnified (x17) due to the mentioned distances. A higher magnification may improve SNR, but can be used only in a case of good mechanical accuracy, that keeps the image in the detector. The resolution target is composed by thin (10 µm) Au foil, that was laser machined to produce slits of varying widths (10, 20, 40, 100 µm), see Fig. 5. An 85 µm Ti foil was placed on the detector to block parasitic light, and additional 50 µm Mylar foil was used for extra protection from shrapnel. The protection foils setup was also used similarly in the future dynamic experiment (Ti and Mylar transmission values are 4% and 80%, accordingly). The origin of the parasitic radiation comes from the heated halfraum that should be filtered out. Unfortunately, a shrapnel managed to penetrate both Ti and Mylar films, and damaged the detector. In order to minimize further risks, image plates were used in the dynamic part of this work.
Fig. 5. An illustration of the target's ensemble. The backlighting beam is focused and heats the Ti foil or wire. The emitted spectrum shadowgraph the halfraum target on the detector. The spatial resolution is extracted from the blur at the shadow edges. A resolution target having many slits replaced the halfraum in static shots to improve resolution measurement.
Figure 5 demonstrates the target holder design and a SEM image of the resolution target. An Al foil of thickness 25 µm (not shown in Fig. 5) was placed on the upper part of the resolution target, covering the target slits, leading to a signal reduction of x6.
The attained lateral resolution results can be seen in Fig. 6, comparing the performance of both a Ti foil, and a 12 µm Ti wire. Line scans of the images are plotted along with the lateral target and slits dimensions in the top part of Fig. 6. The bottom part of Fig. 6 provides the corresponding backlighted images registered on the CCD detector. It can be seen clearly that there is a significant increase in the obtained resolution when using a Ti wire, accompanied by an increase of the signal-to-noise ratio. The measured spatial resolution from the Ti foil is roughly 50 µm, whereas the resolution obtained using the narrow Ti wire is about 12 µm. These values were derived from the measured line-profiles using a Gaussian fitting analysis. Analysis of the imaged attained in Fig. 6 showed a total signal increase factor of 24 in x-ray intensity when switching from the narrowest wire target to a foil. This variation is not scalable with the areal ratio between the two geometries. This result might be related to the volumetric cooling effects of the wire compared with a foil target. This outcome led to use a foil as a backlighting source for the dynamic experiment, rather than the desired narrow wire. The conversion efficiency into 4.7keV was about 0.4% for a foil target, and the SNR was ∼45, when analyzing with 5 × 5 µm pixel size in the image plane. The shadowgraph spectrum was qualitative checked with an Al foil – its theoretical attenuations is 6, while the measured attenuation was 5.5. Backlighter source dimensions in the x and y were extracted from image blur (see Fig. 6).
Fig. 6. Top: The measured spatial resolutions, originated by a Ti wire and a Ti foil. The nominal dimensions of the resolution target are also demonstrated in the data. Bottom: The obtained backlighting images, taken by the detector, from a wire (left) and foil (right) Ti targets. The x-ray source dimensions were estimated to be 50±4 µm and 12±2 µm for the foil and the thinner wire. Intensity analysis showed a total signal increase factor of 24 when switching from the narrowest wire target to a foil. For a 50 µm spot size, the area difference can explain a factor of 4, meaning that a factor of 6 would be discussed later.
4. Dynamic backlighting
The objective of the dynamic experiment is to measure the shock wave location inside the silica foam at a given predesigned time. Four laser beams enter the halfraum, initiating a shock wave that propagates along the foam. The density jump at the wavefront makes it opaque and its location can be seen by an x-ray shadowgraphy. Since the halfraum is opaque to the backlighter x-ray source, slits were machined on both sides of the target's gold coating, and aligned along the optical path between the backlighter target and the detector (see Fig. 4).
The Au halfraum encapsulated a silica foam with a measured density of 141 ± 14 mg/cc. The foam specific weight was estimated as similar (up to 10%) to a test sample measurement. The slits dimensions were 100 µm and 250 µm in height and length respectively. In this shot, an image-plate detector was used, which replaced the former CCD due to shrapnel risks. The backlighting source was a 5 µm thick Ti foil, heated by an additional laser beam of 38 J with a pulse duration of 94 ps, that was focused to reach a 50 µm spot size.
The shadowgraphy that was obtained in the dynamic experiment is brought in Fig. 7. Here, a clear image of the halfraum profile can be seen. A noticeable signal reached the detector through the designed slits, as the entire flange can be seen as well. The inset provides a zoomed image of the slits, as the signal was normalized. A noticeable deep appears through the slits. After merging pixels to reach 5 × 5 µm pixel size in the image plane, an SNR ration of 42 was achieved. The signal was measured to be ∼630, while the noise was estimated to be ∼15. The expected SNR for a measurement through 10% transmission media would be ∼4.
Fig. 7. Dynamic shadowgraph, taken 2.1 ns after the four heating beams reached the halfraum. Noticeable opacity changes can be observed through the slits and along the foam. The inset provides a zoomed image of the slits, as the signal was normalized.
Analysis of the measured attenuation at the slits, brought in the inset of Fig. 7, can be seen in Fig. 8. The line plot of the integrated intensity appears in red. This curve is accompanied by two simulated curves. The blue curve is the simulated transmission variations by an ideal point source. A realistic time-integrated simulated curve is plotted in green, using a convoluted 50 µm source. The point source simulation provides a well-defined shock front that is manifested as a sharp deep at 195 µm.
Fig. 8. Semi-log scale transmittance line plots of the experimental data, along with simulated curves through the slits. The simulations show a point source and realistic x-ray source transmissions. The slits begin 50 µm from the foam edge. The reason we used a Ti foil, is that the estimated SNR for a ∼10 µm wire was below 1, which is not acceptable.
The high transmission area at the beginning of the slits describes the expanded regime of the foam, which exhibit a low-density regime that creates increased transparency. The transmission decreases along the slits until reaching the shock front, which later on, increases again (distance > 200 µm) at the unperturbed foam regime. There is a correlation between the shock locations of in all three curves. The measured transmission of the unperturbed zone also fits the simulations. The expended regime (Fig. 8 left side) shows variation of ∼ 30% between the experiment and simulations. This difference may be attributed to the existence of Au plasma that is generated from the halfraum walls. These Au particles reduce the general opacity of the transmitted backlighted photon through the slits. This effect is not well described in the given simulations.
5. Conclusions
We demonstrated shadowgraphy experiment of a dynamic shock-wave propagating inside a silica foam using a Ti foil as a backlighter source. The attained result fits the predicted simulations of the 50 µm source size (Fig. 8). The experiment was based on a relatively low (38 J) laser beam as the backlighter source. The shadowgraphy was made possible by focusing the laser beam down to a 50 µm spot size, and using a simple and straight-forward approach (i.e., without imaging). Preliminary experiments established lateral resolution values of 50 µm and 12 µm for a Ti foil and a 12 µm wide wire targets, respectively. Backlighting with a thin wire x-ray source reduces the overall signal, compared to a Ti foil (see Fig. 6).
The obtained shock front was observed at the predicted location, near 200 µm. This was manifested in a transmission deep through the slits. The lateral resolution was ∼50 µm, which was limited by the laser spot size heating the Ti foil. A transmission of ∼30% was measured at the already ablated part of the foam. The simulations predicted higher transmission values. This variation could be caused by an Au plasma entering the backlighted regime, which is not well simulated. This demonstration is the facility's benchmark toward backlighting experiments as high intensity sources and high-resolved images are desired. Backlighting using a narrow wire reduces the total backlighted intensity, due to the areal ratios between the laser spot size and wire width. However, an unpredicted intensity decrease (x6, see Fig. 6) was obtained, when using the narrow wire. This could be related to additional dynamics, such as temporal thermal effects. These challenges are to be investigated further on. Future experiments could incorporate radiography images that will be obtained using different x ray sources, such as backlit slits [12,27].
Acknowledgments
We would like to thank the entire National Laser Facility (NLF) personnel for their support on this project. We also want to thank NLF's target group for supplying sufficient targets and overcoming various difficulties and limitations.
Disclosures
There are no other financial and non-financial competing interests to declare in relation to this manuscript.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
1. K. Mussack, B. ∼G. Devolder, P. ∼A. Keiter, J. ∼L. Kline, N. Lanier, G. ∼R. Magelssen, R. ∼R. Peterson, and J. ∼M. Taccetti, “Simulating hohlraum dynamics and radiation flow for Pleiades experiments on NIF,” in APS Division of Plasma Physics Meeting Abstracts, APS Meeting Abstracts (2011), Vol. 53, p. GP9.124.
2. M. R. Baer, “A numerical study of shock wave reflections on low density foam,” Shock Waves 2(2), 121–124 (1992). [CrossRef]
3. C. Mcguffey, M. Dozieres, J. Kim, A. Savin, J. Park, J. Emig, C. Brabetz, L. Carlson, R. F. Heeter, H. S. McLean, J. Moody, M. B. Schneider, M. S. Wei, and F. N. Beg, “Soft X-ray backlighter source driven by a short-pulse laser for pump-probe characterization of warm dense matter,” 122, (2019). [CrossRef]
4. H. M. Johns, C. L. Fryer, S. R. Wood, C. J. Fontes, P. M. Kozlowski, N. E. Lanier, and A. Liao, “High Energy Density Physics A temperature profile diagnostic for radiation waves on OMEGA-60,” High Energy Density Phys. 39, 100939 (2021). [CrossRef]
5. Y. Wu, G. Jain, T. Sizyuk, X. Wang, and A. Hassanein, “Dynamics of laser produced plasma from foam targets for future nanolithography devices and X-ray sources,” Sci. Rep. 11(1), 1–14 (2021). [CrossRef]
6. J. Workman, J. R. Fincke, P. Keiter, G. A. Kyrala, T. Pierce, S. Sublett, J. P. Knauer, H. Robey, B. Blue, S. G. Glendinning, and O. L. Landen, “Development of intense point x-ray sources for backlighting high energy density experiments (invited),” Rev. Sci. Instrum. 75(10), 3915–3920 (2004). [CrossRef]
7. D. L. Matthews, E. M. Campbell, N. M. Ceglio, G. Hermes, R. Kauffman, L. Koppel, R. Lee, K. Manes, V. Rupert, V. W. Slivinsky, R. Turner, and F. Ze, “Characterization of laser-produced plasma x-ray sources for use in x-ray radiography,” J. Appl. Phys. 54(8), 4260–4268 (1983). [CrossRef]
8. M. A. Barrios, S. P. Regan, K. B. Fournier, R. Epstein, R. Smith, A. Lazicki, R. Rygg, D. E. Fratanduono, J. Eggert, H. S. Park, C. Huntington, D. K. Bradley, O. L. Landen, and G. W. Collins, “X-ray area backlighter development at the national ignition facility (invited),” Rev. Sci. Instrum. 85(11), 11D502 (2014). [CrossRef]
9. L. Antonelli, S. Atzeni, A. Schiavi, S. D. Baton, E. Brambrink, M. Koenig, C. Rousseaux, M. Richetta, D. Batani, P. Forestier-Colleoni, E. Le Bel, Y. Maheut, T. Nguyen-Bui, X. Ribeyre, and J. Trela, “Laser-driven shock waves studied by x-ray radiography,” Phys. Rev. E 95(6), 063205 (2017). [CrossRef]
10. T. Ebert, N. W. Neumann, L. N. K. Döhl, J. Jarrett, C. Baird, R. Heathcote, M. Hesse, A. Hughes, P. McKenna, D. Neely, D. Rusby, G. Schaumann, C. Spindloe, A. Tebartz, N. Woolsey, and M. Roth, “Enhanced brightness of a laser-driven X-ray and particle source by microstructured surfaces of silicon targets,” Phys. Plasmas 27(4), 043106 (2020). [CrossRef]
11. C. M. Huntington, C. M. Krauland, C. C. Kuranz, R. P. Drake, H. S. Park, D. H. Kalantar, B. R. Maddox, B. A. Remington, and J. Kline, “Development of a short duration backlit pinhole for radiography on the National Ignition Facility,” Rev. Sci. Instrum. 81(10), 10E536 (2010). [CrossRef]
12. A. B. Bullock, O. L. Landen, B. E. Blue, J. Edwards, and D. K. Bradley, “X-ray induced pinhole closure in point-projection x-ray radiography,” J. Appl. Phys. 100(4), 043301 (2006). [CrossRef]
13. J. Workman, J. R. Fincke, G. A. Kyrala, and T. Pierce, “Uniform large-area x-ray imaging at 9 keV using a backlit pinhole,” Appl. Opt. 44(6), 859–865 (2005). [CrossRef]
14. A. B. Reighard, S. G. Glendinning, P. E. Young, W. W. Hsing, M. Foord, M. Schneider, K. Lu, T. Dittrich, R. Wallace, and C. Sorce, “Long duration backlighter experiments at Omega,” Rev. Sci. Instrum. 79(10), 10E915 (2008). [CrossRef]
15. D. K. Bradley, O. L. Landen, A. B. Bullock, S. G. Glendinning, and R. E. Turner, “Efficient, 1–100-keV x-ray radiography with high spatial and temporal resolution,” Opt. Lett. 27(2), 134 (2002). [CrossRef]
16. S. Y. Tu, G. Y. Hu, W. Y. Miao, B. Zhao, J. Zheng, Y. T. Yuan, X. Y. Zhan, L. F. Hou, S. E. Jiang, and Y. K. Ding, “Efficient multi-keV x-ray source generated by nanosecond laser pulse irradiated multi-layer thin foils target,” Phys. Plasmas 21(4), 043107 (2014). [CrossRef]
17. Y. Kurzweil and G. Hazak, “Inclusion of UTA widths in the Configurationally Resolved Super-Transition-Arrays (CRSTA) method,” High Energy Density Phys. 9(3), 548–552 (2013). [CrossRef]
18. R. M. More, K. H. Warren, D. A. Young, and G. B. Zimmerman, “A new quotidian equation of state (QEOS) for hot dense matter,” Phys. Fluids 31(10), 3059–3078 (1988). [CrossRef]
19. A. Britan, G. Ben-Dor, H. Shapiro, M. Liverts, and I. Shreiber, “Drainage effects on shock wave propagating through aqueous foams,” Colloids Surf., A 309(1-3), 137–150 (2007). [CrossRef]
20. E. I. Moses, “The National Ignition Campaign: Status and progress,” Nucl. Fusion 53(10), 104020 (2013). [CrossRef]
21. P. A. Keiter, A. Comely, J. Morton, and M. Taylor, “Conversion efficiency of high- materials backlighter Conversion efficiency of high- Z backlighter materials a …” Rev. Sci. Instrum. 918, 6–9 (2016). [CrossRef]
22. A. You, M. A. Y. Be, and I. In, “Extended x-ray absorption fine structure measurements of quasi-isentropically compressed vanadium targets on the OMEGA laser,” Physics of Plasmas 15, 6062703 (2018). [CrossRef]
23. M. A. Barrios, K. B. Fournier, S. P. Regan, O. Landen, M. May, Y. P. Opachich, K. Widmann, D. K. Bradley, and G. W. Collins, “Backlighter development at the National Ignition Facility (NIF): Zinc to zirconium,” High Energy Density Phys. 9(3), 626–634 (2013). [CrossRef]
24. M. Primout, D. Babonneau, L. Jacquet, B. Villette, F. Girard, D. Brebion, P. Stemmler, K. B. Fournier, R. Marrs, M. J. May, R. F. Heeter, R. J. Wallace, H. Nishimura, S. Fujioka, M. Tanabe, and H. Nagai, “A new hybrid target concept for multi-keV X-ray sources,” High Energy Density Phys. 9(4), 750–760 (2013). [CrossRef]
25. F. Pérez, J. R. Patterson, M. May, J. D. Colvin, M. M. Biener, A. Wittstock, S. O. Kucheyev, S. Charnvanichborikarn, J. H. Satcher, S. A. Gammon, J. F. Poco, S. Fujioka, Z. Zhang, K. Ishihara, N. Tanaka, T. Ikenouchi, H. Nishimura, and K. B. Fournier, “Bright x-ray sources from laser irradiation of foams with high concentration of Ti,” Phys. Plasmas 21(2), 023102 (2014). [CrossRef]
26. O. L. Landen, D. R. Farley, S. G. Glendinning, L. M. Logory, P. M. Bell, J. A. Koch, F. D. Lee, D. K. Bradley, D. H. Kalantar, C. A. Back, and R. E. Turner, “X-ray backlighting for the National Ignition Facility (invited),” Rev. Sci. Instrum. 72(1), 627–634 (2001). [CrossRef]
27. A. B. R. Cooper, M. B. Schneider, S. A. MacLaren, A. S. Moore, P. E. Young, W. W. Hsing, R. Seugling, M. E. Foord, J. D. Sain, M. J. May, R. E. Marrs, B. R. Maddox, K. Lu, K. Dodson, V. Smalyuk, P. Graham, J. M. Foster, C. A. Back, and J. F. Hund, “Streaked radiography of an irradiated foam sample on the National Ignition Facility,” Phys. Plasmas 20(3), 033301 (2013). [CrossRef]
