Abstract

The study of Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities in a planar geometry at high energy densities at the National Ignition Facility (NIF) requires high spatial resolution imaging. We demonstrate the potential of Fresnel zone plates (FZPs) to achieve resolution that would unlock such studies. FZPs are circular aperiodic gratings that use diffraction to focus x rays and produce an image with high spatial resolution. Taking into account the NIF’s challenging environment, we have designed a specific array of five FZPs for a zinc backlighter to take a radiograph of a target with 9 keV x rays. We measured a mean resolution for the FZP of $1.9\; {{\unicode{x00B5}{\rm m}}} \pm 0.5 \;{{\unicode{x00B5}{\rm m}}}$ and a ${\pm}1 \;{\rm{mm}}$ depth of focus at an x-ray calibration facility as well as a $2.3 \;{\rm{\unicode{x00B5}{\rm m}}} \pm 0.4 \;{{\unicode{x00B5}{\rm m}}}$ resolution on a resolution wire mesh shot on the NIF. We also performed an in-depth analysis of the image quality to assess the capability to resolve the small features present in RT and RM instabilities.

© 2020 Optical Society of America

1. INTRODUCTION

The study of Rayleigh–Taylor (RT) [1,2] and Richtmyer–Meshkov (RM) [3,4] instabilities has been a major topic in both inertial confinement fusion (ICF), where they need to be minimized to achieve ignition, and laboratory astro-physics. These hydrodynamic instabilities occur at the interface of a lower-density material with a higher-density material and develop into a mixing region that can eventually become turbulent [5,6]. Control over the initial and driving conditions in the high-energy-density (HED) field allows the observation of RT and RM instabilities [714]. One common way to observe these instabilities in HED experiments is through the use of x-ray radiography, typically employing pinhole imagers [1518]. Pinhole optics are used widely, as they provide a well-characterized way of obtaining multiple sets of both time integrated and time resolved images. However, since the resolution and solid angle are both dependent on the pinhole diameter, improving resolution results in a loss of throughput. A good candidate to complement pinholes are Fresnel zone plates (FZPs) [19]. Those optics use diffraction to focus x rays and can potentially, in an ideal condition, reach nanometer resolution range [2022]. For example, FZPs are used at synchrotron facilities to focus monochromatic x-ray beams down to tens of nanometers. The imaging resolution of FZPs is limited by both diffraction order blurring and chromatic aberration. Despite these issues, the use of such optics has been successfully demonstrated at high-power laser facilities [2325]. Measurements showed that they could reach resolutions between 3 µm and 8 µm. The FZP aperture diameter is decoupled from the resolution, enabling a larger throughput than a pinhole for the same resolution, with both a field of view and a depth of field (DOF) on the order of 1 mm.

Using FZPs, we are developing a new experimental HED platform at the National Ignition Facility (NIF), based on the one described in Ref.  [15]. The goal of this platform is to be able to image the characteristic features of hydrodynamic instabilities as they approach turbulent transition in a planar geometry. Simulations have shown that the minimum spatial resolution needed to observe the scale lengths associated with the turbulent regime is on the order of a micrometer [26] with a field of view of at least ${{1}}\;{\rm{mm}} {\times} {{1}}\;{\rm{mm}}$. The design goal of this new platform is to produce imaging resolution of 3 µm or better to provide a factor of seven improvement over previous mixed imaging platforms. The potentially high spatial resolution of FZPs makes them suitable for this application. Another advantage of FZPs is that their small size allows them to be designed to replace the widely used pinhole imagers used at the NIF.

A FZP is a circular grating with aperiodic steps. Each wavelength is focused at distance following the formula [27,28]

$${f_{m,\lambda}} = \frac{{{r_1}^2}}{{m*\lambda}},$$
with ${f_{m,\lambda}}$ the focal distance for the wavelength $\lambda$, $m$ the diffraction order, and ${r_1}$ the radius of the first Fresnel zone. The $n$th zone radius, ${r_n}$, is given by
$${r_n} = \sqrt n *{r_1}.$$

As appealing as the FZP can be, there are three major issues that need to be addressed before it can produce a radiograph of RT and RM experiments at the NIF. The first issue is related to the optic itself. As can be seen in Eq. (1), there is a strong dependence on both chromatic and diffraction orders, which significantly increases the background signal. We also need to consider the detector resolution: available detectors to be used with the FZP are currently either an imaging plate (IP) [29] or an x-ray framing camera (FC) with 70 µm and 40 µm resolution, respectively. To bring the resolution down to 3 µm, a high magnification is required. Finally, the velocity of the RT and RM growths can induce motion blur that will have to be considered.

Section 2 of this paper describes the design solutions that allow us to overcome most of the aforementioned constraints. Section 3 discusses the results of the spatial resolution calibration conducted at the Lawrence Livermore National Laboratory (LLNL) x-ray optic calibration laboratory. Section 4 outlines the results of the first calibration shot on the NIF using FZP along with a discussion of its quality in Section 5. Finally, Section 6 presents simulation results demonstrating the use of FZPs to study RM and RT instabilities.

2. DESIGN OF THE FRESNEL ZONE PLATE

Based on Eqs. (1) and (2), we need at least three values to fully calculate the parameter values of a FZP: the wavelength, focal distance, and total size of the FZP.

For the backlighter (BL), we chose to use the zinc (Zn) $H{e_\alpha}$ line (${\sim}{{9}}\;{\rm{keV}}$), as it is a well-characterized BL material at the NIF [30]. It has three main advantages: as can be seen in Fig. 1: the bandwidth of this line is 0.1 keV full width at half maximum (FWHM), reducing the chromatic aberrations; the line is also isolated, as the peak emission of neighboring lines is less than 10% of the chosen line (Fig. 1), and the conversion of laser light to x-ray emission is high for the NIF at 0.15% [30]. As shown in Fig. 2, the point spread function (PSF) of the FZP rapidly increases with energy, but in the 0.1 keV bandwidth of the Zn $H{e_\alpha}$ line, the PSF is still under 1.2 µm, which is compliant with the design requirements indicated by the red dashed horizontal line.

 figure: Fig. 1.

Fig. 1. Zn backlighter spectrum between 7 keV and 11 keV as measured by SuperSnout II (SSII) spectrometer on shot N200105.

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 figure: Fig. 2.

Fig. 2. Calculated point spread function of the FZP variation with photon energy.

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As stated before, with the current available detectors, the high-resolution capability of the FZP means that the total resolution will be detector limited and not optic limited. To overcome this issue, a very high magnification of ${{61.4}\times}$ was chosen for the NIF geometry. The flexibility of FZPs allowed us to use a pre-existing diagnostic configuration by replacing the former pinhole optic. This setup has a 100 mm optic-target standoff and can make use of two detectors: an IP located 6138 mm behind the optic and a FC located 7100 mm behind the optic. The respective resolution of ${\sim}{{70}}\;{{\unicode{x00B5}{\rm m}}}$ and ${\sim}{{40}}\;{{\unicode{x00B5}{\rm m}}}$ and magnification of ${{61.4}\times}$ and ${{71}\times}$ bring the detector resolution to, respectively, 1.14 µm and 0.56 µm. As shown later, those resolutions are, respectively, two and four times lower than the total measured resolution; thus, they are not the limiting factor here. This allows us to calculate the focal distance at 9 keV required for the FZP design, as they follow the thin lens equation: ${{f}}({{9}}\;{\rm{keV}}) = {98.4}\;{\rm{mm}}$. The difference between the two magnifications corresponds only to an optic-target distance change of 220 µm, which, as shown later, is lower than the optic DOF.

Because the FZP has a lower throughput in the first diffraction order than pinholes, it is desirable to have the FZP diameter as large as possible. This dimension is limited only by the manufacturing capabilities for the thinnest zones $\Delta {{{r}}_{{n}}}$. Currently, fabrication methods exist to push $\Delta {{{r}}_{{n}}}$ down to 7 nm [20] and resolution as low as 5 nm [31]. However, these fabrication methods have limits on the aspect ratio and hence are too thin for our design of the 9 keV platform. Additionally, in our configuration, the system resolution is limited by chromatic aberrations and detector resolution long before it starts to be diffraction limited. The outer diameter of the zone plate, and hence the solid angle, is desired to be as large as possible. A compromise between the achievable aspect ratio, the ratio between the optic thickness and the smallest zone width, and its diameter was found for $\Delta {{{r}}_{{n}}} = 60 \;{\rm{nm}}$. The diameter of the FZP is then 225.66 µm diameter and the optic thickness is 1500 nm, giving an aspect ratio of 25. The ideal thickness for a 9 keV gold zone plate is 1790 nm, but as shown later, the optic efficiency is still satisfactory. The FZPs were manufactured by Applied Nanotools Inc. [32], and the essential parameters are summarized in Table 1.

The NIF diagnostic positioning has uncertainty of 200 µm horizontally ($x$) and vertically ($y$) that we must account for to make sure the image falls on the detector. The total surface covered by an image is ${{62}}\;{\rm{mm}} \times {{62}}\;{\rm{mm}}$, due to the size of the IP in use being ${{185}}\;{\rm{mm}} \times {{285}}\;{\rm{mm}}$; there is a ${\pm}800 \;{{\unicode{x00B5}{\rm m}}}$ tolerance in the $x$ direction and ${\pm}1.5 \;{\rm{mm}}$ in the $y$ direction. Moreover, we are using an array of five identical FZPs that follows the pattern presented in Fig. 3 and will create five identical images. The large red circles represent the FZP position aligned in a rotated cross to optimize the coverage on the IP. This presents the advantage of making sure that we can get at least one full image on the detector. Moreover, the different images can be summed up to improve the total signal-to-noise ratio (SNR). However, it can limit the available field of view due to the spacing of the FZPs.

Tables Icon

Table 1. FZP Characteristics

 figure: Fig. 3.

Fig. 3. Pattern of the NIF FZP array. This design has five FZPs (large red circles) arranged so that they are offset vertically and horizontally to maximize the field of view without overlapping the images. The solid lines marked with double slashes represent a displacement of 1.1 mm, and the dashed lines with triangles are 0.25 mm displacements.

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3. RESOLUTION AND DEPTH OF FOCUS MEASUREMENT AT THE LLNL X-RAY CALIBRATION LABORATORY

A first calibration of the zone plate array was carried out at LLNL’s x-ray calibration laboratory [33] using a ∼1 mm tungsten (W, ${{Z}} = {{74}}$) x-ray source to back-illuminate a tungsten wire mesh (50 µm wires separated by 200 µm) with a 300 s exposure time using a coupled charge device (CCD) camera. For practical reasons, it was not possible to reproduce the ${{64}\times}$ magnification of the NIF, and it was instead set at a ${{20\times}}$ value. The resolution of this method, based on previous work [2325,34], was expected to be around 3 µm to 4 µm, thus this magnification combined with the pixel size (24 µm) of the CCD camera allows sufficient resolution measurements down to 1.5 µm. To reduce the chromatic aberration due to the x-ray source spectral emission, we filtered it with 20 µm of copper and 20 µm of nickel; the original and filtered spectra are presented in Fig. 4 showing that the fraction of the spectrum that we use has only a 400 eV bandwidth between 7.95 keV and 8.35 keV.

 figure: Fig. 4.

Fig. 4. Normalized ${{W}}$ source spectra without any filtering (blue) and with filtering (orange).

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Although the energy range of the source is not at the $9 \;{\rm{keV}} \pm 0.05 \;{\rm{keV}}$ energy of the FZP design, the x rays are still focused, but with a different focal length, as defined by Eq. (1). We expect a degradation of the resolution due to chromatic aberration of the wider energy bandwidth. The calculated diffraction efficiency, shown in Fig. 5, has a broad maximum from 7.5 keV to 9 keV, covering the spectral range used for testing.

 figure: Fig. 5.

Fig. 5. Theoretical diffraction efficiency of a 1.5 µm thick Au FZP for the (blue dashed) zeroth order, (orange solid) first order, and (black dotted) third order.

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 figure: Fig. 6.

Fig. 6. (a) Image of the flat field for the five FZPs using the ${{W}}$ source; (b) typical radiograph of the gold wire mesh.

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 figure: Fig. 7.

Fig. 7. Flat field corrected image of Fig. 6(b).

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To reduce the effect of source spatial non-uniformity on our resolution analysis, we first made a flat field measurement without the wire mesh in place [Fig. 6(a)]. A raw data radiograph is presented in Fig. 6(b) and a processed image in Fig. 7. The method to measure the resolution is identical to the one used in Refs.  [23,24,34]. A lineout of a wire edge is taken from the image, then we use a Savitzky–Golay filter (windows of five pixels and third-order polynomial) to reduce the noise. Finally, we take the derivative of the filtered lineout, and the resulting FWHM is the resolution. The error bars are calculated from both the filtering and the FWHM fitting. For each zone plate, the measurement was taken at different horizontal and vertical positions for different distances between the FZP and the wire mesh (drive depth position). For clarity, only the results for the central and left FZP are presented in Fig. 8. Our first observation is that the resolution decreases the more we increase the drive depth position with a best resolution of $1.9 \; {{\unicode{x00B5}{\rm m}}} \pm 0.5 \; {{\unicode{x00B5}{\rm m}}}$ when the SNR is 41. We also had a high photon count at 3200 photons/resolution element/600 ps. Second, despite the parallax difference, all the FZPs have the same resolution. Finally, if we consider our resolution criterion of 3 µm, then the DOF of the optic is about ${\pm}1 \;{\rm{mm}}$. It was important to measure this value of the FZP, as it dictates the alignment tolerance of the optic to optimize the resolution. For instance, the NIF has an approximate drive depth error of ${\pm}0.5\; {\rm{mm}}$; thus, this is compensated for by the high DOF of FZPs. As expected, due to chromatic aberrations, we do not reach the diffraction limit of the FZP, which is known to be $1.22 \times \Delta {{{r}}_{{n}}}$, with $\Delta {{{r}}_{{n}}} = 60 \;{\rm{nm}}$ the last zone of the zone plate. Note that the resolution degradation in Fig. 8 is not symmetrical; this is due to the energy-focal distance relation of the FZP. As we get closer to the source, the photons at nominal energy start to get out of focus, but because photons at lower energy are getting back in focus, the resolution decrease is slower. In our case, when the distance increases, the higher energies that are supposed to be focused are filtered out by the Cu and Ni filters, so the resolution decrease is not smoothed out.

 figure: Fig. 8.

Fig. 8. Resolution measurement versus the distance (drive depth position) from the FZP to the wire mesh. The zero value of the $x$ axis corresponds to the estimated best focal position of the FZP, the plus (minus) values represent an increased (decreased) FZP-mesh distance, and the shift of the peak resolution is due only to positioning measurement error in the lab. The results are presented for the central (blue) and left (red) FZP on horizontal (circle) and vertical (square) axes. The red points have been shifted 100 µm left for visibility.

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 figure: Fig. 9.

Fig. 9. VISRAD [35] front view of the target experimental setup.

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4. RESULTS OF THE NIF RESOLUTION SHOT

A shot with a similar wire mesh was performed at the NIF to assess on-shot resolution of the FZP array (FZPa) with the shot labeled N200105. For the BL, we used a 12 µm thick Zn foil illuminated by 24 NIF beams with a 600 ps square pulse and a total energy of 24 kJ. The foil faced the FZPa optical axis, and the estimated FWHM of the BL was 1 mm (Fig. 9). A tungsten mesh, with 50 µm wires and 100 µm gap, was located 2.5 mm away from the BL. A gold frame was mounted on the mesh to limit the field of view to ${{1}}\;{\rm{mm}} \times {{1}}\;{\rm{mm}}$. This was done to avoid cross-talk among the five high-magnification images. As stated previously we used a ${{180}}\;{\rm{mm}} \times {{290}}\;{\rm{mm}}$ super-resolution SR IP (SRIP) with a ${{20}}\;{\rm{mm}} \times {{20}}\;{\rm{mm}}$ aperture to also get the 100 ps time gated image on the FC camera. To protect the FZP from debris, a 2 mm thick polyimide foil was put in front of the FZP, and a 20 µm thick Zn foil was used to constrain the spectral bandwidth and reduce spectral aberration.

The result of the shot is presented in Figs. 10 and 11. The resolution calculation method was identical to the one in Section 3, i.e., taking a lineout of the mesh, taking the derivative, and measuring the FWHM of this derivative for each edge (Fig. 12). This was repeated for each of the five images, vertically and horizontally and on the full $1 \;{\rm{mm}}^2$ surface of the image. The conclusion of this measurement was that the resolution is identical over the full field of view and over the five images both vertically or horizontally. Thus, we can give a mean value for the resolution of all the FZPs: $2.3 \;{{\unicode{x00B5}{\rm m}}} \pm 0.4 \;{{\unicode{x00B5}{\rm m}}}$.

 figure: Fig. 10.

Fig. 10. Imaging plate scan of the NIF shot N200105. The five images come from the five FZPs used for this shot. The hole in the image 1 area is used for the time gated detector.

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 figure: Fig. 11.

Fig. 11. Zoom on image 1 in Fig. 10. The time gated image captured by the framing camera was added in the IP aperture position. We also present a lineout of a wire on the right.

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 figure: Fig. 12.

Fig. 12. Plot of (a) (blue solid) lineout in Fig. 11 and (black dashed) filtered lineout; (b) (blue solid) derivative of (a) and (black dashed) curve used to fit the FWHM.

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5. DISCUSSION OF NIF IMAGE QUALITY

A. High Resolution

The resolution of FZPs measured in this paper is close to the $2.7 \;{{\unicode{x00B5}{\rm m}}} \pm 0.3 \;{{\unicode{x00B5}{\rm m}}}$ FWHM resolution measured previously in Ref. [23], while no multilayer mirror was used here to reduce the BL bandwidth. The reason is that the Zn $H{e_\alpha}$ line already has a natural energy bandwidth of ∼0.1 keV, ensuring a quasi-monochromaticity with the help of only a Zn filter.

B. High Background Level

A horizontal lineout of image 4 in Fig. 10 is presented in Fig. 13(a). It shows that on this axis, the BL can be considered “flat,” as the background level, represented by the black dashed-dotted line, is quite straight. On the contrary, this is not the case on the vertical axis, as can be seen in Fig. 13(b), where the same line has an irregular shape. In both cases, there is a high background level in the Au mask area due to the cross-talk with other channels. The Au mask is not thick enough to block the high energy photons coming from the BL. These high energy photons are not focused by the FZP onto the detector at this location, so they are not imaging the mesh, but their accumulation significantly increases the background level. This is accentuated in the imaging region inside the mask where there is no background mitigation, as we can see by the first-order background level.

 figure: Fig. 13.

Fig. 13. Lineout taken from image 4 in Fig. 10 on the (a) horizontal axis as indicated by the white dashed box and (b) vertical axis as indicated by the blue dotted box.

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 figure: Fig. 14.

Fig. 14. Zoom on mesh image of image 4 in Fig. 10 with enhanced color scale. Interlaced low-resolution, low-intensity images coming from the zeroth order can be observed. They are shifted about 65 µm down and 65 µm right from the first-order image.

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C. FZP Tilt

As one can observe in Fig. 11, there are interlaced, low-resolution, low-intensity mesh images shifted from the first-order image. To make this more obvious, we zoomed in on the top part of image 4 in Fig. 14. Those are translated into bumps and holes in the lineout in Fig. 13(a), labeled zeroth order. There is a shift between the two images of 65 µm in both vertical and horizontal directions. The high-resolution image is obviously the first diffraction order of the FZP. The low-resolution images are coming from the non-diffracted photons. In theory, the zeroth diffraction order of a FZP acts like a pinhole, so in our case, a 225 µm diameter pinhole. An estimation of the low-resolution image can be given by comparing a lineout of the first order to a lineout of the zeroth order. The zeroth-order lineout can be obtained using the dark region of a W wire, as it should not have any first order included. Figure 15 shows that both lineouts are comparable if we include a 90 µm Gaussian blur in the first-order lineout. Thus, the low-resolution image has a resolution close to 90 µm. This resolution is better than the theoretical resolution of the zeroth diffraction order pinhole effect. One possible explanation for this effect is that because the outer zones of the FZP are so thin (under 100 nm), the effective FZP diameter contributing to zeroth-order imaging comprises only zones that have a size over 100 nm, corresponding to a diameter of about 100 µm, which is consistent with the measured resolution.

 figure: Fig. 15.

Fig. 15. Comparison between: (blue solid line) lineout of the zeroth diffraction order, as indicated by the black dotted box in Fig. 10, and (orange dashed line) lineout of the first diffraction order, as indicated by the white dashed box in Fig. 10, with a 90 µm Gaussian blur.

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An improvement to the diagnostic to understand the zeroth order includes the replacement of one of the FZPs with a 225 µm pinhole that will also allow to do a flat field correction of the image.

The horizontal and vertical shifts of the different orders can easily be explained by a tilt of the FZPa. When a FZP is tilted, the focal axis of the first diffraction order is also tilted by the same angle, warping the image and shifting it. Raytracing simulations were performed to confirm this. The results for non-tilted, (${\theta _{{x}}}{= 10^\circ}$, ${\theta _{{y}}}{= 10^\circ}$) and (${\theta _{{x}}}{= 0.8^\circ}$, ${\theta _{{y}}}{= 0.8^\circ}$) tilt are presented in Fig. 16. The warping seen for the (10°, 10°) case results in a loss of resolution. The observed shift of in our experiments corresponds to the (0.8°, 0.8°) tilt. It was shown in Ref.  [36] that this tilt results in a less than 0.5 µm PSF increase, thus having little impact on the resolution goal of 3 µm goal. The reason that the zeroth order is not shifted comes from the fact that the tilt of the FZP changes only the effective size of the pinhole but not the position of the image compared to a non-tilted FZP.

 figure: Fig. 16.

Fig. 16. Raytracing simulation for different FZP tilts.

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6. USING FRESNEL ZONE PLATE TO STUDY RAYLEIGH–TAYLOR AND RICHTMYER–MESHKOV INSTABILITIES

Although Sections 4 and 5 highlighted that the performances of FZP optics for stationary targets met the 3 µm resolution requirement, we still need to assess that they are useful to RT and RM instabilities study. The main difficulty, apart from the resolution requirement, comes from the motion blur of instability growth, or spikes, motion. Results from Ref.  [15] allow the calculation of velocities that can reach values up to 50 µm/ns.

Figure 11 shows that on the same shot, we were able to capture time resolved data on the FC. The SNR is lower due to an additional filtering of 2 mm of polyimide in front of the FC, but the resolution is identical to the time integrated data. Having a 100 ps gating time allows us to reduce the motion blur by a factor of six compared to a time gated image that is limited by the 600 ps BL pulse width. This brings the resolution down to 3 µm for interface velocities up to 30 µm/ns. One caveat of the FC though is the total size of the strips, which is ${{38}}\;{\rm{mm}} \times {{38}}\;{\rm{mm}}$, thus reducing the field of view to a maximum of ${{530}}\;{\rm{\unicode{x00B5}{\rm m}}} \times {{530}}\;{\rm{\unicode{x00B5}{\rm m}}}$.

 figure: Fig. 17.

Fig. 17. Schematic view of experimental target.

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 figure: Fig. 18.

Fig. 18. (a) HYDRA simulation of a hydrodynamic instability 50 ns after the main drive start. Target parameters can be seen in Fig. 17; (b) synthetic radiograph obtained by raytracing 1,000,000 rays through the simulation presented in (a), using two time steps in a 100 ps gate time.

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Using a hydrodynamic code, HYDRA [37], we performed a 2D simulation of our experiment. The experimental platform is based on Ref.  [15], which has more detailed information about ablator design and drives. The target comprises a plastic ablator with an original density of 1.4 g/cc and pre-imposed ripples (200 µm wavelength and 15 µm amplitude) at the interface to the carbon foam of density 0.16 g/cc (Fig. 17). The simulations can output the density distribution of a RT spike at the times we plan to probe the experiment, at around 50 ns after the main drive. The result of the simulation is shown in Fig. 18(a). To take into account the motion blur, we used two time steps of the simulations separated by 100 ps as an input to a raytracing code to generate a synthetic radiograph that will be obtained on the FC [Fig. 18(b)]. We used 1,000,000 rays per time step for an energy range of $9 \;{\rm{keV}} \pm 0.1\; {\rm{keV}}$ and blurred the image to the measured diagnostic resolution. This image shows that with the zone plate, we are able to observe a “roll-up” in the tip of the spike with enough resolution to observe distinctive features of the instability.

An additional challenge is the alignment precision required in the vertical axis to get the spike image onto the FC camera strip and obtain an image similar to the one in Fig. 18(b). Considering the vertical dimension of the strip and the high magnification, the vertical field of view of the FC strip is reduced to about 550 µm, thus requiring an alignment precision on the order of 150 µm at the target.

7. CONCLUSION

We report the first x-ray radiograph using FZPs on the NIF. The preliminary calibration with an x-ray source showed the potential $1.9 \;{{\unicode{x00B5}{\rm m}}} \pm 0.5 {{\unicode{x00B5}{\rm m}}}$ resolution with a DOF of ${\pm}1 \;{\rm{mm}}$. The on-shot resolution of the FZPa was measured to be $2.3 \;{{\unicode{x00B5}{\rm m}}} \pm 0.4 \;{{\unicode{x00B5}{\rm m}}}$ over a ${{1}}\;{\rm{mm}} \times {{1}}\;{\rm{mm}}$ field of view with both time resolved and time integrated detectors, exceeding the requirements. A laser-produced x-ray Zn BL was used as the radiograph source to obtain such results. The analysis of the image allowed a better understanding of the use of FZPs in a laser–plasma interaction environment and led to planned improvements to the system such as the optimization of the BL source or the addition of a pinhole to perform a flat field on the image for better image quality. It was shown that the FZP has the required resolution, field of view, and time resolution to allow an in-depth study of the RT and RM instabilities in HED experiments using high-power lasers at the NIF. Future work will experimentally prove this capability.

Funding

Lawrence Livermore National Laboratory (DE-AC52-07NA27344).

Acknowledgment

The authors thank the LLNL target fabrication team, and staff at the NIF for support during shots. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-JRNL-813934.

Disclosures

The authors declare no conflicts of interest.

REFERENCES

1. Lord Rayleigh, Scientific Papers (1900), Vol. II, p. 200.

2. G. I. Taylor, “The formation of a blast wave by a very intense explosion I. Theoretical discussion,” Proc. R. Soc. A 201, 159–174 (1950). [CrossRef]  

3. R. D. Richtmyer, “Taylor instability in shock acceleration of compressible fluids,” Commun. Pure Appl. Math. 13, 297–319 (1960). [CrossRef]  

4. E. E. Meshkov, “Instability of the interface of two gases accelerated by a shock wave,” Fluid Dyn. 4, 101–104 (1969). [CrossRef]  

5. Y. Zhou, “Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II,” Phys. Rep. 723-725, 1–160 (2017). [CrossRef]  

6. Y. Zhou, “Unification and extension of the similarity scaling criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations,” Phys. Plasmas 14, 082701 (2007). [CrossRef]  

7. M. Brouillette and B. Sturtevant, “Experiments on the Richtmyer–Meshkov instability: single-scale perturbations on a continuous interface,” J. Fluid Mech. 263, 271–292 (1994). [CrossRef]  

8. M. Vetter and B. Sturtevant, “Experiments on the Richtmyer-Meshkov instability of an air/sf6 interface,” Shock Waves 4, 247–252 (1995). [CrossRef]  

9. J. W. Jacobs and J. M. Sheeley, “Experimental study of incompressible Richtmyer–Meshkov instability,” Phys. Fluids 8, 405–415 (1996). [CrossRef]  

10. J. W. Jacobs and V. V. Krivets, “Experiments on the late-time development of single-mode Richtmyer–Meshkov instability,” Phys. Fluids 17, 034105 (2005). [CrossRef]  

11. B. J. Balakumar, G. C. Orlicz, C. D. Tomkins, and K. P. Prestridge, “Simultaneous particle-image velocimetry–planar laser-induced fluorescence measurements of Richtmyer–Meshkov instability growth in a gas curtain with and without reshock,” Phys. Fluids 20, 124103 (2008). [CrossRef]  

12. E. Leinov, G. Malamud, Y. Elbaz, L. A. Levin, G. Ben-Dorg, D. Shbarts, and O. Sadot, “Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions,” J. Fluid Mech. 626, 449–475 (2009). [CrossRef]  

13. M. S. Roberts and J. W. Jacobs, “The effects of forced small-wavelength, finite-bandwidth initial perturbations and miscibility on the turbulent Rayleigh–Taylor instability,” J. Fluid Mech. 787, 50–83 (2016). [CrossRef]  

14. K. Prestridge, G. Orlicz, S. Balasubramanian, and B. J. Balakumar, “Experiments of the Richtmyer–Meshkov instability,” Philos. Trans. R. Soc. A 371, 20120165 (2013). [CrossRef]  

15. S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017). [CrossRef]  

16. T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019). [CrossRef]  

17. C. Huntington, K. Raman, S. Nagel, S. MacLaren, T. Baumann, J. Bender, S. Prisbrey, L. Simmons, P. Wang, and Y. Zhou, “Split radiographic tracer technique to measure the full width of a high energy density mixing layer,” High Energy Density Phys. 35, 100733 (2020). [CrossRef]  

18. A. Casner and S. Jacquemot, “Special issue: inertial fusion state of the art–a collection of overview and technical papers from IFSA2017,” Nucl. Fusion 59, 030201 (2019). [CrossRef]  

19. J. Kirz, “Phase zone plates for x rays and the extreme UV,” J. Opt. Soc. Am. 64, 301–309 (1974). [CrossRef]  

20. I. Mohacsi, I. Vartiainen, and B. E. A. Rosner, “Interlaced zone plate optics for hard x-ray imaging in the 10 nm range,” Sci. Rep. 7, 43624 (2017). [CrossRef]  

21. C. David, S. Gorelick, and S. E. A. Rutishauser, “Nanofocusing of hard x-ray free electron laser pulses using diamond based Fresnel zone plates,” Sci. Rep. 1, 57 (2011). [CrossRef]  

22. Y. Suzuki, A. Takeuchi, H. Takenaka, and I. Okada, “Fabrication and performance test of Fresnel zone plate with 35 nm outermost zone width in hard x-ray region,” X-Ray Opt. Instrum. 2010, 824387 (2010). [CrossRef]  

23. A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017). [CrossRef]  

24. A. Do, M. Briat, S. D. Baton, M. Krumrey, L. Lecherbourg, B. Loupias, F. Pérez, P. Renaudin, C. Rubbelynck, and P. Troussel, “Two-channel high-resolution quasi-monochromatic x-ray imager for AL and TI plasma,” Rev. Sci. Instrum. 89, 113702 (2018). [CrossRef]  

25. K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020). [CrossRef]  

26. A. R. Miles, B. Blue, M. J. Edwards, J. A. Greenough, J. F. Hansen, H. F. Robey, R. P. Drake, C. Kuranz, and D. R. Leibrandt, “Transition to turbulence and effect of initial conditions on three-dimensional compressible mixing in planar blast-wave-driven systems,” Phys. Plasmas 12, 056317 (2005). [CrossRef]  

27. K. Kamiya, “Theory of fresnel zone plate,” Sci. Light 12, 35–49 (1963).

28. G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, and J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 KeV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998). [CrossRef]  

29. B. R. Maddox, H. S. Park, B. A. Remington, N. Izumi, S. Chen, C. Chen, G. Kimminau, Z. Ali, M. J. Haugh, and Q. Ma, “High-energy x-ray backlighter spectrum measurements using calibrated image plates,” Rev. Sci. Instrum. 82, 023111 (2011). [CrossRef]  

30. M. Barrios, K. Fournier, S. Regan, O. Landen, M. May, Y. Opachich, K. Widmann, D. Bradley, and G. Collins, “Backlighter development at the National Ignition Facility (NIF): zinc to zirconium,” High Energy Density Phys. 9, 626–634 (2013). [CrossRef]  

31. D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014). [CrossRef]  

32. Applied Nanotools Inc., https://www.appliednt.com/xray-zone-plates/.

33. B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018). [CrossRef]  

34. A. Do, M. Briat, A. Chaleil, C. Rubbelynck, M. Lebugle, C. David, and P. Troussel, “Characterization of a two-channel, high resolution hard x-ray microscope using Fresnel zone plates for laser-plasma interaction experiments,” Rev. Sci. Instrum. 89, 10G122 (2018). [CrossRef]  

35. J. MacFarlane, “Visrad–a 3-D view factor code and design tool for high-energy density physics experiments,” J. Quant. Spectrosc. Radiat. Transfer 81, 287–300 (2003). [CrossRef]  

36. S. S. Ali, K. Li, M. Wojcik, and C. Jacobsen, “Zone plate performance as a function of tilt analyzed via multislice simulations,” Microsc. Microanal. 24, 298–299 (2018). [CrossRef]  

37. M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, “Three-dimensional hydra simulations of national ignition facility targets,” Phys. Plasmas 8, 2275–2280 (2001). [CrossRef]  

References

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  1. Lord Rayleigh, Scientific Papers (1900), Vol. II, p. 200.
  2. G. I. Taylor, “The formation of a blast wave by a very intense explosion I. Theoretical discussion,” Proc. R. Soc. A 201, 159–174 (1950).
    [Crossref]
  3. R. D. Richtmyer, “Taylor instability in shock acceleration of compressible fluids,” Commun. Pure Appl. Math. 13, 297–319 (1960).
    [Crossref]
  4. E. E. Meshkov, “Instability of the interface of two gases accelerated by a shock wave,” Fluid Dyn. 4, 101–104 (1969).
    [Crossref]
  5. Y. Zhou, “Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II,” Phys. Rep. 723-725, 1–160 (2017).
    [Crossref]
  6. Y. Zhou, “Unification and extension of the similarity scaling criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations,” Phys. Plasmas 14, 082701 (2007).
    [Crossref]
  7. M. Brouillette and B. Sturtevant, “Experiments on the Richtmyer–Meshkov instability: single-scale perturbations on a continuous interface,” J. Fluid Mech. 263, 271–292 (1994).
    [Crossref]
  8. M. Vetter and B. Sturtevant, “Experiments on the Richtmyer-Meshkov instability of an air/sf6 interface,” Shock Waves 4, 247–252 (1995).
    [Crossref]
  9. J. W. Jacobs and J. M. Sheeley, “Experimental study of incompressible Richtmyer–Meshkov instability,” Phys. Fluids 8, 405–415 (1996).
    [Crossref]
  10. J. W. Jacobs and V. V. Krivets, “Experiments on the late-time development of single-mode Richtmyer–Meshkov instability,” Phys. Fluids 17, 034105 (2005).
    [Crossref]
  11. B. J. Balakumar, G. C. Orlicz, C. D. Tomkins, and K. P. Prestridge, “Simultaneous particle-image velocimetry–planar laser-induced fluorescence measurements of Richtmyer–Meshkov instability growth in a gas curtain with and without reshock,” Phys. Fluids 20, 124103 (2008).
    [Crossref]
  12. E. Leinov, G. Malamud, Y. Elbaz, L. A. Levin, G. Ben-Dorg, D. Shbarts, and O. Sadot, “Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions,” J. Fluid Mech. 626, 449–475 (2009).
    [Crossref]
  13. M. S. Roberts and J. W. Jacobs, “The effects of forced small-wavelength, finite-bandwidth initial perturbations and miscibility on the turbulent Rayleigh–Taylor instability,” J. Fluid Mech. 787, 50–83 (2016).
    [Crossref]
  14. K. Prestridge, G. Orlicz, S. Balasubramanian, and B. J. Balakumar, “Experiments of the Richtmyer–Meshkov instability,” Philos. Trans. R. Soc. A 371, 20120165 (2013).
    [Crossref]
  15. S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
    [Crossref]
  16. T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
    [Crossref]
  17. C. Huntington, K. Raman, S. Nagel, S. MacLaren, T. Baumann, J. Bender, S. Prisbrey, L. Simmons, P. Wang, and Y. Zhou, “Split radiographic tracer technique to measure the full width of a high energy density mixing layer,” High Energy Density Phys. 35, 100733 (2020).
    [Crossref]
  18. A. Casner and S. Jacquemot, “Special issue: inertial fusion state of the art–a collection of overview and technical papers from IFSA2017,” Nucl. Fusion 59, 030201 (2019).
    [Crossref]
  19. J. Kirz, “Phase zone plates for x rays and the extreme UV,” J. Opt. Soc. Am. 64, 301–309 (1974).
    [Crossref]
  20. I. Mohacsi, I. Vartiainen, and B. E. A. Rosner, “Interlaced zone plate optics for hard x-ray imaging in the 10 nm range,” Sci. Rep. 7, 43624 (2017).
    [Crossref]
  21. C. David, S. Gorelick, and S. E. A. Rutishauser, “Nanofocusing of hard x-ray free electron laser pulses using diamond based Fresnel zone plates,” Sci. Rep. 1, 57 (2011).
    [Crossref]
  22. Y. Suzuki, A. Takeuchi, H. Takenaka, and I. Okada, “Fabrication and performance test of Fresnel zone plate with 35 nm outermost zone width in hard x-ray region,” X-Ray Opt. Instrum. 2010, 824387 (2010).
    [Crossref]
  23. A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017).
    [Crossref]
  24. A. Do, M. Briat, S. D. Baton, M. Krumrey, L. Lecherbourg, B. Loupias, F. Pérez, P. Renaudin, C. Rubbelynck, and P. Troussel, “Two-channel high-resolution quasi-monochromatic x-ray imager for AL and TI plasma,” Rev. Sci. Instrum. 89, 113702 (2018).
    [Crossref]
  25. K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
    [Crossref]
  26. A. R. Miles, B. Blue, M. J. Edwards, J. A. Greenough, J. F. Hansen, H. F. Robey, R. P. Drake, C. Kuranz, and D. R. Leibrandt, “Transition to turbulence and effect of initial conditions on three-dimensional compressible mixing in planar blast-wave-driven systems,” Phys. Plasmas 12, 056317 (2005).
    [Crossref]
  27. K. Kamiya, “Theory of fresnel zone plate,” Sci. Light 12, 35–49 (1963).
  28. G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, and J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 KeV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998).
    [Crossref]
  29. B. R. Maddox, H. S. Park, B. A. Remington, N. Izumi, S. Chen, C. Chen, G. Kimminau, Z. Ali, M. J. Haugh, and Q. Ma, “High-energy x-ray backlighter spectrum measurements using calibrated image plates,” Rev. Sci. Instrum. 82, 023111 (2011).
    [Crossref]
  30. M. Barrios, K. Fournier, S. Regan, O. Landen, M. May, Y. Opachich, K. Widmann, D. Bradley, and G. Collins, “Backlighter development at the National Ignition Facility (NIF): zinc to zirconium,” High Energy Density Phys. 9, 626–634 (2013).
    [Crossref]
  31. D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
    [Crossref]
  32. Applied Nanotools Inc., https://www.appliednt.com/xray-zone-plates/ .
  33. B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
    [Crossref]
  34. A. Do, M. Briat, A. Chaleil, C. Rubbelynck, M. Lebugle, C. David, and P. Troussel, “Characterization of a two-channel, high resolution hard x-ray microscope using Fresnel zone plates for laser-plasma interaction experiments,” Rev. Sci. Instrum. 89, 10G122 (2018).
    [Crossref]
  35. J. MacFarlane, “Visrad–a 3-D view factor code and design tool for high-energy density physics experiments,” J. Quant. Spectrosc. Radiat. Transfer 81, 287–300 (2003).
    [Crossref]
  36. S. S. Ali, K. Li, M. Wojcik, and C. Jacobsen, “Zone plate performance as a function of tilt analyzed via multislice simulations,” Microsc. Microanal. 24, 298–299 (2018).
    [Crossref]
  37. M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, “Three-dimensional hydra simulations of national ignition facility targets,” Phys. Plasmas 8, 2275–2280 (2001).
    [Crossref]

2020 (2)

C. Huntington, K. Raman, S. Nagel, S. MacLaren, T. Baumann, J. Bender, S. Prisbrey, L. Simmons, P. Wang, and Y. Zhou, “Split radiographic tracer technique to measure the full width of a high energy density mixing layer,” High Energy Density Phys. 35, 100733 (2020).
[Crossref]

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

2019 (2)

A. Casner and S. Jacquemot, “Special issue: inertial fusion state of the art–a collection of overview and technical papers from IFSA2017,” Nucl. Fusion 59, 030201 (2019).
[Crossref]

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

2018 (4)

A. Do, M. Briat, S. D. Baton, M. Krumrey, L. Lecherbourg, B. Loupias, F. Pérez, P. Renaudin, C. Rubbelynck, and P. Troussel, “Two-channel high-resolution quasi-monochromatic x-ray imager for AL and TI plasma,” Rev. Sci. Instrum. 89, 113702 (2018).
[Crossref]

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

A. Do, M. Briat, A. Chaleil, C. Rubbelynck, M. Lebugle, C. David, and P. Troussel, “Characterization of a two-channel, high resolution hard x-ray microscope using Fresnel zone plates for laser-plasma interaction experiments,” Rev. Sci. Instrum. 89, 10G122 (2018).
[Crossref]

S. S. Ali, K. Li, M. Wojcik, and C. Jacobsen, “Zone plate performance as a function of tilt analyzed via multislice simulations,” Microsc. Microanal. 24, 298–299 (2018).
[Crossref]

2017 (4)

A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017).
[Crossref]

I. Mohacsi, I. Vartiainen, and B. E. A. Rosner, “Interlaced zone plate optics for hard x-ray imaging in the 10 nm range,” Sci. Rep. 7, 43624 (2017).
[Crossref]

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Y. Zhou, “Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II,” Phys. Rep. 723-725, 1–160 (2017).
[Crossref]

2016 (1)

M. S. Roberts and J. W. Jacobs, “The effects of forced small-wavelength, finite-bandwidth initial perturbations and miscibility on the turbulent Rayleigh–Taylor instability,” J. Fluid Mech. 787, 50–83 (2016).
[Crossref]

2014 (1)

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

2013 (2)

M. Barrios, K. Fournier, S. Regan, O. Landen, M. May, Y. Opachich, K. Widmann, D. Bradley, and G. Collins, “Backlighter development at the National Ignition Facility (NIF): zinc to zirconium,” High Energy Density Phys. 9, 626–634 (2013).
[Crossref]

K. Prestridge, G. Orlicz, S. Balasubramanian, and B. J. Balakumar, “Experiments of the Richtmyer–Meshkov instability,” Philos. Trans. R. Soc. A 371, 20120165 (2013).
[Crossref]

2011 (2)

C. David, S. Gorelick, and S. E. A. Rutishauser, “Nanofocusing of hard x-ray free electron laser pulses using diamond based Fresnel zone plates,” Sci. Rep. 1, 57 (2011).
[Crossref]

B. R. Maddox, H. S. Park, B. A. Remington, N. Izumi, S. Chen, C. Chen, G. Kimminau, Z. Ali, M. J. Haugh, and Q. Ma, “High-energy x-ray backlighter spectrum measurements using calibrated image plates,” Rev. Sci. Instrum. 82, 023111 (2011).
[Crossref]

2010 (1)

Y. Suzuki, A. Takeuchi, H. Takenaka, and I. Okada, “Fabrication and performance test of Fresnel zone plate with 35 nm outermost zone width in hard x-ray region,” X-Ray Opt. Instrum. 2010, 824387 (2010).
[Crossref]

2009 (1)

E. Leinov, G. Malamud, Y. Elbaz, L. A. Levin, G. Ben-Dorg, D. Shbarts, and O. Sadot, “Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions,” J. Fluid Mech. 626, 449–475 (2009).
[Crossref]

2008 (1)

B. J. Balakumar, G. C. Orlicz, C. D. Tomkins, and K. P. Prestridge, “Simultaneous particle-image velocimetry–planar laser-induced fluorescence measurements of Richtmyer–Meshkov instability growth in a gas curtain with and without reshock,” Phys. Fluids 20, 124103 (2008).
[Crossref]

2007 (1)

Y. Zhou, “Unification and extension of the similarity scaling criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations,” Phys. Plasmas 14, 082701 (2007).
[Crossref]

2005 (2)

J. W. Jacobs and V. V. Krivets, “Experiments on the late-time development of single-mode Richtmyer–Meshkov instability,” Phys. Fluids 17, 034105 (2005).
[Crossref]

A. R. Miles, B. Blue, M. J. Edwards, J. A. Greenough, J. F. Hansen, H. F. Robey, R. P. Drake, C. Kuranz, and D. R. Leibrandt, “Transition to turbulence and effect of initial conditions on three-dimensional compressible mixing in planar blast-wave-driven systems,” Phys. Plasmas 12, 056317 (2005).
[Crossref]

2003 (1)

J. MacFarlane, “Visrad–a 3-D view factor code and design tool for high-energy density physics experiments,” J. Quant. Spectrosc. Radiat. Transfer 81, 287–300 (2003).
[Crossref]

2001 (1)

M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, “Three-dimensional hydra simulations of national ignition facility targets,” Phys. Plasmas 8, 2275–2280 (2001).
[Crossref]

1998 (1)

G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, and J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 KeV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998).
[Crossref]

1996 (1)

J. W. Jacobs and J. M. Sheeley, “Experimental study of incompressible Richtmyer–Meshkov instability,” Phys. Fluids 8, 405–415 (1996).
[Crossref]

1995 (1)

M. Vetter and B. Sturtevant, “Experiments on the Richtmyer-Meshkov instability of an air/sf6 interface,” Shock Waves 4, 247–252 (1995).
[Crossref]

1994 (1)

M. Brouillette and B. Sturtevant, “Experiments on the Richtmyer–Meshkov instability: single-scale perturbations on a continuous interface,” J. Fluid Mech. 263, 271–292 (1994).
[Crossref]

1974 (1)

1969 (1)

E. E. Meshkov, “Instability of the interface of two gases accelerated by a shock wave,” Fluid Dyn. 4, 101–104 (1969).
[Crossref]

1963 (1)

K. Kamiya, “Theory of fresnel zone plate,” Sci. Light 12, 35–49 (1963).

1960 (1)

R. D. Richtmyer, “Taylor instability in shock acceleration of compressible fluids,” Commun. Pure Appl. Math. 13, 297–319 (1960).
[Crossref]

1950 (1)

G. I. Taylor, “The formation of a blast wave by a very intense explosion I. Theoretical discussion,” Proc. R. Soc. A 201, 159–174 (1950).
[Crossref]

Ali, S. S.

S. S. Ali, K. Li, M. Wojcik, and C. Jacobsen, “Zone plate performance as a function of tilt analyzed via multislice simulations,” Microsc. Microanal. 24, 298–299 (2018).
[Crossref]

Ali, Z.

B. R. Maddox, H. S. Park, B. A. Remington, N. Izumi, S. Chen, C. Chen, G. Kimminau, Z. Ali, M. J. Haugh, and Q. Ma, “High-energy x-ray backlighter spectrum measurements using calibrated image plates,” Rev. Sci. Instrum. 82, 023111 (2011).
[Crossref]

Ames, A.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Ampleford, D. J.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Arikawa, Y.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Ayers, J.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Azechi, H.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Balakumar, B. J.

K. Prestridge, G. Orlicz, S. Balasubramanian, and B. J. Balakumar, “Experiments of the Richtmyer–Meshkov instability,” Philos. Trans. R. Soc. A 371, 20120165 (2013).
[Crossref]

B. J. Balakumar, G. C. Orlicz, C. D. Tomkins, and K. P. Prestridge, “Simultaneous particle-image velocimetry–planar laser-induced fluorescence measurements of Richtmyer–Meshkov instability growth in a gas curtain with and without reshock,” Phys. Fluids 20, 124103 (2008).
[Crossref]

Balasubramanian, S.

K. Prestridge, G. Orlicz, S. Balasubramanian, and B. J. Balakumar, “Experiments of the Richtmyer–Meshkov instability,” Philos. Trans. R. Soc. A 371, 20120165 (2013).
[Crossref]

Ball, C. R.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Baojun, Z.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Barrios, M.

M. Barrios, K. Fournier, S. Regan, O. Landen, M. May, Y. Opachich, K. Widmann, D. Bradley, and G. Collins, “Backlighter development at the National Ignition Facility (NIF): zinc to zirconium,” High Energy Density Phys. 9, 626–634 (2013).
[Crossref]

Barrios, M. A.

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Baton, S. D.

A. Do, M. Briat, S. D. Baton, M. Krumrey, L. Lecherbourg, B. Loupias, F. Pérez, P. Renaudin, C. Rubbelynck, and P. Troussel, “Two-channel high-resolution quasi-monochromatic x-ray imager for AL and TI plasma,” Rev. Sci. Instrum. 89, 113702 (2018).
[Crossref]

A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017).
[Crossref]

Baumann, T.

C. Huntington, K. Raman, S. Nagel, S. MacLaren, T. Baumann, J. Bender, S. Prisbrey, L. Simmons, P. Wang, and Y. Zhou, “Split radiographic tracer technique to measure the full width of a high energy density mixing layer,” High Energy Density Phys. 35, 100733 (2020).
[Crossref]

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Bell, P.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Bender, J.

C. Huntington, K. Raman, S. Nagel, S. MacLaren, T. Baumann, J. Bender, S. Prisbrey, L. Simmons, P. Wang, and Y. Zhou, “Split radiographic tracer technique to measure the full width of a high energy density mixing layer,” High Energy Density Phys. 35, 100733 (2020).
[Crossref]

Bender, J. D.

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Ben-Dorg, G.

E. Leinov, G. Malamud, Y. Elbaz, L. A. Levin, G. Ben-Dorg, D. Shbarts, and O. Sadot, “Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions,” J. Fluid Mech. 626, 449–475 (2009).
[Crossref]

Benedetti, L. R.

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Blue, B.

A. R. Miles, B. Blue, M. J. Edwards, J. A. Greenough, J. F. Hansen, H. F. Robey, R. P. Drake, C. Kuranz, and D. R. Leibrandt, “Transition to turbulence and effect of initial conditions on three-dimensional compressible mixing in planar blast-wave-driven systems,” Phys. Plasmas 12, 056317 (2005).
[Crossref]

Bourdon, C. J.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Boutin, J.-Y.

G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, and J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 KeV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998).
[Crossref]

Bradley, D.

M. Barrios, K. Fournier, S. Regan, O. Landen, M. May, Y. Opachich, K. Widmann, D. Bradley, and G. Collins, “Backlighter development at the National Ignition Facility (NIF): zinc to zirconium,” High Energy Density Phys. 9, 626–634 (2013).
[Crossref]

Bradley, D. K.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Briat, M.

A. Do, M. Briat, A. Chaleil, C. Rubbelynck, M. Lebugle, C. David, and P. Troussel, “Characterization of a two-channel, high resolution hard x-ray microscope using Fresnel zone plates for laser-plasma interaction experiments,” Rev. Sci. Instrum. 89, 10G122 (2018).
[Crossref]

A. Do, M. Briat, S. D. Baton, M. Krumrey, L. Lecherbourg, B. Loupias, F. Pérez, P. Renaudin, C. Rubbelynck, and P. Troussel, “Two-channel high-resolution quasi-monochromatic x-ray imager for AL and TI plasma,” Rev. Sci. Instrum. 89, 113702 (2018).
[Crossref]

Brouillette, M.

M. Brouillette and B. Sturtevant, “Experiments on the Richtmyer–Meshkov instability: single-scale perturbations on a continuous interface,” J. Fluid Mech. 263, 271–292 (1994).
[Crossref]

Bruni, R.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Cabana, J.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Cardenas, T.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Casner, A.

A. Casner and S. Jacquemot, “Special issue: inertial fusion state of the art–a collection of overview and technical papers from IFSA2017,” Nucl. Fusion 59, 030201 (2019).
[Crossref]

Cauchon, G.

G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, and J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 KeV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998).
[Crossref]

Celestre, R.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Chaleil, A.

A. Do, M. Briat, A. Chaleil, C. Rubbelynck, M. Lebugle, C. David, and P. Troussel, “Characterization of a two-channel, high resolution hard x-ray microscope using Fresnel zone plates for laser-plasma interaction experiments,” Rev. Sci. Instrum. 89, 10G122 (2018).
[Crossref]

Chao, W.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Chen, C.

B. R. Maddox, H. S. Park, B. A. Remington, N. Izumi, S. Chen, C. Chen, G. Kimminau, Z. Ali, M. J. Haugh, and Q. Ma, “High-energy x-ray backlighter spectrum measurements using calibrated image plates,” Rev. Sci. Instrum. 82, 023111 (2011).
[Crossref]

Chen, S.

B. R. Maddox, H. S. Park, B. A. Remington, N. Izumi, S. Chen, C. Chen, G. Kimminau, Z. Ali, M. J. Haugh, and Q. Ma, “High-energy x-ray backlighter spectrum measurements using calibrated image plates,” Rev. Sci. Instrum. 82, 023111 (2011).
[Crossref]

Collins, G.

M. Barrios, K. Fournier, S. Regan, O. Landen, M. May, Y. Opachich, K. Widmann, D. Bradley, and G. Collins, “Backlighter development at the National Ignition Facility (NIF): zinc to zirconium,” High Energy Density Phys. 9, 626–634 (2013).
[Crossref]

David, C.

A. Do, M. Briat, A. Chaleil, C. Rubbelynck, M. Lebugle, C. David, and P. Troussel, “Characterization of a two-channel, high resolution hard x-ray microscope using Fresnel zone plates for laser-plasma interaction experiments,” Rev. Sci. Instrum. 89, 10G122 (2018).
[Crossref]

C. David, S. Gorelick, and S. E. A. Rutishauser, “Nanofocusing of hard x-ray free electron laser pulses using diamond based Fresnel zone plates,” Sci. Rep. 1, 57 (2011).
[Crossref]

Day, T.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Dervieux, V.

A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017).
[Crossref]

Descalle, M.-A.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Desjardins, T.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

DeVolder, B.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Dhez, P.

G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, and J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 KeV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998).
[Crossref]

Di Stefano, C.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Dittrich, T. R.

M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, “Three-dimensional hydra simulations of national ignition facility targets,” Phys. Plasmas 8, 2275–2280 (2001).
[Crossref]

Do, A.

A. Do, M. Briat, A. Chaleil, C. Rubbelynck, M. Lebugle, C. David, and P. Troussel, “Characterization of a two-channel, high resolution hard x-ray microscope using Fresnel zone plates for laser-plasma interaction experiments,” Rev. Sci. Instrum. 89, 10G122 (2018).
[Crossref]

A. Do, M. Briat, S. D. Baton, M. Krumrey, L. Lecherbourg, B. Loupias, F. Pérez, P. Renaudin, C. Rubbelynck, and P. Troussel, “Two-channel high-resolution quasi-monochromatic x-ray imager for AL and TI plasma,” Rev. Sci. Instrum. 89, 113702 (2018).
[Crossref]

A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017).
[Crossref]

Doane, D. M.

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Donovan, P.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Doss, F.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Drake, R. P.

A. R. Miles, B. Blue, M. J. Edwards, J. A. Greenough, J. F. Hansen, H. F. Robey, R. P. Drake, C. Kuranz, and D. R. Leibrandt, “Transition to turbulence and effect of initial conditions on three-dimensional compressible mixing in planar blast-wave-driven systems,” Phys. Plasmas 12, 056317 (2005).
[Crossref]

Edwards, M. J.

A. R. Miles, B. Blue, M. J. Edwards, J. A. Greenough, J. F. Hansen, H. F. Robey, R. P. Drake, C. Kuranz, and D. R. Leibrandt, “Transition to turbulence and effect of initial conditions on three-dimensional compressible mixing in planar blast-wave-driven systems,” Phys. Plasmas 12, 056317 (2005).
[Crossref]

Edwards, S.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Elbaz, Y.

E. Leinov, G. Malamud, Y. Elbaz, L. A. Levin, G. Ben-Dorg, D. Shbarts, and O. Sadot, “Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions,” J. Fluid Mech. 626, 449–475 (2009).
[Crossref]

Farley Law, K. F.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Fein, J. R.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Felker, S.

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Fierro, F.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Fitzsimmons, P.

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Flippo, K.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Flippo, K. A.

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Fournier, K.

M. Barrios, K. Fournier, S. Regan, O. Landen, M. May, Y. Opachich, K. Widmann, D. Bradley, and G. Collins, “Backlighter development at the National Ignition Facility (NIF): zinc to zirconium,” High Energy Density Phys. 9, 626–634 (2013).
[Crossref]

Fujioka, S.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Gentile, N. A.

M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, “Three-dimensional hydra simulations of national ignition facility targets,” Phys. Plasmas 8, 2275–2280 (2001).
[Crossref]

Gontier, D.

A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017).
[Crossref]

Gonzales, R.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Goodwin, L.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Gorelick, S.

C. David, S. Gorelick, and S. E. A. Rutishauser, “Nanofocusing of hard x-ray free electron laser pulses using diamond based Fresnel zone plates,” Sci. Rep. 1, 57 (2011).
[Crossref]

Greenough, J. A.

A. R. Miles, B. Blue, M. J. Edwards, J. A. Greenough, J. F. Hansen, H. F. Robey, R. P. Drake, C. Kuranz, and D. R. Leibrandt, “Transition to turbulence and effect of initial conditions on three-dimensional compressible mixing in planar blast-wave-driven systems,” Phys. Plasmas 12, 056317 (2005).
[Crossref]

Haan, S. W.

M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, “Three-dimensional hydra simulations of national ignition facility targets,” Phys. Plasmas 8, 2275–2280 (2001).
[Crossref]

Hamilton, C.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Hansen, J. F.

A. R. Miles, B. Blue, M. J. Edwards, J. A. Greenough, J. F. Hansen, H. F. Robey, R. P. Drake, C. Kuranz, and D. R. Leibrandt, “Transition to turbulence and effect of initial conditions on three-dimensional compressible mixing in planar blast-wave-driven systems,” Phys. Plasmas 12, 056317 (2005).
[Crossref]

Haugh, M. J.

B. R. Maddox, H. S. Park, B. A. Remington, N. Izumi, S. Chen, C. Chen, G. Kimminau, Z. Ali, M. J. Haugh, and Q. Ma, “High-energy x-ray backlighter spectrum measurements using calibrated image plates,” Rev. Sci. Instrum. 82, 023111 (2011).
[Crossref]

Hau-Riege, S.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Holder, J. P.

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Huntington, C.

C. Huntington, K. Raman, S. Nagel, S. MacLaren, T. Baumann, J. Bender, S. Prisbrey, L. Simmons, P. Wang, and Y. Zhou, “Split radiographic tracer technique to measure the full width of a high energy density mixing layer,” High Energy Density Phys. 35, 100733 (2020).
[Crossref]

Huntington, C. M.

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Idir, M.

G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, and J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 KeV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998).
[Crossref]

Ishigure, K.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Izumi, N.

B. R. Maddox, H. S. Park, B. A. Remington, N. Izumi, S. Chen, C. Chen, G. Kimminau, Z. Ali, M. J. Haugh, and Q. Ma, “High-energy x-ray backlighter spectrum measurements using calibrated image plates,” Rev. Sci. Instrum. 82, 023111 (2011).
[Crossref]

Jacobs, J. W.

M. S. Roberts and J. W. Jacobs, “The effects of forced small-wavelength, finite-bandwidth initial perturbations and miscibility on the turbulent Rayleigh–Taylor instability,” J. Fluid Mech. 787, 50–83 (2016).
[Crossref]

J. W. Jacobs and V. V. Krivets, “Experiments on the late-time development of single-mode Richtmyer–Meshkov instability,” Phys. Fluids 17, 034105 (2005).
[Crossref]

J. W. Jacobs and J. M. Sheeley, “Experimental study of incompressible Richtmyer–Meshkov instability,” Phys. Fluids 8, 405–415 (1996).
[Crossref]

Jacobsen, C.

S. S. Ali, K. Li, M. Wojcik, and C. Jacobsen, “Zone plate performance as a function of tilt analyzed via multislice simulations,” Microsc. Microanal. 24, 298–299 (2018).
[Crossref]

Jacquemot, S.

A. Casner and S. Jacquemot, “Special issue: inertial fusion state of the art–a collection of overview and technical papers from IFSA2017,” Nucl. Fusion 59, 030201 (2019).
[Crossref]

Jones, O.

M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, “Three-dimensional hydra simulations of national ignition facility targets,” Phys. Plasmas 8, 2275–2280 (2001).
[Crossref]

Kaczala, D. N.

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Kamiya, K.

K. Kamiya, “Theory of fresnel zone plate,” Sci. Light 12, 35–49 (1963).

Kato, H.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Kaznatcheev, K.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Kerbel, G. D.

M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, “Three-dimensional hydra simulations of national ignition facility targets,” Phys. Plasmas 8, 2275–2280 (2001).
[Crossref]

Kilcoyne, A. L. D.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Kimminau, G.

B. R. Maddox, H. S. Park, B. A. Remington, N. Izumi, S. Chen, C. Chen, G. Kimminau, Z. Ali, M. J. Haugh, and Q. Ma, “High-energy x-ray backlighter spectrum measurements using calibrated image plates,” Rev. Sci. Instrum. 82, 023111 (2011).
[Crossref]

Kirz, J.

Kozioziemski, B. J.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Krivets, V. V.

J. W. Jacobs and V. V. Krivets, “Experiments on the late-time development of single-mode Richtmyer–Meshkov instability,” Phys. Fluids 17, 034105 (2005).
[Crossref]

Krumrey, M.

A. Do, M. Briat, S. D. Baton, M. Krumrey, L. Lecherbourg, B. Loupias, F. Pérez, P. Renaudin, C. Rubbelynck, and P. Troussel, “Two-channel high-resolution quasi-monochromatic x-ray imager for AL and TI plasma,” Rev. Sci. Instrum. 89, 113702 (2018).
[Crossref]

Kuranz, C.

A. R. Miles, B. Blue, M. J. Edwards, J. A. Greenough, J. F. Hansen, H. F. Robey, R. P. Drake, C. Kuranz, and D. R. Leibrandt, “Transition to turbulence and effect of initial conditions on three-dimensional compressible mixing in planar blast-wave-driven systems,” Phys. Plasmas 12, 056317 (2005).
[Crossref]

Landen, O.

M. Barrios, K. Fournier, S. Regan, O. Landen, M. May, Y. Opachich, K. Widmann, D. Bradley, and G. Collins, “Backlighter development at the National Ignition Facility (NIF): zinc to zirconium,” High Energy Density Phys. 9, 626–634 (2013).
[Crossref]

Le Breton, J.-P.

G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, and J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 KeV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998).
[Crossref]

Lebugle, M.

A. Do, M. Briat, A. Chaleil, C. Rubbelynck, M. Lebugle, C. David, and P. Troussel, “Characterization of a two-channel, high resolution hard x-ray microscope using Fresnel zone plates for laser-plasma interaction experiments,” Rev. Sci. Instrum. 89, 10G122 (2018).
[Crossref]

Lecherbourg, L.

A. Do, M. Briat, S. D. Baton, M. Krumrey, L. Lecherbourg, B. Loupias, F. Pérez, P. Renaudin, C. Rubbelynck, and P. Troussel, “Two-channel high-resolution quasi-monochromatic x-ray imager for AL and TI plasma,” Rev. Sci. Instrum. 89, 113702 (2018).
[Crossref]

A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017).
[Crossref]

Lee, S.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Leibrandt, D. R.

A. R. Miles, B. Blue, M. J. Edwards, J. A. Greenough, J. F. Hansen, H. F. Robey, R. P. Drake, C. Kuranz, and D. R. Leibrandt, “Transition to turbulence and effect of initial conditions on three-dimensional compressible mixing in planar blast-wave-driven systems,” Phys. Plasmas 12, 056317 (2005).
[Crossref]

Leinov, E.

E. Leinov, G. Malamud, Y. Elbaz, L. A. Levin, G. Ben-Dorg, D. Shbarts, and O. Sadot, “Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions,” J. Fluid Mech. 626, 449–475 (2009).
[Crossref]

Levin, L. A.

E. Leinov, G. Malamud, Y. Elbaz, L. A. Levin, G. Ben-Dorg, D. Shbarts, and O. Sadot, “Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions,” J. Fluid Mech. 626, 449–475 (2009).
[Crossref]

Li, H.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Li, K.

S. S. Ali, K. Li, M. Wojcik, and C. Jacobsen, “Zone plate performance as a function of tilt analyzed via multislice simulations,” Microsc. Microanal. 24, 298–299 (2018).
[Crossref]

Liu, C.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Lord Rayleigh,

Lord Rayleigh, Scientific Papers (1900), Vol. II, p. 200.

Loupias, B.

A. Do, M. Briat, S. D. Baton, M. Krumrey, L. Lecherbourg, B. Loupias, F. Pérez, P. Renaudin, C. Rubbelynck, and P. Troussel, “Two-channel high-resolution quasi-monochromatic x-ray imager for AL and TI plasma,” Rev. Sci. Instrum. 89, 113702 (2018).
[Crossref]

A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017).
[Crossref]

Ma, Q.

B. R. Maddox, H. S. Park, B. A. Remington, N. Izumi, S. Chen, C. Chen, G. Kimminau, Z. Ali, M. J. Haugh, and Q. Ma, “High-energy x-ray backlighter spectrum measurements using calibrated image plates,” Rev. Sci. Instrum. 82, 023111 (2011).
[Crossref]

MacFarlane, J.

J. MacFarlane, “Visrad–a 3-D view factor code and design tool for high-energy density physics experiments,” J. Quant. Spectrosc. Radiat. Transfer 81, 287–300 (2003).
[Crossref]

MacLaren, S.

C. Huntington, K. Raman, S. Nagel, S. MacLaren, T. Baumann, J. Bender, S. Prisbrey, L. Simmons, P. Wang, and Y. Zhou, “Split radiographic tracer technique to measure the full width of a high energy density mixing layer,” High Energy Density Phys. 35, 100733 (2020).
[Crossref]

MacLaren, S. A.

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Maddox, B. R.

B. R. Maddox, H. S. Park, B. A. Remington, N. Izumi, S. Chen, C. Chen, G. Kimminau, Z. Ali, M. J. Haugh, and Q. Ma, “High-energy x-ray backlighter spectrum measurements using calibrated image plates,” Rev. Sci. Instrum. 82, 023111 (2011).
[Crossref]

Maia, F.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Malamud, G.

E. Leinov, G. Malamud, Y. Elbaz, L. A. Levin, G. Ben-Dorg, D. Shbarts, and O. Sadot, “Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions,” J. Fluid Mech. 626, 449–475 (2009).
[Crossref]

Marchesini, S.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Marinak, M. M.

M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, “Three-dimensional hydra simulations of national ignition facility targets,” Phys. Plasmas 8, 2275–2280 (2001).
[Crossref]

Matsuo, K.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

May, M.

M. Barrios, K. Fournier, S. Regan, O. Landen, M. May, Y. Opachich, K. Widmann, D. Bradley, and G. Collins, “Backlighter development at the National Ignition Facility (NIF): zinc to zirconium,” High Energy Density Phys. 9, 626–634 (2013).
[Crossref]

McCarville, T. J.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Meng, Y. S.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Merritt, E.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Meshkov, E. E.

E. E. Meshkov, “Instability of the interface of two gases accelerated by a shock wave,” Fluid Dyn. 4, 101–104 (1969).
[Crossref]

Miles, A. R.

A. R. Miles, B. Blue, M. J. Edwards, J. A. Greenough, J. F. Hansen, H. F. Robey, R. P. Drake, C. Kuranz, and D. R. Leibrandt, “Transition to turbulence and effect of initial conditions on three-dimensional compressible mixing in planar blast-wave-driven systems,” Phys. Plasmas 12, 056317 (2005).
[Crossref]

Mohacsi, I.

I. Mohacsi, I. Vartiainen, and B. E. A. Rosner, “Interlaced zone plate optics for hard x-ray imaging in the 10 nm range,” Sci. Rep. 7, 43624 (2017).
[Crossref]

Morita, H.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Munro, D.

M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, “Three-dimensional hydra simulations of national ignition facility targets,” Phys. Plasmas 8, 2275–2280 (2001).
[Crossref]

Nagamatsu, N.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Nagatomo, H.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Nagel, S.

C. Huntington, K. Raman, S. Nagel, S. MacLaren, T. Baumann, J. Bender, S. Prisbrey, L. Simmons, P. Wang, and Y. Zhou, “Split radiographic tracer technique to measure the full width of a high energy density mixing layer,” High Energy Density Phys. 35, 100733 (2020).
[Crossref]

Nagel, S. R.

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Nishibata, J.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Obst, L.

A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017).
[Crossref]

Okada, I.

Y. Suzuki, A. Takeuchi, H. Takenaka, and I. Okada, “Fabrication and performance test of Fresnel zone plate with 35 nm outermost zone width in hard x-ray region,” X-Ray Opt. Instrum. 2010, 824387 (2010).
[Crossref]

Ollivier, M.

G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, and J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 KeV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998).
[Crossref]

Opachich, Y.

M. Barrios, K. Fournier, S. Regan, O. Landen, M. May, Y. Opachich, K. Widmann, D. Bradley, and G. Collins, “Backlighter development at the National Ignition Facility (NIF): zinc to zirconium,” High Energy Density Phys. 9, 626–634 (2013).
[Crossref]

Orlicz, G.

K. Prestridge, G. Orlicz, S. Balasubramanian, and B. J. Balakumar, “Experiments of the Richtmyer–Meshkov instability,” Philos. Trans. R. Soc. A 371, 20120165 (2013).
[Crossref]

Orlicz, G. C.

B. J. Balakumar, G. C. Orlicz, C. D. Tomkins, and K. P. Prestridge, “Simultaneous particle-image velocimetry–planar laser-induced fluorescence measurements of Richtmyer–Meshkov instability growth in a gas curtain with and without reshock,” Phys. Fluids 20, 124103 (2008).
[Crossref]

Padmore, H. A.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Pardini, T.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Park, H. S.

B. R. Maddox, H. S. Park, B. A. Remington, N. Izumi, S. Chen, C. Chen, G. Kimminau, Z. Ali, M. J. Haugh, and Q. Ma, “High-energy x-ray backlighter spectrum measurements using calibrated image plates,” Rev. Sci. Instrum. 82, 023111 (2011).
[Crossref]

Pérez, F.

A. Do, M. Briat, S. D. Baton, M. Krumrey, L. Lecherbourg, B. Loupias, F. Pérez, P. Renaudin, C. Rubbelynck, and P. Troussel, “Two-channel high-resolution quasi-monochromatic x-ray imager for AL and TI plasma,” Rev. Sci. Instrum. 89, 113702 (2018).
[Crossref]

A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017).
[Crossref]

Perry, T. S.

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Philippe, N.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Pichet-Thomasset, M.

G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, and J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 KeV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998).
[Crossref]

Pickworth, L. A.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Pollaine, S.

M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, “Three-dimensional hydra simulations of national ignition facility targets,” Phys. Plasmas 8, 2275–2280 (2001).
[Crossref]

Prestridge, K.

K. Prestridge, G. Orlicz, S. Balasubramanian, and B. J. Balakumar, “Experiments of the Richtmyer–Meshkov instability,” Philos. Trans. R. Soc. A 371, 20120165 (2013).
[Crossref]

Prestridge, K. P.

B. J. Balakumar, G. C. Orlicz, C. D. Tomkins, and K. P. Prestridge, “Simultaneous particle-image velocimetry–planar laser-induced fluorescence measurements of Richtmyer–Meshkov instability growth in a gas curtain with and without reshock,” Phys. Fluids 20, 124103 (2008).
[Crossref]

Prisbrey, S.

C. Huntington, K. Raman, S. Nagel, S. MacLaren, T. Baumann, J. Bender, S. Prisbrey, L. Simmons, P. Wang, and Y. Zhou, “Split radiographic tracer technique to measure the full width of a high energy density mixing layer,” High Energy Density Phys. 35, 100733 (2020).
[Crossref]

Quintana, T.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Raman, K.

C. Huntington, K. Raman, S. Nagel, S. MacLaren, T. Baumann, J. Bender, S. Prisbrey, L. Simmons, P. Wang, and Y. Zhou, “Split radiographic tracer technique to measure the full width of a high energy density mixing layer,” High Energy Density Phys. 35, 100733 (2020).
[Crossref]

Raman, K. S.

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Randolph, R.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Rasmus, A.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Regan, S.

M. Barrios, K. Fournier, S. Regan, O. Landen, M. May, Y. Opachich, K. Widmann, D. Bradley, and G. Collins, “Backlighter development at the National Ignition Facility (NIF): zinc to zirconium,” High Energy Density Phys. 9, 626–634 (2013).
[Crossref]

Remington, B. A.

B. R. Maddox, H. S. Park, B. A. Remington, N. Izumi, S. Chen, C. Chen, G. Kimminau, Z. Ali, M. J. Haugh, and Q. Ma, “High-energy x-ray backlighter spectrum measurements using calibrated image plates,” Rev. Sci. Instrum. 82, 023111 (2011).
[Crossref]

Renaudin, P.

A. Do, M. Briat, S. D. Baton, M. Krumrey, L. Lecherbourg, B. Loupias, F. Pérez, P. Renaudin, C. Rubbelynck, and P. Troussel, “Two-channel high-resolution quasi-monochromatic x-ray imager for AL and TI plasma,” Rev. Sci. Instrum. 89, 113702 (2018).
[Crossref]

A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017).
[Crossref]

Reverdin, C.

A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017).
[Crossref]

Richtmyer, R. D.

R. D. Richtmyer, “Taylor instability in shock acceleration of compressible fluids,” Commun. Pure Appl. Math. 13, 297–319 (1960).
[Crossref]

Roberts, M. S.

M. S. Roberts and J. W. Jacobs, “The effects of forced small-wavelength, finite-bandwidth initial perturbations and miscibility on the turbulent Rayleigh–Taylor instability,” J. Fluid Mech. 787, 50–83 (2016).
[Crossref]

Robey, H. F.

A. R. Miles, B. Blue, M. J. Edwards, J. A. Greenough, J. F. Hansen, H. F. Robey, R. P. Drake, C. Kuranz, and D. R. Leibrandt, “Transition to turbulence and effect of initial conditions on three-dimensional compressible mixing in planar blast-wave-driven systems,” Phys. Plasmas 12, 056317 (2005).
[Crossref]

Robinson, J.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Romaine, S.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Rosner, B. E. A.

I. Mohacsi, I. Vartiainen, and B. E. A. Rosner, “Interlaced zone plate optics for hard x-ray imaging in the 10 nm range,” Sci. Rep. 7, 43624 (2017).
[Crossref]

Rubbelynck, C.

A. Do, M. Briat, S. D. Baton, M. Krumrey, L. Lecherbourg, B. Loupias, F. Pérez, P. Renaudin, C. Rubbelynck, and P. Troussel, “Two-channel high-resolution quasi-monochromatic x-ray imager for AL and TI plasma,” Rev. Sci. Instrum. 89, 113702 (2018).
[Crossref]

A. Do, M. Briat, A. Chaleil, C. Rubbelynck, M. Lebugle, C. David, and P. Troussel, “Characterization of a two-channel, high resolution hard x-ray microscope using Fresnel zone plates for laser-plasma interaction experiments,” Rev. Sci. Instrum. 89, 10G122 (2018).
[Crossref]

A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017).
[Crossref]

Rutishauser, S. E. A.

C. David, S. Gorelick, and S. E. A. Rutishauser, “Nanofocusing of hard x-ray free electron laser pulses using diamond based Fresnel zone plates,” Sci. Rep. 1, 57 (2011).
[Crossref]

Sadot, O.

E. Leinov, G. Malamud, Y. Elbaz, L. A. Levin, G. Ben-Dorg, D. Shbarts, and O. Sadot, “Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions,” J. Fluid Mech. 626, 449–475 (2009).
[Crossref]

Sakata, S.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Sakawa, Y.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Sano, T.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Sauneuf, R.

G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, and J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 KeV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998).
[Crossref]

Savage, L.

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Schmidt, D.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Sedillo, T.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Seugling, R. M.

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Shapiro, D. A.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Shbarts, D.

E. Leinov, G. Malamud, Y. Elbaz, L. A. Levin, G. Ben-Dorg, D. Shbarts, and O. Sadot, “Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions,” J. Fluid Mech. 626, 449–475 (2009).
[Crossref]

Sheeley, J. M.

J. W. Jacobs and J. M. Sheeley, “Experimental study of incompressible Richtmyer–Meshkov instability,” Phys. Fluids 8, 405–415 (1996).
[Crossref]

Shuwang, G.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Simmons, L.

C. Huntington, K. Raman, S. Nagel, S. MacLaren, T. Baumann, J. Bender, S. Prisbrey, L. Simmons, P. Wang, and Y. Zhou, “Split radiographic tracer technique to measure the full width of a high energy density mixing layer,” High Energy Density Phys. 35, 100733 (2020).
[Crossref]

Soullié, G.

A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017).
[Crossref]

Stemmler, P.

A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017).
[Crossref]

Stone, J.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Sturtevant, B.

M. Vetter and B. Sturtevant, “Experiments on the Richtmyer-Meshkov instability of an air/sf6 interface,” Shock Waves 4, 247–252 (1995).
[Crossref]

M. Brouillette and B. Sturtevant, “Experiments on the Richtmyer–Meshkov instability: single-scale perturbations on a continuous interface,” J. Fluid Mech. 263, 271–292 (1994).
[Crossref]

Suzuki, Y.

Y. Suzuki, A. Takeuchi, H. Takenaka, and I. Okada, “Fabrication and performance test of Fresnel zone plate with 35 nm outermost zone width in hard x-ray region,” X-Ray Opt. Instrum. 2010, 824387 (2010).
[Crossref]

Takenaka, H.

Y. Suzuki, A. Takeuchi, H. Takenaka, and I. Okada, “Fabrication and performance test of Fresnel zone plate with 35 nm outermost zone width in hard x-ray region,” X-Ray Opt. Instrum. 2010, 824387 (2010).
[Crossref]

Takeuchi, A.

Y. Suzuki, A. Takeuchi, H. Takenaka, and I. Okada, “Fabrication and performance test of Fresnel zone plate with 35 nm outermost zone width in hard x-ray region,” X-Ray Opt. Instrum. 2010, 824387 (2010).
[Crossref]

Takizawa, R.

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

Taylor, G. I.

G. I. Taylor, “The formation of a blast wave by a very intense explosion I. Theoretical discussion,” Proc. R. Soc. A 201, 159–174 (1950).
[Crossref]

Tomkins, C. D.

B. J. Balakumar, G. C. Orlicz, C. D. Tomkins, and K. P. Prestridge, “Simultaneous particle-image velocimetry–planar laser-induced fluorescence measurements of Richtmyer–Meshkov instability growth in a gas curtain with and without reshock,” Phys. Fluids 20, 124103 (2008).
[Crossref]

Troussel, P.

A. Do, M. Briat, S. D. Baton, M. Krumrey, L. Lecherbourg, B. Loupias, F. Pérez, P. Renaudin, C. Rubbelynck, and P. Troussel, “Two-channel high-resolution quasi-monochromatic x-ray imager for AL and TI plasma,” Rev. Sci. Instrum. 89, 113702 (2018).
[Crossref]

A. Do, M. Briat, A. Chaleil, C. Rubbelynck, M. Lebugle, C. David, and P. Troussel, “Characterization of a two-channel, high resolution hard x-ray microscope using Fresnel zone plates for laser-plasma interaction experiments,” Rev. Sci. Instrum. 89, 10G122 (2018).
[Crossref]

A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017).
[Crossref]

G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, and J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 KeV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998).
[Crossref]

Tyliszczak, T.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Vartiainen, I.

I. Mohacsi, I. Vartiainen, and B. E. A. Rosner, “Interlaced zone plate optics for hard x-ray imaging in the 10 nm range,” Sci. Rep. 7, 43624 (2017).
[Crossref]

Vetter, M.

M. Vetter and B. Sturtevant, “Experiments on the Richtmyer-Meshkov instability of an air/sf6 interface,” Shock Waves 4, 247–252 (1995).
[Crossref]

Vogel, J. K.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Wang, P.

C. Huntington, K. Raman, S. Nagel, S. MacLaren, T. Baumann, J. Bender, S. Prisbrey, L. Simmons, P. Wang, and Y. Zhou, “Split radiographic tracer technique to measure the full width of a high energy density mixing layer,” High Energy Density Phys. 35, 100733 (2020).
[Crossref]

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Warwick, T.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Welser-Sherrill, L.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Widmann, K.

M. Barrios, K. Fournier, S. Regan, O. Landen, M. May, Y. Opachich, K. Widmann, D. Bradley, and G. Collins, “Backlighter development at the National Ignition Facility (NIF): zinc to zirconium,” High Energy Density Phys. 9, 626–634 (2013).
[Crossref]

Wilson, C.

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

Wojcik, M.

S. S. Ali, K. Li, M. Wojcik, and C. Jacobsen, “Zone plate performance as a function of tilt analyzed via multislice simulations,” Microsc. Microanal. 24, 298–299 (2018).
[Crossref]

Wu, M.

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

Yang, L. L.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Yu, Y.-S.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Zhou, Y.

C. Huntington, K. Raman, S. Nagel, S. MacLaren, T. Baumann, J. Bender, S. Prisbrey, L. Simmons, P. Wang, and Y. Zhou, “Split radiographic tracer technique to measure the full width of a high energy density mixing layer,” High Energy Density Phys. 35, 100733 (2020).
[Crossref]

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

Y. Zhou, “Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II,” Phys. Rep. 723-725, 1–160 (2017).
[Crossref]

Y. Zhou, “Unification and extension of the similarity scaling criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations,” Phys. Plasmas 14, 082701 (2007).
[Crossref]

Commun. Pure Appl. Math. (1)

R. D. Richtmyer, “Taylor instability in shock acceleration of compressible fluids,” Commun. Pure Appl. Math. 13, 297–319 (1960).
[Crossref]

Fluid Dyn. (1)

E. E. Meshkov, “Instability of the interface of two gases accelerated by a shock wave,” Fluid Dyn. 4, 101–104 (1969).
[Crossref]

High Energy Density Phys. (4)

T. Desjardins, C. Di Stefano, T. Day, D. Schmidt, E. Merritt, F. Doss, K. Flippo, T. Cardenas, B. DeVolder, P. Donovan, S. Edwards, F. Fierro, R. Gonzales, L. Goodwin, C. Hamilton, T. Quintana, R. Randolph, A. Rasmus, T. Sedillo, C. Wilson, and L. Welser-Sherrill, “A platform for thin-layer Richtmyer-Meshkov at OMEGA and the NIF,” High Energy Density Phys. 33, 100705 (2019).
[Crossref]

C. Huntington, K. Raman, S. Nagel, S. MacLaren, T. Baumann, J. Bender, S. Prisbrey, L. Simmons, P. Wang, and Y. Zhou, “Split radiographic tracer technique to measure the full width of a high energy density mixing layer,” High Energy Density Phys. 35, 100733 (2020).
[Crossref]

K. Matsuo, T. Sano, K. Ishigure, H. Kato, N. Nagamatsu, Z. Baojun, G. Shuwang, H. Nagatomo, N. Philippe, Y. Sakawa, Y. Arikawa, S. Sakata, S. Lee, K. F. Farley Law, H. Morita, C. Liu, H. Li, J. Nishibata, R. Takizawa, H. Azechi, and S. Fujioka, “Flash x-ray backlight technique using a Fresnel phase zone plate for measuring interfacial instability,” High Energy Density Phys. 36, 100837 (2020).
[Crossref]

M. Barrios, K. Fournier, S. Regan, O. Landen, M. May, Y. Opachich, K. Widmann, D. Bradley, and G. Collins, “Backlighter development at the National Ignition Facility (NIF): zinc to zirconium,” High Energy Density Phys. 9, 626–634 (2013).
[Crossref]

J. Fluid Mech. (3)

M. Brouillette and B. Sturtevant, “Experiments on the Richtmyer–Meshkov instability: single-scale perturbations on a continuous interface,” J. Fluid Mech. 263, 271–292 (1994).
[Crossref]

E. Leinov, G. Malamud, Y. Elbaz, L. A. Levin, G. Ben-Dorg, D. Shbarts, and O. Sadot, “Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions,” J. Fluid Mech. 626, 449–475 (2009).
[Crossref]

M. S. Roberts and J. W. Jacobs, “The effects of forced small-wavelength, finite-bandwidth initial perturbations and miscibility on the turbulent Rayleigh–Taylor instability,” J. Fluid Mech. 787, 50–83 (2016).
[Crossref]

J. Opt. Soc. Am. (1)

J. Quant. Spectrosc. Radiat. Transfer (1)

J. MacFarlane, “Visrad–a 3-D view factor code and design tool for high-energy density physics experiments,” J. Quant. Spectrosc. Radiat. Transfer 81, 287–300 (2003).
[Crossref]

Microsc. Microanal. (1)

S. S. Ali, K. Li, M. Wojcik, and C. Jacobsen, “Zone plate performance as a function of tilt analyzed via multislice simulations,” Microsc. Microanal. 24, 298–299 (2018).
[Crossref]

Nat. Photonics (1)

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft x-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Nucl. Fusion (1)

A. Casner and S. Jacquemot, “Special issue: inertial fusion state of the art–a collection of overview and technical papers from IFSA2017,” Nucl. Fusion 59, 030201 (2019).
[Crossref]

Philos. Trans. R. Soc. A (1)

K. Prestridge, G. Orlicz, S. Balasubramanian, and B. J. Balakumar, “Experiments of the Richtmyer–Meshkov instability,” Philos. Trans. R. Soc. A 371, 20120165 (2013).
[Crossref]

Phys. Fluids (3)

J. W. Jacobs and J. M. Sheeley, “Experimental study of incompressible Richtmyer–Meshkov instability,” Phys. Fluids 8, 405–415 (1996).
[Crossref]

J. W. Jacobs and V. V. Krivets, “Experiments on the late-time development of single-mode Richtmyer–Meshkov instability,” Phys. Fluids 17, 034105 (2005).
[Crossref]

B. J. Balakumar, G. C. Orlicz, C. D. Tomkins, and K. P. Prestridge, “Simultaneous particle-image velocimetry–planar laser-induced fluorescence measurements of Richtmyer–Meshkov instability growth in a gas curtain with and without reshock,” Phys. Fluids 20, 124103 (2008).
[Crossref]

Phys. Plasmas (4)

S. R. Nagel, K. S. Raman, C. M. Huntington, S. A. MacLaren, P. Wang, M. A. Barrios, T. Baumann, J. D. Bender, L. R. Benedetti, D. M. Doane, S. Felker, P. Fitzsimmons, K. A. Flippo, J. P. Holder, D. N. Kaczala, T. S. Perry, R. M. Seugling, L. Savage, and Y. Zhou, “A platform for studying the Rayleigh–Taylor and Richtmyer–Meshkov instabilities in a planar geometry at high energy density at the national ignition facility,” Phys. Plasmas 24, 072704 (2017).
[Crossref]

A. R. Miles, B. Blue, M. J. Edwards, J. A. Greenough, J. F. Hansen, H. F. Robey, R. P. Drake, C. Kuranz, and D. R. Leibrandt, “Transition to turbulence and effect of initial conditions on three-dimensional compressible mixing in planar blast-wave-driven systems,” Phys. Plasmas 12, 056317 (2005).
[Crossref]

M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, “Three-dimensional hydra simulations of national ignition facility targets,” Phys. Plasmas 8, 2275–2280 (2001).
[Crossref]

Y. Zhou, “Unification and extension of the similarity scaling criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations,” Phys. Plasmas 14, 082701 (2007).
[Crossref]

Phys. Rep. (1)

Y. Zhou, “Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II,” Phys. Rep. 723-725, 1–160 (2017).
[Crossref]

Proc. R. Soc. A (1)

G. I. Taylor, “The formation of a blast wave by a very intense explosion I. Theoretical discussion,” Proc. R. Soc. A 201, 159–174 (1950).
[Crossref]

Rev. Sci. Instrum. (6)

B. J. Kozioziemski, J. Ayers, P. Bell, D. K. Bradley, M.-A. Descalle, S. Hau-Riege, T. J. McCarville, T. Pardini, L. A. Pickworth, J. K. Vogel, J. Stone, J. Robinson, D. J. Ampleford, C. R. Ball, C. J. Bourdon, J. R. Fein, M. Wu, A. Ames, R. Bruni, and S. Romaine, “An x-ray optic calibration facility for high energy density diagnostics,” Rev. Sci. Instrum. 89, 10G112 (2018).
[Crossref]

A. Do, M. Briat, A. Chaleil, C. Rubbelynck, M. Lebugle, C. David, and P. Troussel, “Characterization of a two-channel, high resolution hard x-ray microscope using Fresnel zone plates for laser-plasma interaction experiments,” Rev. Sci. Instrum. 89, 10G122 (2018).
[Crossref]

G. Cauchon, M. Pichet-Thomasset, R. Sauneuf, P. Dhez, M. Idir, M. Ollivier, P. Troussel, J.-Y. Boutin, and J.-P. Le Breton, “Imaging of laser produced plasma at 1.43 KeV using Fresnel zone plate and Bragg–Fresnel lens,” Rev. Sci. Instrum. 69, 3186–3193 (1998).
[Crossref]

B. R. Maddox, H. S. Park, B. A. Remington, N. Izumi, S. Chen, C. Chen, G. Kimminau, Z. Ali, M. J. Haugh, and Q. Ma, “High-energy x-ray backlighter spectrum measurements using calibrated image plates,” Rev. Sci. Instrum. 82, 023111 (2011).
[Crossref]

A. Do, P. Troussel, S. D. Baton, V. Dervieux, D. Gontier, L. Lecherbourg, B. Loupias, L. Obst, F. Pérez, P. Renaudin, C. Reverdin, C. Rubbelynck, P. Stemmler, and G. Soullié, “High-resolution quasi-monochromatic x-ray imaging using a Fresnel phase zone plate and a multilayer mirror,” Rev. Sci. Instrum. 88, 013701 (2017).
[Crossref]

A. Do, M. Briat, S. D. Baton, M. Krumrey, L. Lecherbourg, B. Loupias, F. Pérez, P. Renaudin, C. Rubbelynck, and P. Troussel, “Two-channel high-resolution quasi-monochromatic x-ray imager for AL and TI plasma,” Rev. Sci. Instrum. 89, 113702 (2018).
[Crossref]

Sci. Light (1)

K. Kamiya, “Theory of fresnel zone plate,” Sci. Light 12, 35–49 (1963).

Sci. Rep. (2)

I. Mohacsi, I. Vartiainen, and B. E. A. Rosner, “Interlaced zone plate optics for hard x-ray imaging in the 10 nm range,” Sci. Rep. 7, 43624 (2017).
[Crossref]

C. David, S. Gorelick, and S. E. A. Rutishauser, “Nanofocusing of hard x-ray free electron laser pulses using diamond based Fresnel zone plates,” Sci. Rep. 1, 57 (2011).
[Crossref]

Shock Waves (1)

M. Vetter and B. Sturtevant, “Experiments on the Richtmyer-Meshkov instability of an air/sf6 interface,” Shock Waves 4, 247–252 (1995).
[Crossref]

X-Ray Opt. Instrum. (1)

Y. Suzuki, A. Takeuchi, H. Takenaka, and I. Okada, “Fabrication and performance test of Fresnel zone plate with 35 nm outermost zone width in hard x-ray region,” X-Ray Opt. Instrum. 2010, 824387 (2010).
[Crossref]

Other (2)

Lord Rayleigh, Scientific Papers (1900), Vol. II, p. 200.

Applied Nanotools Inc., https://www.appliednt.com/xray-zone-plates/ .

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Figures (18)

Fig. 1.
Fig. 1. Zn backlighter spectrum between 7 keV and 11 keV as measured by SuperSnout II (SSII) spectrometer on shot N200105.
Fig. 2.
Fig. 2. Calculated point spread function of the FZP variation with photon energy.
Fig. 3.
Fig. 3. Pattern of the NIF FZP array. This design has five FZPs (large red circles) arranged so that they are offset vertically and horizontally to maximize the field of view without overlapping the images. The solid lines marked with double slashes represent a displacement of 1.1 mm, and the dashed lines with triangles are 0.25 mm displacements.
Fig. 4.
Fig. 4. Normalized ${{W}}$ source spectra without any filtering (blue) and with filtering (orange).
Fig. 5.
Fig. 5. Theoretical diffraction efficiency of a 1.5 µm thick Au FZP for the (blue dashed) zeroth order, (orange solid) first order, and (black dotted) third order.
Fig. 6.
Fig. 6. (a) Image of the flat field for the five FZPs using the ${{W}}$ source; (b) typical radiograph of the gold wire mesh.
Fig. 7.
Fig. 7. Flat field corrected image of Fig. 6(b).
Fig. 8.
Fig. 8. Resolution measurement versus the distance (drive depth position) from the FZP to the wire mesh. The zero value of the $x$ axis corresponds to the estimated best focal position of the FZP, the plus (minus) values represent an increased (decreased) FZP-mesh distance, and the shift of the peak resolution is due only to positioning measurement error in the lab. The results are presented for the central (blue) and left (red) FZP on horizontal (circle) and vertical (square) axes. The red points have been shifted 100 µm left for visibility.
Fig. 9.
Fig. 9. VISRAD [35] front view of the target experimental setup.
Fig. 10.
Fig. 10. Imaging plate scan of the NIF shot N200105. The five images come from the five FZPs used for this shot. The hole in the image 1 area is used for the time gated detector.
Fig. 11.
Fig. 11. Zoom on image 1 in Fig. 10. The time gated image captured by the framing camera was added in the IP aperture position. We also present a lineout of a wire on the right.
Fig. 12.
Fig. 12. Plot of (a) (blue solid) lineout in Fig. 11 and (black dashed) filtered lineout; (b) (blue solid) derivative of (a) and (black dashed) curve used to fit the FWHM.
Fig. 13.
Fig. 13. Lineout taken from image 4 in Fig. 10 on the (a) horizontal axis as indicated by the white dashed box and (b) vertical axis as indicated by the blue dotted box.
Fig. 14.
Fig. 14. Zoom on mesh image of image 4 in Fig. 10 with enhanced color scale. Interlaced low-resolution, low-intensity images coming from the zeroth order can be observed. They are shifted about 65 µm down and 65 µm right from the first-order image.
Fig. 15.
Fig. 15. Comparison between: (blue solid line) lineout of the zeroth diffraction order, as indicated by the black dotted box in Fig. 10, and (orange dashed line) lineout of the first diffraction order, as indicated by the white dashed box in Fig. 10, with a 90 µm Gaussian blur.
Fig. 16.
Fig. 16. Raytracing simulation for different FZP tilts.
Fig. 17.
Fig. 17. Schematic view of experimental target.
Fig. 18.
Fig. 18. (a) HYDRA simulation of a hydrodynamic instability 50 ns after the main drive start. Target parameters can be seen in Fig. 17; (b) synthetic radiograph obtained by raytracing 1,000,000 rays through the simulation presented in (a), using two time steps in a 100 ps gate time.

Tables (1)

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Table 1. FZP Characteristics

Equations (2)

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f m , λ = r 1 2 m λ ,
r n = n r 1 .

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