Single-bunch imaging of detonation fronts using scattered synchrotron radiation

The Dynamic Compression Sector (DCS)¹ and 32-ID-B at the Advanced Photon Source (APS) have been used for time-resolved X-ray diffraction,^2–5 small-angle X-ray scattering (SAXS),^6–9 and radiography^{2–4,10–14} to provide a comprehensive characterization of the rapid evolution of materials under extreme conditions, such as high explosive (HE) materials during detonation. Traditionally, X-ray optics have been used to switch between the focused pink beam for small-angle scattering and diffraction and the white beam for imaging, requiring re-alignment of beamline end stations due to the two modes typically having slightly different beam paths. Focused pink beam operation using Kirkpatrick-Baez optics typically produces beams 10s of microns in size and can reduce, through mirrors acting as low-pass filters, the contribution from undesired harmonics at higher energies for diffraction and SAXS measurements. Conversely, an unfiltered and the unfocused white beam provides high photon flux useful for high resolution radiography, sometimes referred to as phase contrast imaging,^2–4,11,12 but the beam extent is limited by the overall undulator output and (often fixed) upstream beam-defining slits. The resulting maximum field of view, at DCS, for example, varies from about 2.1 mm × 1.4 mm in the upstream B hutch to about 3.7 mm × 2.5 mm in the downstream E hutch.¹ Switching between focused-beam diffraction/SAXS and imaging modes is a relatively inefficient and time-consuming process due to the need to realign the experimental and detector setups and limits the amount of data that can be collected in the finite time allotted for any single use of the beamline.

An alternative approach that eliminates the need to switch between pink and white beams is to insert a strongly scattering material near a focal point in the beam upstream of the sample to produce a divergent X-ray beam while preserving the SAXS detector position and beam conditioning for SAXS. An ideal scattering material would have a uniform scattering intensity across a wide range of scattering angles to produce a consistent intensity of X-rays around the point source. Our initial tests of this approach utilized glassy carbon (GC), which is often used as a standard for SAXS measurements¹⁵ and thus readily available. More effective scattering sources may be found, as discussed below. However, the stability of GC in the X-ray beam and the relative plateau in the GC scattering profile covering a portion of the q range used in the experiments, as shown in Fig. 1, made it an attractive material to test the imaging technique.

This scatter-beam imaging (SBI) approach creates a point-source projection radiograph of the sample and is capable of imaging the entirety of centimeter-scale objects using focused X-ray beams. SBI is a complementary radiography technique to high resolution white beam radiography, as SBI radiographs lack phase contrast information, are photon starved, and are of lower resolution compared to white beam images. However, the wide field of view in SBI enables insight into macroscale evolution across a centimeter sized object and can provide a straightforward method for positioning samples prior to detonation for time-resolved SAXS measurements of HE materials, where positioning the sample with 50-μm accuracy is essential to ensure timing precision better than 10 ns during subsequent analysis of time-resolved small-angle scattering or diffraction.⁹ 

Scatter-beam imaging is particularly useful for detonation imaging. Explosives cannot sustain detonations below their critical diameter,¹⁶ which for some materials can be near centimeter length scales. Thus, alternative means to white beam imaging such as SBI are needed to image the propagation of a detonation through an entire HE charge at synchrotron sources.

In the data presented below, we highlight the complementarity of white beam radiography and SBI during the detonation of HE materials. We demonstrate the utility of SBI, using GC as a scattering source, in providing a unique understanding of the macroscale evolution of detonating HE charges, and show how data can be quantitatively analyzed to determine densities in cylindrically symmetrical samples.

Ultrasmall angle X-ray scattering of GC was performed at beamline 9-ID at the Advanced Photon Source (APS). Synchrotron X-ray radiography was performed at DCS, beamline 35-ID-B, at the APS, with the light source operating in either twenty four bunch or hybrid-singlet bunch modes with a pulse periodicity of 153.4 ns and 3.682 μs and a pulse full width at half maximum (FWHM) of 80 and 120 ps,¹⁷ respectively. White beam imaging was conducted with the DCS beamline configured to use the U27 undulator with a 30 mm gap, resulting in a polychromatic, unfocused beam with a first harmonic energy of about 16.9 keV with a beam size of about 1.5 × 1.5 mm. SBI utilized the focused pink beam mode with a spot size of approximately 100 × 50 μm. Two separate undulator conditions were used: (1) a nominal energy of approximately 14.5 keV from the 1st harmonic isolated using Si mirrors and (2) a broader spectrum with peaks at approximately 11.5 and 23 keV from the 1st and 2nd harmonics isolated with Rh mirrors.¹ In each case, two mirrors were used in a Kirkpatrick-Baez configuration.

Experiments were conducted using a detonation tank and a detector array described previously.⁶ In brief, the detector array consisted of an Lu2SiO5(Ce) scintillator (DMI/Reading Imaging) that either coated a 75 mm diameter fiber optic taper to a 40 mm image intensifier (MCP140, Photek) or directly coated the image intensifier. Four identical area detectors (PI-MAX4:1024i, Princeton Instruments), each with a camera lens (Milvus 100 mm f/2M ZF.2, Zeiss), were arrayed equidistantly from the image intensifier and configured such that the optical output of the image intensifier passed through three beam splitters (Edmunds Optics) prior to illuminating each detector. The PI-MAX detectors are capable of collecting two images spaced at least 450 ns apart and have a dynamic range of about 60 000 counts with a dark signal of about 600 counts. Experimentally, linearity was preserved when the maximum counts in a single image were fewer than 20 000 per pixel. Bright and dark reference images were collected for each experiment, and images of HE detonation were normalized by subtracting the dark reference from both the bright image and the shot images and then dividing the dark-subtracted shot images by the dark-subtracted bright images.

For SBI, a 2 mm thick plate of GC (Alfa Aesar) was placed in the path of the X-ray beam upstream of the detonation tank to induce divergent scattering of the X-ray beam for the purpose of imaging the sample. The ratio of the GC-sample and GC-detector distances sets the magnification in SBI. At DCS, the beamline components and the detonation tank constrained the placement of GC to GC-sample distances of about 25–100 cm, while the hutch size allowed for GC-detector distances of about 60–400 cm. GC has a relatively flat scattering profile from very low values of q up to around 0.1 Å⁻¹ (Fig. 1), providing reasonably uniform scattering across a portion of the image. For a typical configuration where the field of view at the sample plane was around two centimeters, the q range captured by the detectors spans from around 0.04 Å⁻¹ to either roughly 0.2 Å⁻¹ or 0.4 Å⁻¹ if the beam is centered in the image or at the image edge, respectively. The scattered intensity relative to the low end of the imaged q range drops to about 84% at q = 0.1 Å⁻¹, 25% at q = 0.2 Å⁻¹, 7% at q = 0.3 Å⁻¹, and 3% at q = 0.4 Å⁻¹. The available distances in the DCS B-hutch, X-ray energies used, GC as a scattering source, and detector used in these studies limit the field of view at the sample to around 6 cm. However, maximizing the field of view for SBI would have the effect of changing the scattering region from SAXS to diffraction for the purposes of scattering experiments.

Because the scattered intensity from GC decays appreciably in the q range used, some non-uniformity of the errors was expected from simple counting statistics. Errors in the circular integration of the scattering profile from glassy carbon were experimentally quantified by generating a mean and standard deviation from a histogram of counts obtained across each azimuthal arc. In general, the calculated standard deviation was within 10% of the mean for q values up to around 0.2 and between 10% and 15% for q values between roughly 0.2 and 0.4. Any spatial contrast variation must deviate from the surrounding material by greater than this amount.

Explosive charges were fabricated at the Lawrence Livermore National Laboratory. Pentaerythritol tetranitrate (PETN), hexanitrostilbene (HNS), and 3,4-bis(3-nitro-furazan-4-yl)furoxan (DNTF) were pressed using 500 mg into 6.35 mm diameter cylinders of 10.13, 10.26, and 9.12 mm heights and densities of 1.60, 1.55, and 1.73 g/cm³, respectively. Octol (70% octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine, 30% 2,4,6-trinitrotoluene) pellets were pressed into 9.53 mm diameter, 15.77 mm tall cylinders using 2.00 grams of material, which resulted in a nominal density of 1.78 g/cm³, while ultra-fine 2,4,6-triamino-1,3,5-trinitrobenzene (UFTATB) pellets were pressed into 9.53 mm diameter, 16.50 mm tall cylinders using 2.14 g of material for a nominal density of 1.82 g/cm³. Exploding foil initiators were used to detonate the smaller 500 mg explosives, while a detonator consisting of an explosive foil, a small ∼100 mg PETN or CL-20 charge, and an aluminum flyer which shock-initiates detonation was used for the larger Octol and UFTATB charges. The explosive pellets were held on top of the initiators by a spring-loaded piezo timing pin (Dynasen) at the top of the sample.

High resolution white beam radiographs (Fig. 2) serve as a comparative reference for the SBI data below. The spatially coherent X-ray beam yields a narrow-field view of sections of the HE charge that provides insight into pre-existing microstructural defects in the charge prior to detonation [Figs. 2(a), 2(c), and 2(e)]. Furthermore, high resolution imaging of the charge during detonation can show subtle differences on how the detonation front propagates through different HE materials, as well as the evolution of the gas trailing the detonation front [Figs. 2(b), 2(d), and 2(f)]. As an example, the angle between the HE charge and the ejecta trailing the detonation front can be measured and used in conjunction with the tabulated detonation velocity for the given HE to yield a maximum particle velocity in the expanding gas. For PETN, HNS, and DNTF shown in Fig. 2, the measured angles of 34°, 42.8°, and 33.5° yield particle velocities of 5.2 km/s, 6.3 km/s, and 5.8 km/s, respectively.

SBI radiograph sequences that capture the detonation event for two materials, Octol and UFTATB, are presented in Fig. 3, where the GC and detector distances were set to produce images of the entire HE charge. These images were collected in the pink beam mode at approximately 23 keV using the second harmonic, with the synchrotron operating in twenty four bunch mode. The first image in each sequence [Figs. 3(a) and 3(e)] shows the detonation front starting to propagate through the HE charge near the base, imaged shortly following the initiator's impact. Black arrows in the images approximate the height of the detonation front apex. The second images [Figs. 3(b) and 3(f)] show a striking difference between the two materials: while the Octol has detonated in its entirety behind the detonation front, dead zones of undetonated UFTATB remain at the lower periphery of the charge, identified in the images by white arrowheads. Dead zones are a known feature of non-ideal HE materials¹⁸ and in this case arise from differences on how the detonation front expands through the HE from the area of initiation.^18–24 The final image in the UFTATB sequence [Fig. 3(h)] shows that the dead zones persist, leaving fragments of undetonated HE behind.

SBI radiography of cylindrically symmetric samples such as HE charges can be used for single slice computed tomography reconstruction. This can be used to extract the density of the compressed material and resultant detonation products near and behind the detonation front, respectively. SAXS data of silver behenate at the sample position are analyzed with the Nika software package²⁵ to precisely determine geometric parameters of the cone-beam geometry. Cylindrical symmetry, as present in pressed HE charges [Fig. 4(a)], is exploited to recover density from scatter-beam radiography. One can either feed copies of a single X-ray image at multiple angles into a computed tomography filtered back projection algorithm or one can perform essentially a mathematically equivalent, geometrically corrected, Abel inversion.²⁶ The computed tomography reconstruction package, Livermore Tomography Tools, contains capabilities for either option.

The X-ray distribution used from the isolated 1st harmonic of the U27 undulator, as calculated using XOP2.4,²⁷ is about 14.5 keV with about 0.8 keV FWHM. This relatively high monochromaticity, in combination with the assumption that the atomic composition of the static material and detonation products is the same, leads to reconstructions in which the linear attenuation coefficients are proportional to density [Fig. 4(b)]. Horizontal bands along the z axis of the HE charge seen in Figs. 4(b) and 4(c) are ring artifacts arising from non-ideality and noise in pixels near the center of the image subsequently fed into the Abel inversion reconstruction. Empirically, the uncertainty relative to undetonated full density explosive in this reconstructed slice is within about 7% for much of the image away from the central region and its ring artifacts. However, near the edges of the image, the uncertainty may approach or even exceed 10%. A density plot relative to the undetonated explosive [Fig. 4(c)] shows that near the detonation front, the density of the HE increases to about 120% of the initial value. The spatial resolution for the geometry used and estimated geometric unsharpness²⁸ is approximately 0.4 mm horizontally and 0.2 mm vertically. The compression observed vicinal to the detonation front is consistent with thermochemical calculations, which predict the Chapman-Jouguet density to be roughly 30% higher than the initial density.^29,30 The density of the products can also be estimated, which is needed for calculating the scattering contrast between the condensing nanoparticulates observed by SAXS and the background gas. Without this estimation, the absolute intensity observed by SAXS is ambiguous because it depends on the number density of particulates and their contrast.³¹ 

Synchrotron-based, single X-ray pulse SBI provides a novel, accessible diagnostic tool to explore fast dynamic processes such as those inherent in detonating HE charges. The temporal and spatial resolutions available with this technique compare favorably with proton radiography^19,32–34 and flash X-ray^21,35–39 systems, and the transmission radiographs provide a clear benefit over visible light photographic methods^36,40 for understanding changes throughout the sample volume. While pulsed white beam imaging can provide high resolution, time-resolved phase contrast images such as those shown in Fig. 2, the native beam area size limits the spatial region that can be explored.^{1–4,10–12} SBI provides the same temporal resolution necessary to investigate the rapid process of HE detonation while simultaneously offering a view of the entire sample.

However, a low signal relative to the white beam limits the SBI technique. The low signal level is clearly seen in Fig. 3 where the light source was operating in the 24-bunch mode. In this scenario, images are relatively photon starved, thus determining the precise position of the detonation front apex can be challenging. Even in the hybrid-singlet mode as used for Fig. 4, the signal can be limiting. Measuring the edge of detonation products as they expand outwards behind the front and its angle with respect to the HE charge edge can be performed albeit with greater uncertainty than white beam measurements as in Fig. 2. Two sources of photon loss bear mention. First, only a small portion of the solid angle of the scattered beam is used for images and collected by the detector. SBI is best accomplished when the primary beam is blocked prior to interacting with the sample (particularly if the sample exhibits strong scattering). For example, in Fig. 3, the central beam is incident on the stainless-steel detonator housing at the bottom of the charges, while in Fig. 4, the primary beam is incident on the timing pin. Second, ultimately, the intensity of the scattered X-rays from the GC is a function of the total scattering volume, contrast, and absorption of the GC.

While GC was used as a scattering source for this study, we expect that better scattering sources are possible to improve the signal in SBI radiographs. An ideal scattering material will contain phases that have a large contrast with the surrounding medium and have size distributions that are conducive to producing a constant scattered intensity across much of the resulting image. The intensity across the region of interest should ideally vary minimally (e.g., less than a factor of ten) to enable a reasonable photon flux and a dynamic range. As with GC, other scattering materials should be stable in the X-ray beam for robust measurements. Another experimental parameter to consider is the undulator profile for the beam line in use, as the undulator settings and beam line optics can be used to isolate X-rays of specific energies. Because the scattering vector q is inversely related to the X-ray wavelength, the small angle scattering will depend strongly on the selected energy.

In this manuscript, we have described a straightforward method of producing a divergent beam for wide-field transmission X-ray radiography during experiments using focused synchrotron radiation such as SAXS or X-ray diffraction. SBI is achieved by placing a material with high X-ray transmission and intense small-angle scattering upstream from the sample in the collimated and focused beam to act as a point-source illumination. The material must possess a relatively flat X-ray intensity profile across the angular range required to illuminate the sample and detector, given possible source to sample and sample to detector distances to achieve the desired magnification. With a prudent choice of geometry, this setup, with a fast detector array at a synchrotron, provides a diagnostic tool that can probe sub-microsecond dynamic phenomena across a centimeter-scale field of view while using a focused, sub-millimeter beam. This imaging method is well-suited for examining the detonation of centimeter-scale explosive charges, as the detonation event can be followed through its entirety. While the imaging approach suffers from a low signal, improvements in the selection of the upstream scattering material and in beam line components may lead to substantial signal gains in the future.

We thank particularly S. Bastea for insightful discussions. We also acknowledge C. May, P. Pagoria, and the HEAF staff at LLNL, and B. Jensen, D. Dattelbaum, and M. Firestone of LANL. This work was funded at its initial stages by LLNL LDRD 14-ERD-018 and at its latter stages by NNSA's Office of Defense and Nuclear Nonproliferation and Science Campaign 2 and performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. M. H. Nielsen acknowledges additional support from the Lawrence Fellowship at LLNL. The Dynamic Compression Sector at the Advanced Photon Source (DCS@APS) is managed by Washington State University and funded by the National Nuclear Security Administration of the U.S. Department of Energy under Cooperative Agreement No. DE-NA0002442. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by the Argonne National Laboratory under Contract No. DE-AC02-06CH11357. The authors are grateful for the support from beamline staff at beamlines 9-ID, 35-ID, and LLNL-JRNL-741424.