A 7.2 keV spherical x-ray crystal backlighter for two-frame, two-color backlighting at Sandia’s Z Pulsed Power Facility

For more than three decades, spherical crystal based, monochromatic x-ray backlighter radiography^1–8 has been an essential probe for high-energy density physics (HEDP) experiments. Bent-crystal microscopes can provide high spatial resolution over a centimeter-size field of view. They operate within a narrow spectral bandwidth (⁠$ΔE/E≈1 0 − 3 −1 0 − 4$⁠), which results in nearly monochromatic images that allow for an easier interpretation compared to broadband images, for example, from point-projection backlighter systems.

For the last eight years, the majority of experiments at Sandia’s Z Pulsed Power Facility (“Z”)⁹ studying inertial confinement fusion used the immense magnetic pressure generated by Z to implode empty, gas- or liquid-filled, hollow Be cylinders (liners) for studies of, for example, the Magneto-Rayleigh-Taylor instability without^10,11 or with pre-imposed axial magnetic field,^12,13 or the electrothermal instability.^14,15 Understanding and mitigating these instabilities is important for the Magnetized Liner Inertial Fusion (MagLIF) concept,^16,17 where fusion fuel is magnetized with an external field coil, preheated with a multi-kJ laser pulse, and compressed using Z to achieve thermonuclear conditions.¹⁸ 

In a typical backlighter experiment as shown in Fig. 1, the 527-nm, 1-kJ, 1-ns Z-Beamlet Laser (ZBL)¹⁹ is used to generate a plasma x-ray source. The ZBL provides two spatially and temporally separated foci in the Z target chamber, enabling two-frame imaging with an inter-frame time range of 2-20 ns.²⁰ 

The spherical-crystal imaging system at Z consists of either two quartz (1 0 1) crystals using the 1.865 keV Si $He α$ emission line or two quartz (2 2 3) crystals using the 6.151 keV Mn $He α$ intercombination line.²¹ Note that we omit the conjugate plane in the designation of the Miller indices for quartz crystals [e.g., quartz $( 2 2 4 ¯ 3 )$ becomes quartz (2 2 3)] for consistency with the other crystals mentioned here. The backlighter systems operate at a magnification of 5.8, using crystals with $R=250 mm$ radius of curvature. X-rays emitted from the two sources penetrate the imploding liner at the center of Z, are reflected and focused by the two crystals, pass through two return apertures for debris and background mitigation, and are then detected with image plate detectors. The large amount of debris generated in a Z experiment requires significant shielding of the detectors, which are placed inside of a 1-in. tungsten enclosure (the “backlighter camera”).

While the x-ray optical design or crystal dimensions stayed unchanged since 2008,²⁰ the crystal mounting hardware and its alignment precision were improved in 2013²² after identifying potential issues due to the movement of the crystal between alignment and downline shot. The design was changed from an assembly of commercial miniature stages to a monolithic Al block with flexure arms and locking set screw combination to adjust only tip and tilt of the crystal, while the distance to the liner stays fixed, see Fig. 1(a).

For implosions at high convergence ratios $C R >15$⁠, where C_R = r_i(0)/r_i(t) and r_i the inner radius of the liner, the Be liners become too opaque for 6 keV x-rays to determine the position of the inner radius $r i ( t )$ with high confidence. Hence, a backlighter system with higher x-ray energy was required. Design requirements were that it performs similar to or better than the 6 keV system in terms of image brightness, spatial resolution, and the Bragg angle which affects astigmatism. In Secs. II–V, we describe these requirements in more detail, determine potential candidates for above 6-keV backlighting, present the chosen 7.2 keV backlighter system as well as laser-only tests to determine image brightness and spatial resolution, and finally we show examples of 7.2 keV radiographs at the Z Pulsed Power Facility.

When the liner converges radially during the Z implosion, its density increases. High-quality compressions require a stable (straight) inner wall during the implosion to reach high stagnation pressures and temperatures. The trajectory and integrity of the inner wall are experimentally measured by taking x-ray radiographs at various stages during the implosion, which requires that the liner be partially transparent for the probe x-rays. Assuming a perfect, cold compression without any mass losses, the density ρ of a cylindrical liner with inner radius r_i and wall thickness d depends on the convergence ratio as

The strongest absorption of x-rays penetrating the liner occurs along the inner wall surface. This limb thickness is a function of C_R as well and can be calculated as

Both Eqs. (1) and (2) are used to calculate the limb transmission according to the Beer-Lambert law $T=exp ( − μ ρ L )$⁠, where μ denotes the mass attenuation coefficient. Here we use cold, solid density values for simplicity.

Figure 2(a) shows the limb transmission vs. C_R for a Be liner with r_i = 3.44 mm and d = 0.4 mm. The plots show the limb transmission scaling for five different x-ray emission lines from He-like ions or cold $K α$ lines. The limb transmission decreases strongly with increasing C_R for x-ray energies below 10 keV. Above 10 keV, the transmission stays high even at C_R = 20. A limb transmission of about 50% yields an optimum contrast and requires x-ray energies near or above 10 keV. However, both the ZBL laser conversion efficiency into x-rays (see Fig. 10 in Ref. 19) and the integrated reflectivity of any suitable crystals²³ quickly drop with increasing x-ray energy, rendering sources near or above 10 keV unusable with the present capabilities.

The limb transmission for the 6.151 keV Mn $He α$ x-ray backlighter system is below 5% for $C R >5$ [see Fig. 2(b)], which can complicate the interpretation of experimental radiographs as the measurement of the inner radius suffers from a poor signal-to-noise ratio. Increasing the backlighter energy by only one (two) keV, which corresponds to an increase of 17% (30%) relative x-ray energy, increases the transmission by about five (ten) times. This is a significant improvement in transmission for a modest change in x-ray energy.

The idealized calculations from above are corroborated by synthetic radiographs from a 3D resistive-MHD GORGON simulation²⁴ of an imploding liner at Z. This simulation imploded a MagLIF-scale beryllium liner with r_i = 2.325 mm and $d=0.465 mm$¹⁸ but used a liquid deuterium fill to reduce the final convergence achieved. Note that the initial inner radius and wall thickness are slightly different to the Be liner used in the analytical example above. This target stagnates at larger radii compared with a high-convergence MagLIF target since it was intended to be more easily diagnosed with radiography. Figure 3 shows a density slice at peak compression (an inner surface convergence of C_R = 12 resulting in a $400μ m$ inner diameter), as well as synthetic radiographs for 6, 7.2, or 10 keV x-rays. Figure 4 shows axially averaged line outs of the transmission images. Similar to Fig. 2, the liner is opaque for 6 keV x-rays with a limb transmission of less than 1%. At 7.2 keV, the limb transmission is about 4%, sufficient to locate the inner surface. This further indicates that raising the x-ray backlighter energy by 1 keV or more will lead to significant contrast enhancement. At 10 keV energy, the transmission retains at about 27%; however, as mentioned above, a 10 keV x-ray backlighter system is currently not attainable at our facility.

Another design requirement for a higher-energy backlighter system at Z was to keep the Bragg angle of the new system close to $8 3 °$⁠, which is close to the Bragg angles of the existing 1.865 and 6.151 keV systems and allows for two-color imaging (using two different sources and crystals) with the ZBL.²⁰ It also simplifies the testing of the new system during downline shots at Z because one frame can be used with the reliable 6.2 keV system, while the other frame can be used to test the new system without risking a complete data loss if the new system experiences issues.

Another reason to keep the Bragg angle close to the existing system is the integration at Z. The liner is always at the Z center, which means that a new backlighter system with an angle different than $8 3 °$ needs the detector (and x-ray source) at a different position. Figure 5 shows a computer aided design model of the backlighter camera sitting on top of the cover plates of the magnetically insulated transmission lines (MITLs). The camera housing can accommodate two 75-mm long image plate detectors and has room for a future upgrade with a time-gated detector. The housing is made out of $1 ″$ tungsten plates for debris and background protection, weighs about 400 kg, and can only be moved with a crane. The MITL plates have dedicated cutouts for the camera, which restricts camera positioning. Furthermore, the camera snout reaches into the blast shield that is used to contain debris created following the liner implosion, and hence the blast shield needs to be specifically designed for the camera. In the case of MagLIF, the superstructure that is used to separate the magnetic field coils²⁵ surrounds the target. It has specific slots cut into this structure for both the incident and reflected x-ray backlighter paths. Another important constraint is the return current can, which limits the Bragg angle to less than $8 6 °$ for the current MagLIF geometry.

All the hardware on Z could have been modified for a new backlighter system if absolutely needed, but this would have required significant engineering efforts. However, in Sec. III, we show that re-engineering was not needed since promising imaging systems near $8 3 °$ could be identified.

A typical backlighter shot uses two 1-kJ, 1-ns ZBL pulses at 527 nm, each of which has a conversion efficiency of about $( 1 − 2 ) ×1 0 − 3$ into the Mn He_α line complex.^19,26 At keV plasma temperatures, most of the He_α emission is either in the resonance (⁠$1s2p 1 P 1 →1 s 2 1 S 0$⁠) or intercombination (⁠$1s2p 3 P 1 →1 s 2 1 S 0$⁠) lines of the spectrum. Hence, the conversion efficiency into the 6.151 keV Mn intercombination line is estimated to be about $5×1 0 − 4$⁠, which corresponds to $5×1 0 14$ 6.151-keV photons emitted from each source. This backlighter configuration generates images with a brightness of about 2 photons per $μ m 2$⁠, with a detector-limited resolution of about $12μ m$ in the object plane.²⁷ A requirement for the higher-energy backlighter system was that the new system should generate images with similar magnification, resolution, and image brightness as the existing 6.151-keV system.

Suitable x-ray crystal and spectral-line combinations were taken from Ref. 23. The range of Bragg angles was restricted to $( 8 3 ° ± 1 ° )$ to fulfill the Bragg angle requirements mentioned above. The list of spectral lines was limited to the He-like resonance and intercombination lines for the elements Si to Ge since these lines can be efficiently generated with the ZBL. The best candidates are presented in Table I. For each match, we show the source element, line energy, crystal material with corresponding Miller indices (h k l), and 2d lattice spacings, as well as the Bragg angle and integrated reflectivity $R int$⁠. The integrated reflectivity was calculated with X-ray Oriented Programs (XOP’s)²⁸ multi-lamellar model for a bent crystal with 250 mm radius and $70μ m$ thickness. Knowledge of the ZBL laser energy to x-ray energy conversion efficiency^19,26 lets us calculate the expected image brightness for a ZBL-backlighter system with magnification of six.²⁷ These results are listed in the last column of Table I.

The table shows that the already-used 1.865 and 6.151 keV backlighter systems are indeed the most efficient combinations for their respective energy. The overall most efficient crystal is Ge (2 2 0) with $R int =843.15μ rad$ in combination with the Ar intercombination line at 3.124 keV. While Ar cannot be easily used as a ZBL target, this crystal is used for self-emission imaging of the imploding liner at Z.¹⁸ Above 6.151 keV, the image brightness for matching combinations quickly approaches only a few photons per pixel. The highest image brightness for a working combination above 6.151 keV is the Co resonance line at 7.242 keV with a Ge (3 3 5) crystal. The expected image brightness at 7.2 keV is two times lower than at 6.2 keV, which would still be acceptable. If the image brightness is too low, the x-ray source can be moved 31.6 mm inside the Rowland circle to increase the image brightness about twofold at the cost of field of view.³ 

Before fielding the 7.2 keV backlighter system on Z, the crystals were tested in one of the target chambers at the Z-Backlighter facility.¹⁹ The ZBL was used in single-frame configuration, delivering 1–1.5 kJ in a 1-ns pulse. A 0.5-ns, 100-J picket preceded the main pulse by 3.5 ns to enhance the x-ray yield.²⁹ The laser was focused onto 25-μm thick Co foils to generate the 7.242 keV characteristic line radiation. A spherical Ge (3 3 5) crystal with $R=250 mm$ and rectangular aperture (28 mm meridional, 10 mm sagittal) was set up in a backlighter configuration with the x-ray source on the Rowland circle. Both a static, 150 lines-per-inch (lpi) W mesh and a 0.5-mm-thick W knife edge served as radiography objects, placed at a distance of 146.6 mm from the crystal. A filtered Fuji TR image plate was used as the detector, placed at 850 mm from the crystal to yield a magnification of 5.8, identical to the 6.151-keV backlighter system.²⁰ Since the crystal aperture is identical to the aperture of the 6.151-keV crystals, the field of view of $11.4×4.1 mm 2$ is also identical.

The W mesh was used to verify the magnification and, in the unobstructed areas, the flat field homogeneity. The knife edge was used to infer the spatial resolution of the combined image plate plus crystal imaging system. Multiple shots were taken with the knife in either the horizontal or vertical direction to measure the resolution in both the sagittal and meridional directions. The image plates were scanned with a Fuji FLA7000 scanner with $25×25μ m 2$ pixel size; the data were corrected for fading using our own calibration curve. Figure 6(a) shows a magnified view of the mesh wires and the tungsten knife edge, which covers the right half of the image. The red box marks the area taken to infer the edge spread function (ESF) 10%-90% width, which is used here to determine the spatial resolution of the system. Figure 6(b) shows the line out of the data, together with a fit assuming a Gaussian line spread function.

The measured data were further compared with ray-tracing simulations using the code described in Ref. 27. The simulations used the as-fielded distances. The source photon yield was calculated from the laser energy using conversion efficiencies measured earlier.^19,26 The rocking curve was imported into the simulation from an XOP data table. The simulated detector had 25 μm pixel size; the image was post-processed using a 65-μm Gaussian point spread function³⁰ to simulate the IP resolution.

Table II shows the simulated ESF widths and image brightness, compared with the measurements. Due to astigmatism, the sagittal and meridional ESFs are different; the resolution of this backlighter system is slightly better in the meridional (radial on Z) direction. The ray-tracing simulations assume a perfect crystal with zero surface defects, which for a perfect detector results in better resolution than measured.²⁷ The image plate detector limits the system spatial resolution, as in the 6.151-keV backlighter system. However, the comparison to the ray-trcing model shows that the Ge crystal is of high quality and does not degrade the spatial resolution.

The comparison of the simulated and measured image brightness shows that the real system is about a factor of two brighter than anticipated. The error quoted for the experimental data represents the minimum/maximum shot-to-shot variation of the measurements, normalized to 1 kJ laser energy. The exact origin of the discrepancy between the model and experiment is currently not known. Calculating the expected image brightness depends on many parameters that are not well benchmarked: the conversion efficiency of laser into a single spectral line is not well known and had to be estimated; furthermore the calculated crystal reflectivity could also be wrong by some factor. As stated in Ref. 23, the crystal reflectivity in these calculations is strongly affected by the temperature (Debye-Waller) factor. In most cases, a temperature factor between 0.8 and 0.9 yields satisfying results; a lower temperature factor results in a lower integrated reflectivity. Here, a factor of 0.8 was chosen, which may underestimate the reflection efficiency.

After confirming with laser-only shots that the 7.2-keV backlighter meets the requirements, the system was fielded at Z. The first integrated Z shots testing this new capability fielded the 6.2-keV backlighter for the first frame and the new 7.2-keV backlighter for the second frame during an early time of the implosion. The two-color configuration was selected for a direct comparison of both systems in a dynamic radiography experiment and to reduce the risk for data loss for the case that the 7.2-keV system does not produce an image. Figure 7(a) shows the two radiographs obtained for an imploding liner with “thick ends” (the two bulges, top left and right).³¹ The left radiograph was taken with the 6.151-keV backlighter, and the right radiograph was taken 5 ns later with the 7.242-keV backlighter. Figure 7(b) shows a line out of the area marked by the red lines in (a). The top of the radiographs features a shadow of the top Helmholtz B-field coil on top of the liner.²⁵ In this experiment, the limb transmission of the 7.2-keV x-rays is about a factor of three better than the 6.2-keV transmission, and the 7.2-keV image shows a better contrast in this area than the 6.2-keV image. A darker feature appears in both images right at the inner wall of the liner at $r≈2.3$ mm, which shows up in the line outs as a small dip with higher absorption. This feature is from a sub-100-nm, high-opacity Pt coating that was vapor-deposited at the inner wall to locally enhance radiographic contrast (see Ref. 12 for a detailed discussion of the radiographic tracer-layer technique).

An examination of the object-free image area in Fig. 7(a) for radii greater than 3 mm reveals a gradient in the top-down direction of the 7.2-keV image, which is absent in the 6.2-keV image. A second set of two-color radiographs in another Z shot also showed a homogeneous flat field for 6.2-keV x-rays but again a vertical gradient in the 7.2-keV image, as well as a much dimmer exposure indicating an alignment issue with the 7.2-keV system. A vertical gradient in the backlighter image cannot be created by misalignment of the Bragg angle, which would result in a horizontal gradient. A vertical gradient can be created by partial clipping of the x-ray beam after the crystal reflection, for example, at the 3-mm diameter return aperture. However, a pointing error of the reflected x-ray beam could be ruled out because the image was centered at the image plate detector. These observations suggest that neither the crystal nor the return apertures were misaligned, leaving the x-ray source as the culprit. Post-shot ray-tracing simulations showed that an x-ray source movement of about 1 mm or more in the vertical direction (up) could reproduce the experimental radiographs.

The x-ray source (laser targets) are Co foils glued onto 3-mm diameter Al disks, which in turn are held in place by gravity in a cutout area on a larger Al laser target holder. Figure 8(a) shows two Mn foils on their Al disks in the laser target holder. This configuration has worked well for many years without any issues or clipped radiographs. However, Mn and the Al disk are anti-ferromagnetic and not affected by the fringe magnetic fields at Z, whereas Co is strongly ferromagnetic. The experiment in Fig. 7 used an applied magnetic field from Helmholtz coils.²⁵ The fringe magnetic field strength from the field coils can reach 0.5 T or more near the laser targets at an early time in the current discharge. The magnetic force vector at the target location points in a direction that pulls the Co targets up and towards the Z center. As a result, the entire Al disk flips into an almost vertical orientation, which leads to a vertical shift of the apparent x-ray source when the laser hits and also to a reduced laser-to-x-ray energy conversion.

To eliminate the Co target movement in the following shots, a retaining clamp was designed and manufactured in-house with selective laser sintering. Figure 8(b) shows the re-designed laser target block with the retaining clamp.

Figure 9 shows two 7.2-keV radiographs of a Z shot using the clamp. The images are well exposed, have a homogeneous flat field distribution, and exhibit a high contrast. The total laser energies were 1.2 kJ in the first frame and 1 kJ in the second frame; the distributions of energy into the prepulse and main pulse are shown in the picture. Both images have a photon fluence of 5–6 $photons /μ m 2$⁠, which is amongst the highest fluence radiographs recorded at Z.

The liner in the radiographs shown in Fig. 9 was filled with liquid D₂ and had an on-axis Be rod with a machined sinusoidal perturbation. The primary goal of this experiment was not to achieve the highest compression but to observe the evolution of the on-axis rod surface modulations during the deceleration phase nearing stagnation. The initial liner diameter was much larger than a standard MagLIF-liner, resulting in a high areal density which necessitated the use of the 7.2-keV system over the 6.2-keV system for improved visibility of the inner rod. In the 15 ns between frame 1 and frame 2, both the liner and the inner rod are compressed, the amplitude of the rod surface modulation increases, and an axial asymmetry in the compression is evident. These radiographs were taken at C_R of about 4-5. In subsequent campaigns, 7.2-keV radiographs with C_R up to about 20 have been measured. Data analysis is still ongoing and results will be published in future articles.

A comparison of 14 Z experiments, where seven experiments used the 6.2 keV backlighter system and seven used the new 7.2 keV backlighter system, for a total of 28 radiographs, showed that on average the 7.2 keV radiographs $( ≈ 7 photons / μ m 2 )$ are about 1.7 times brighter than the 6.2 keV radiographs $( ≈ 4 photons / μ m 2 )$⁠. One notable difference between the 6.2 and 7.2 keV systems is that the 6.2 keV backlighter uses the intercombination line and the 7.2 keV backlighter uses the resonance line of the He-like spectrum. The efficiency for imaging may depend on the optical depth of the line, which varies between the resonance and intercombination lines. Furthermore, surrounding hardware or dynamic processes in a Z experiment may adversely or positively affect the laser-plasma interaction and x-ray generation during the shot. For example, hardware such as the light-blocking filters, Be debris shields or the Be return current can attenuate 6.2-keV x-rays more than 7.2-keV x-rays. Potential parasitic radiation emission at an early time during the Z discharge could lead to preheat of the target, crystal, or both, affecting the efficiency of the imaging system. These factors change from experiment to experiment and are very hard if not impossible to predict.

A 7.242-keV backlighter system using a spherical Ge (335) crystal and the Co $He α$ resonance line has been developed and fielded at the Z Pulsed Power Facility at Sandia National Laboratories, NM, USA. The crystal and x-ray source parameters were chosen after a systematic evaluation was performed to find spectral-line and spherical-crystal matches suitable for high-resolution imaging with a Bragg angle near $8 3 °$⁠. The 7.242-keV backlighter system operates at a Bragg angle of $82. 8 °$⁠, which is compatible with the existing 1.865-keV (⁠$83. 9 °$⁠) and 6.151-keV (⁠$83.1 9 °$⁠) backlighter systems. Laser-only tests at the Z-Backlighter facility confirmed that the new backlighter system meets the requirements with an image brightness of more than 2 $photons /μ m 2$ and spatial resolution of better than 15 μm (10%-90% knife edge width). The first dynamic radiographs at the Z facility revealed that fringe magnetic fields during an early time of the Z current discharge pull the Co targets out of their nominal positions, which results in compromised radiographs that have a poor exposure as well as a vertical gradient. This issue was eliminated by adding a retaining clamp to the laser target holder. Subsequent Z shots produced successful 7.242-keV radiographs with a high contrast and transmission through the liner, a homogeneous flat field, and an image brightness above 5 $photons /μ m 2$⁠. This new 7.242-keV backlighter system has now been added as a standard diagnostic at Z and is available to experimenters.

The authors would like to thank the Sandia MagLIF, Z operations, Z-Beamlet, target fabrication, Z center section, Z diagnostics, CMDAS, Lab 101, and gas fill teams. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under Contract No. DE-NA-0003525.