Analysis and implementation of a space resolving spherical crystal spectrometer for x-ray Thomson scattering experiments

Progress toward absolute calibrations of DC x-ray sources from 1 keV to >30 keV for Z diagnostics applications

Numerous x-ray diagnostics at the Z facility, time-resolved and time-integrated, would benefit from a local calibrated x-ray source. For many years, Z has used low-power Manson x-ray sources to provide some characterization information for components of Z diagnostics below 30 keV. More recently, we have acquired TruFocus x-ray sources, which operate at voltages up to 100 kV depending on the anode material and model. These DC sources have demonstrated good stability and repeatability. Absolute calibrations of either sources or detectors usually involve another calibrated detector from another source, which has not been readily available locally. Therefore, we have adopted the strategy of characterizing a sensitive semiconductor diode detector by controlling or inferring the active volume. This characterized detector is then used to scale the Manson x-ray spectral shape as measured by an Amptek energy-resolving detector. The result agrees well with the modeled source spectrum. We can apply this technique to the TruFocus as well.

Machine learning based unfolding of x-ray spectra from filter stack spectrometer data

We demonstrate the application of neural networks to perform x-ray spectra unfolding from data collected by filter stack spectrometers. A filter stack spectrometer consists of a series of filter-detector pairs, where the detectors behind each filter measure the energy deposition through each layer as photo-stimulated luminescence (PSL). The network is trained on synthetic data, assuming x-rays of energies <1 MeV and of two different distribution functions (Maxwellian and Gaussian) and the corresponding measured PSL values obtained from five different filter stack spectrometer designs. Predicted unfolds of single distributions are near identical reproductions of the ground truth spectra, with differences in the values lower than 20% at the higher energy end in some cases. The neural network has also demonstrated robustness to experimental measurement errors of <5% and some capability of performing unfolds for linear combinations of the two distributions without previous training. The network can perform unfolds at rates >1 Hz, ideal for application to some high-repetition-rate systems.

Plasmoid Formation and Strong Radiative Cooling in a Driven Magnetic Reconnection Experiment

We present the first experimental study of plasmoid formation in a magnetic reconnection layer undergoing rapid radiative cooling, a regime relevant to extreme astrophysical plasmas. Two exploding aluminum wire arrays, driven by the Z machine, generate a reconnection layer (S_{L}≈120) in which the cooling rate far exceeds the hydrodynamic transit rate (τ_{hydro}/τ_{cool}>100). The reconnection layer generates a transient burst of >1  keV x-ray emission, consistent with the formation and subsequent rapid cooling of the layer. Time-gated x-ray images show fast-moving (up to 50  km s^{-1}) hotspots in the layer, consistent with the presence of plasmoids in 3D resistive magnetohydrodynamic simulations. X-ray spectroscopy shows that these hotspots generate the majority of Al K-shell emission (around 1.6 keV) prior to the onset of cooling, and exhibit temperatures (170 eV) much greater than that of the plasma inflows and the rest of the reconnection layer, thus providing insight into the generation of high-energy radiation in radiatively cooled reconnection events.

A generalized approach to x-ray data modeling for high-energy-density plasma experiments

Accurate understanding of x-ray diagnostics is crucial for both interpreting high-energy-density experiments and testing simulations through quantitative comparisons. X-ray diagnostic models are complex. Past treatments of individual x-ray diagnostics on a case-by-case basis have hindered universal diagnostic understanding. Here, we derive a general formula for modeling the absolute response of non-focusing x-ray diagnostics, such as x-ray imagers, one-dimensional space-resolved spectrometers, and x-ray power diagnostics. The present model is useful for both data modeling and data processing. It naturally accounts for the x-ray crystal broadening. The new model verifies that standard approaches for a crystal response can be good approximations, but they can underestimate the total reflectivity and overestimate spectral resolving power by more than a factor of 2 in some cases near reflectivity edge features. We also find that a frequently used, simplified-crystal-response approximation for processing spectral data can introduce an absolute error of more than an order of magnitude and the relative spectral radiance error of a factor of 3. The present model is derived with straightforward geometric arguments. It is more general and is recommended for developing a unified picture and providing consistent treatment over multiple x-ray diagnostics. Such consistency is crucial for reliable multi-objective data analyses.

Radiation, optical, power flow, and electrical diagnostics at the Z facility: Layout and techniques utilized to operate in the harsh environment

The Z machine is a current driver producing up to 30 MA in 100 ns that utilizes a wide range of diagnostics to assess accelerator performance and target behavior conduct experiments that use the Z target as a source of radiation or high pressures. We review the existing suite of diagnostic systems, including their locations and primary configurations. The diagnostics are grouped in the following categories: pulsed power diagnostics, x-ray power and energy, x-ray spectroscopy, x-ray imaging (including backlighting, power flow, and velocimetry), and nuclear detectors (including neutron activation). We will also briefly summarize the primary imaging detectors we use at Z: image plates, x-ray and visible film, microchannel plates, and the ultrafast x-ray imager. The Z shot produces a harsh environment that interferes with diagnostic operation and data retrieval. We term these detrimental processes "threats" of which only partial quantifications and precise sources are known. We summarize the threats and describe techniques utilized in many of the systems to reduce noise and backgrounds.

Imaging x-ray spectrometer at the high energy density instrument of the European x-ray free electron laser

A multipurpose imaging x-ray crystal spectrometer is developed for the high energy density instrument of the European X-ray Free Electron Laser. The spectrometer is designed to measure x rays in the energy range of 4-10 keV, providing high-resolution, spatially resolved spectral measurements. A toroidally bent germanium (Ge) crystal is used, allowing x-ray diffraction from the crystal to image along a one-dimensional spatial profile while spectrally resolving along the other. A detailed geometrical analysis is performed to determine the curvature of the crystal. The theoretical performance of the spectrometer in various configurations is calculated by ray-tracing simulations. The key properties of the spectrometer, including the spectral and spatial resolution, are demonstrated experimentally on different platforms. Experimental results prove that this Ge spectrometer is a powerful tool for spatially resolved measurements of x-ray emission, scattering, or absorption spectra in high energy density physics.

Temperature distributions and gradients in laser-heated plasmas relevant to magnetized liner inertial fusion

We present two-dimensional temperature measurements of magnetized and unmagnetized plasma experiments performed at Z relevant to the preheat stage in magnetized liner inertial fusion. The deuterium gas fill was doped with a trace amount of argon for spectroscopy purposes, and time-integrated spatially resolved spectra and narrow-band images were collected in both experiments. The spectrum and image data were included in two separate multiobjective analysis methods to extract the electron temperature spatial distribution T_{e}(r,z). The results indicate that the magnetic field increases T_{e}, the axial extent of the laser heating, and the magnitude of the radial temperature gradients. Comparisons with simulations reveal that the simulations overpredict the extent of the laser heating and underpredict the temperature. Temperature gradient scale lengths extracted from the measurements also permit an assessment of the importance of nonlocal heat transport.

A spherical crystal diffraction imager for Sandia's Z Pulsed Power Facility

Sandia's Z Pulsed Power Facility is able to dynamically compress matter to extreme states with exceptional uniformity, duration, and size, which are ideal for investigating fundamental material properties of high energy density conditions. X-ray diffraction (XRD) is a key atomic scale probe since it provides direct observation of the compression and strain of the crystal lattice and is used to detect, identify, and quantify phase transitions. Because of the destructive nature of Z-Dynamic Material Property (DMP) experiments and low signal vs background emission levels of XRD, it is very challenging to detect a diffraction signal close to the Z-DMP load and to recover the data. We have developed a new Spherical Crystal Diffraction Imager (SCDI) diagnostic to relay and image the diffracted x-ray pattern away from the load debris field. The SCDI diagnostic utilizes the Z-Beamlet laser to generate 6.2-keV Mn-He_α x rays to probe a shock-compressed material on the Z-DMP load. A spherically bent crystal composed of highly oriented pyrolytic graphite is used to collect and focus the diffracted x rays into a 1-in. thick tungsten housing, where an image plate is used to record the data.

Quartz conditioning crystal for X-ray rocking curve topography

A large α-quartz crystal designed to condition the monochromatic beam at beamline 1-BM of the Advanced Photon Source is presented. The purpose of this crystal was to provide a precise match to the Bragg angle of quartz crystals that are commonly used to make analyzers for plasma diagnostics. In order to characterize these analyzers, area detectors need to be positioned at distances from the analyzer at upwards of 1000 mm. As a result of this precise matching, a Bragg-reflected beam from such an analyzer is precisely parallel to the beam incident on the conditioning crystal. This situation alleviates the need to adjust the position of the area detector as the distance between the analyzer and the area detector is varied. That is, there is no need to account for vertical displacement of the diffracted-beam image as a function of this distance. Additionally, verification that the analyzer is set to the correct Bragg reflection is obtained by scanning this distance, because only for a spurious reflection will there be a vertical displacement. This is a very useful check. To commission the conditioning crystal, diffraction from a high-quality flat quartz crystal was mapped using a CCD. Bragg diffraction from the 40\overline 40 reflection at 8.5 keV was studied over an area of 23 × 31 mm. The theoretical Darwin width of the flat sample in this case was 4.7 µrad. An FWHM value near 6 µrad was measured over almost the entire mapped area. These data demonstrate that the resolution function for this four-crystal arrangement is ∼4 µrad. Data are also presented for a 0.1 mm-thick α-quartz wafer pressed into a concave form, having a nominal radius of 500 mm and intended for use as an analyzer. Because analyzers are bent crystals, diffraction occurs in narrow bands. When a multiple exposure is made as a function of rocking angle a striped pattern is obtained, which is commonly referred to as a zebra-stripe pattern. A series of zebra stripes from the 30\overline 3\overline 3 Bragg reflection of the bent wafer over its 25 mm-diameter area were recorded on a CCD. The zebra-stripe pattern was analyzed to show a uniform bending to a radius of 497.0 ± 0.3 mm, in support of the nominal value. An r.m.s. slope error of 7 µrad was also obtained from this analysis.

On evaluating x-ray imaging crystals with synchrotron radiation

Bent crystals used in diagnostics of plasmas combine x-rays diffracted from across the crystal. Therefore imperfections in the resulting 1-D spectrum or 2-D image are not the best way to find out why one particular crystal may differ in its performance from another and what, if anything, to do about it. Instead, here we want to measure the diffraction locally, with the necessary resolution. Nominally monochromatic and unidirectional radiation from the synchrotron's standard x-ray optics proved to be insufficient for the purpose. Here much better radiation comes from the x-ray topography setup at the x-ray optics testing beamline 1-BM at the Advanced Photon Source, thanks to a specially designed quartz conditioning crystal. Some worrisome features in a bent crystal's diffraction have thereby disappeared, while minor fabrication flaws remain highly visible.

Note: Narrow x-ray reflections are easier to locate with sandpaper

Synchrotrons can provide almost perfectly unidirectional and monochromatic x-rays. Such x-rays reflect from ideal crystals only over a minute part of the angular range that must be searched for the reflection. Spoiling the incoming x-rays' directionality with sandpaper makes it easier to find the reflection.

Benchmark Experiment for Photoionized Plasma Emission from Accretion-Powered X-Ray Sources

The interpretation of x-ray spectra emerging from x-ray binaries and active galactic nuclei accreted plasmas relies on complex physical models for radiation generation and transport in photoionized plasmas. These models have not been sufficiently experimentally validated. We have developed a highly reproducible benchmark experiment to study spectrum formation from a photoionized silicon plasma in a regime comparable to astrophysical plasmas. Ionization predictions are higher than inferred from measured absorption spectra. Self-emission measured at adjustable column densities tests radiation transport effects, demonstrating that the resonant Auger destruction assumption used to interpret black hole accretion spectra is inaccurate.

X-ray focusing properties of doubly bent crystals

The focusing properties of several bent crystal geometries, including the newly introduced Pestehe & Askari general point-focusing system [Pestehe & Askari Germi (2012),Opt. Soc. Am. A,29, 68–77; Pestehe & Askari Germi (2012),J. Appl. Cryst.45, 890–901], on an arbitrarily positioned detector plane are investigated and illustrated. The properties of the focal points and the generated images are theoretically related to the local, ℓ, and directional, γ, positions of the detector plane for a given position of a point source on the Rowland circle. A general relation is derived for the detector positioning to obtain a specially focused image. This formula for the polar position of the detector plane, given by the two ℓ and γ variables, enables the exact determination of the system astigmatism and the exact calculation of the sagittal and meridional image positions for the spectrometer under study. The astigmatisms of the above-mentioned bent crystal geometries have been studied, and their sagittal and meridional focal positions and characteristics have been obtained and are illustrated. It is also shown that there is a possibility of designing a spectrometer to focus rays from a linear source onto a point on the Rowland circle.

Systematic search for spherical crystal X-ray microscopes matching 1-25 keV spectral line sources

Spherical-crystal microscopes are used as high-resolution imaging devices for monochromatic x-ray radiography or for imaging the source itself. Crystals and Miller indices (hkl) have to be matched such that the resulting lattice spacing d is close to half the spectral wavelength used for imaging, to fulfill the Bragg equation with a Bragg angle near 90^∘ which reduces astigmatism. Only a few suitable crystal and spectral-line combinations have been identified for applications in the literature, suggesting that x-ray imaging using spherical crystals is constrained to a few chance matches. In this article, after performing a systematic, automated search over more than 9 × 10⁶ possible combinations for x-ray energies between 1 and 25 keV, for six crystals with arbitrary Miller-index combinations hkl between 0 and 20, we show that a matching, efficient crystal and spectral-line pair can be found for almost every He_α or K_α x-ray source for the elements Ne to Sn. Using the data presented here it should be possible to find a suitable imaging combination using an x-ray source that is specifically selected for a particular purpose, instead of relying on the limited number of existing crystal imaging systems that have been identified to date.

Cross-calibration of Fuji TR image plate and RAR 2492 x-ray film to determine the response of a DITABIS Super Micron image plate scanner

Fuji TR image plate is frequently used as a replacement detector medium for x-ray imaging and spectroscopy diagnostics at NIF, Omega, and Z facilities. However, the familiar Fuji BAS line of image plate scanners is no longer supported by the industry, and so a replacement scanning system is needed. While the General Electric Typhoon line of scanners could replace the Fuji systems, the shift away from photo stimulated luminescence units to 16-bit grayscale Tag Image File Format (TIFF) leaves a discontinuity when comparing data collected from both systems. For the purposes of quantitative spectroscopy, a known unit of intensity applied to the grayscale values of the TIFF is needed. The DITABIS Super Micron image plate scanning system was tested and shown to potentially rival the resolution and dynamic range of Kodak RAR 2492 x-ray film. However, the absolute sensitivity of the scanner is unknown. In this work, a methodology to cross calibrate Fuji TR image plate and the absolutely calibrated Kodak RAR 2492 x-ray film is presented. Details of the experimental configurations used are included. An energy dependent scale factor to convert Fuji TR IP scanned on a DITABIS Super Micron scanner from 16-bit grayscale TIFF to intensity units (i.e., photons per square micron) is discussed.

High energy X-ray pinhole imaging at the Z facility

A new high photon energy (hν > 15 keV) time-integrated pinhole camera (TIPC) has been developed as a diagnostic instrument at the Z facility. This camera employs five pinholes in a linear array for recording five images at once onto an image plate detector. Each pinhole may be independently filtered to yield five different spectral responses. The pinhole array is fabricated from a 1-cm thick tungsten block and is available with either straight pinholes or conical pinholes. Each pinhole within the array block is 250 μm in diameter. The five pinholes are splayed with respect to each other such that they point to the same location in space, and hence present the same view of the radiation source at the Z facility. The fielding distance from the radiation source is 66 cm and the nominal image magnification is 0.374. Initial experimental results from TIPC are shown to illustrate the performance of the camera.

Spherical quartz crystals investigated with synchrotron radiation

The quality of x-ray spectra and images obtained from plasmas with spherically bent crystals depends in part on the crystal's x-ray diffraction across the entire crystal surface. We employ the energy selectivity and high intensity of synchrotron radiation to examine typical spherical crystals from alpha-quartz for their diffraction quality, in a perpendicular geometry that is particularly convenient to examine sagittal focusing. The crystal's local diffraction is not ideal: the most noticeable problems come from isolated regions that so far have failed to correlate with visible imperfections. Excluding diffraction from such problem spots has little effect on the focus beyond a decrease in background.

Performance of bent-crystal x-ray microscopes for high energy density physics research

We present calculations for the field of view (FOV), image fluence, image monochromaticity, spectral acceptance, and image aberrations for spherical crystal microscopes, which are used as self-emission imaging or backlighter systems at large-scale high energy density physics facilities. Our analytic results are benchmarked with ray-tracing calculations as well as with experimental measurements from the 6.151 keV backlighter system at Sandia National Laboratories. The analytic expressions can be used for x-ray source positions anywhere between the Rowland circle and object plane. This enables quick optimization of the performance of proposed but untested, bent-crystal microscope systems to find the best compromise between FOV, image fluence, and spatial resolution for a particular application.