Quantifying electron temperature distributions from time-integrated x-ray emission spectra.

K-shell x-ray emission spectroscopy is a standard tool used to diagnose the plasma conditions created in high-energy-density physics experiments. In the simplest approach, the emissivity-weighted average temperature of the plasma can be extracted by fitting an emission spectrum to a single temperature condition. It is known, however, that a range of plasma conditions can contribute to the measured spectra due to a combination of the evolution of the sample and spatial gradients. In this work, we define a parameterized model of the temperature distribution and use Markov Chain Monte Carlo sampling of the input parameters, yielding uncertainties in the fit parameters to assess the uniqueness of the inferred temperature distribution. We present the analysis of time-integrated S and Fe x-ray spectroscopic data from the Orion laser facility and demonstrate that while fitting each spectral region to a single temperature yields two different temperatures, both spectra can be fit simultaneously with a single temperature distribution. We find that fitting both spectral regions together requires a maximum temperature of 1310-70 +90 eV with significant contributions from temperatures down to 200 eV.

A new benchmark of soft X-ray transition energies of Ne , CO 2 , and SF 6 : paving a pathway towards ppm accuracy.

Abstract: A key requirement for the correct interpretation of high-resolution X-ray spectra is that transition energies are known with high accuracy and precision. We investigate the K-shell features of Ne , CO 2 , and SF 6 gases, by measuring their photo ion-yield spectra at the BESSY II synchrotron facility simultaneously with the 1s-np fluorescence emission of He-like ions produced in the Polar-X EBIT. Accurate ab initio calculations of transitions in these ions provide the basis of the calibration. While the CO 2 result agrees well with previous measurements, the SF 6 spectrum appears shifted by ∼ 0.5 eV, about twice the uncertainty of the earlier results. Our result for Ne shows a large departure from earlier results, but may suffer from larger systematic effects than our other measurements. The molecular spectra agree well with our results of time-dependent density functional theory. We find that the statistical uncertainty allows calibrations in the desired range of 1-10 meV, however, systematic contributions still limit the uncertainty to ∼ 40-100 meV, mainly due to the temporal stability of the monochromator energy scale. Combining our absolute calibration technique with a relative energy calibration technique such as photoelectron energy spectroscopy will be necessary to realize its full potential of achieving uncertainties as low as 1-10 meV.

Microcalorimeter measurement of x-ray spectra from a high-temperature magnetically confined plasma.

A NASA-built x-ray microcalorimeter spectrometer has been installed on the MST facility at the Wisconsin Plasma Physics Laboratory and has recorded x-ray photons emitted by impurity ions of aluminum in a majority deuterium plasma. Much of the x-ray microcalorimeter development has been driven by the needs of astrophysics missions, where imaging arrays with few-eV spectral resolution are required. The goal of our project is to adapt these single-photon-counting microcalorimeters for magnetic fusion energy research and demonstrate the value of such measurements for fusion science. Microcalorimeter spectrometers combine the best characteristics of the x-ray instrumentation currently available on fusion devices: high spectral resolution similar to an x-ray crystal spectrometer and the broadband coverage of an x-ray pulse height analysis system. Fusion experiments are increasingly employing high-Z plasma-facing components and require measurement of the concentration of all impurity ion species in the plasma. This diagnostic has the capability to satisfy this need for multi-species impurity ion data and will also contribute to measurements of impurity ion temperature and flow velocity, Zeff, and electron density. Here, we introduce x-ray microcalorimeter detectors and discuss the diagnostic capability for magnetic fusion energy experiments. We describe our experimental setup and spectrometer operation approach at MST, and we present the results from an initial measurement campaign.

Recent enhancements in the performance of the Orion high-resolution x-ray spectrometers.

During the past few years, the Orion high-resolution x-ray spectrometers have been successful tools for measuring x-ray spectra from plasmas generated in the Orion laser facility. Duplicate spectrometers also operate successfully at the Livermore EBIT-I and SuperEBIT electron beam ion traps for measuring x-ray polarization. We have recently implemented very high-quality, optically bonded, spherically bent quartz crystals to remove the structure in the x-ray image that had been observed in earlier measurements. The structure had been caused by focusing defects and limited the accuracy of our measurements. We present before and after images that show a drastic improvement. We, furthermore, have implemented a spherically bent potassium acid phthalate (KAP) crystal on one of our spectrometers. The KAP crystal was prepared in a similar fashion, and we present measurements of the N Ly-ß and Ne Lyß lines taken in first- and second-order reflections at 600 and 1200 eV, respectively. These measurements confirm that KAP crystals can be produced at a quality suitable for extending the spectral coverage to wavelengths longer than those accessible by different quartz crystals, especially those that cover the astrophysically important lines of iron.

Absolute throughput calibration of multiple spherical crystals for the Orion High-REsolution X-ray spectrometer (OHREX).

We present absolute throughput analysis of several crystals for the Orion High-REsolution X-ray (OHREX) imaging crystal spectrometer using ray tracing and experimental measurements. The OHREX spectrometer is a high-resolution x-ray spectrometer designed to measure spectral line shapes at the Orion laser facility. The spectrometer is fielded with up to two spherical crystals simultaneously covering two independent spectral ranges. Each crystal has a nominal radius of curvature of R = 67.2 cm and is fielded at a nominal Bragg angle of 51.3°. To cover different bands of interest, several different crystals are available, including Ge (111), KAP, and several cuts of quartz, whose resolving power λ/Δλ exceeds 10 000. The calibrated response of the available crystals has previously been reported from measurements at the EBIT-I electron beam ion trap at Lawrence Livermore National Laboratory. Here, we model the absolute throughput of each crystal using ray tracing and verify the results using experimental data for the quartz (101¯1) crystal.

High-Precision Determination of Oxygen K_{α} Transition Energy Excludes Incongruent Motion of Interstellar Oxygen.

We demonstrate a widely applicable technique to absolutely calibrate the energy scale of x-ray spectra with experimentally well-known and accurately calculable transitions of highly charged ions, allowing us to measure the K-shell Rydberg spectrum of molecular O_{2} with 8 meV uncertainty. We reveal a systematic ∼450 meV shift from previous literature values, and settle an extraordinary discrepancy between astrophysical and laboratory measurements of neutral atomic oxygen, the latter being calibrated against the aforementioned O_{2} literature values. Because of the widespread use of such, now deprecated, references, our method impacts on many branches of x-ray absorption spectroscopy. Moreover, it potentially reduces absolute uncertainties there to below the meV level.

High resolution, high signal-to-noise crystal spectrometer for measurements of line shifts in high-density plasmas.

The Orion high-resolution x-ray (OHREX) spectrometer has been a successful tool for measuring the shapes of density-broadened spectral lines produced in short-pulse heated plasmas at the Orion laser facility. We have recently outfitted the instrument with a charge-couple device (CCD) camera, which greatly increased the accuracy with which we can perform line-shift measurements. Because OHREX is located on the outside of the Orion target chamber, no provisions for the shielding of electromagnetic pulses are required. With the CCD, we obtained a higher signal-to-noise ratio than we previously obtained with an image-plate detector. This allowed us to observe structure in the image produced by the diffraction from the two OHREX crystals, which was highly reproducible from shot to shot. This structure will ultimately limit the accuracy of our spectroscopic measurements.

Measurements of the effective electron density in an electron beam ion trap using extreme ultraviolet spectra and optical imaging.

In an electron beam ion trap (EBIT), the ions are not confined to the electron beam, but rather oscillate in and out of the beam. As a result, the ions do not continuously experience the full density of the electron beam. To determine the effective electron density, n e,eff, experienced by the ions, the electron beam size, the nominal electron density n e, and the ion distribution around the beam, i.e., the so-called ion cloud, must be measured. We use imaging techniques in the extreme ultraviolet (EUV) and optical to determine these. The electron beam width is measured using 3d → 3p emission from Fe xii and xiii between 185 and 205 Å. These transitions are fast and the EUV emission occurs only within the electron beam. The measured spatial emission profile and variable electron current yield a nominal electron density range of n e ∼ 1011-1013 cm-3. We determine the size of the ion cloud using optical emission from metastable levels of ions with radiative lifetimes longer than the ion orbital periods. The resulting emission maps out the spatial distribution of the ion cloud. We find a typical electron beam radius of ∼60 µm and an ion cloud radius of ∼300 µm. These yield a spatially averaged effective electron density, n e,eff, experienced by the ions in EBIT spanning ∼ 5 × 109-5 × 1011 cm-3.

The Warm Electron Beam Ion Trap (WEBIT): An instrument for ground calibration of space-borne x-ray spectrometers.

The warm electron beam ion trap (WEBIT) at Lawrence Livermore National Laboratory is being developed as a pre-launch, ground calibration source for space-borne, high-throughput, high-resolution x-ray spectrometers, such as the x-ray imaging and spectroscopy mission Resolve quantum calorimeter. Historically, calibration sources for calorimeter spectrometers have relied on characteristic line emission from x-ray tubes, fluorescing metals, and radioactive sources. The WEBIT, by contrast, relies on emission from x-ray transitions in highly charged ions, for example, hydrogen-like and helium-like ions, whose energies are well known and whose line shapes are relatively simple. The WEBIT can create astrophysically relevant ions whose x-ray emission falls in the 0.3-12 keV science bandpass of Resolve and has a portable design advantageous for a calibration source. The WEBIT will be used to help calibrate Resolve's instrumental line shape and gain scale as a function of various operational parameters during both detector subsystem level testing and instrumental level testing.

Experimental comparison of spherically bent HAPG and Ge crystals.

The Orion high-resolution X-ray (OHREX) imaging spherically bent crystal spectrometer, operated with both image plates and CCD cameras, provides time-averaged plasma diagnostics through high-resolution spectroscopy with good signal-to-noise at the Orion laser facility. In order to provide time-resolved spectra, the OHREX will be outfitted with a streak camera, and in this case, even higher signal to noise will be desired. Using the OHREX's sister instrument, the EBIT High-resolution X-ray (EBHiX) spectrometer, at the LLNL electron beam ion trap EBIT-I, we therefore compare the efficiency of a high-quality Ge (111) crystal (2d = 6.532 Å) with that of a higher integrated reflectivity, but lower-resolution highly annealed pyrolytic graphite (HAPG) crystal (2d = 6.708 Å) in the energy range 2408-2452 eV. We find that the HAPG provides overall more signal across the entire image; however, because of the much better focusing properties of the Ge crystal, the latter provides more signal within the central 100 µm of the spatial profile in the cross-dispersion direction and is thus more suitable for the narrow entrance window of the Livermore-built streak camera.

Calibration of the OHREX high-resolution imaging crystal spectrometer at the Livermore electron beam ion traps.

We report the calibration of the Orion High-Resolution X-ray (OHREX) imaging crystal spectrometer at the EBIT-I electron beam ion trap at Livermore. Two such instruments, dubbed OHREX-1 and OHREX-2, are fielded for plasma diagnostics at the Orion laser facility in the United Kingdom. The OHREX spectrometer can simultaneously house two spherically bent crystals with a radius of curvature of r = 67.2 cm. The focusing properties of the spectrometer allow both for larger distance to the source due to the increase in collected light and for observation of extended sources. OHREX is designed to cover a 2.5°-3° spectral range at Bragg angles around 51.3°. The typically high resolving powers at these large Bragg angles are ideally suited for line shape diagnostics. For instance, the nominal resolving power of the instrument (>10 000) is much higher than the effective resolving power associated with the Doppler broadening due to the temperature of the trapped ions in EBIT-I. The effective resolving power is only around 3000 at typical EBIT-I conditions, which nevertheless is sufficient to set up and test the instrument's spectral characteristics. We have calibrated the spectral range for a number of crystals using well known reference lines in the first and second order and derived the ion temperatures from these lines. We have also made use of the 50 µm size of the EBIT-I source width to characterize the spatial focusing of the spectrometer.

Characterization of an atomic hydrogen source for charge exchange experiments.

We characterized the dissociation fraction of a thermal dissociation atomic hydrogen source by injecting the mixed atomic and molecular output of the source into an electron beam ion trap containing highly charged ions and recording the x-ray spectrum generated by charge exchange using a high-resolution x-ray calorimeter spectrometer. We exploit the fact that the charge exchange state-selective capture cross sections are very different for atomic and molecular hydrogen incident on the same ions, enabling a clear spectroscopic diagnostic of the neutral species.

L-shell spectroscopic diagnostics of radiation from krypton HED plasma sources.

X-ray spectroscopy is a useful tool for diagnosing plasma sources due to its non-invasive nature. One such source is the dense plasma focus (DPF). Recent interest has developed to demonstrate its potential application as a soft x-ray source. We present the first spectroscopic studies of krypton high energy density plasmas produced on a 3 kJ DPF device in Singapore. In order to diagnose spectral features, and to obtain a more comprehensive understanding of plasma parameters, a new non-local thermodynamic equilibrium L-shell kinetic model for krypton was developed. It has the capability of incorporating hot electrons, with different electron distribution functions, in order to examine the effects that they have on emission spectra. To further substantiate the validity of this model, it is also benchmarked with data gathered from experiments on the electron beam ion trap (EBIT) at Lawrence Livermore National Laboratory, where data were collected using the high resolution EBIT calorimeter spectrometer.

Imaging crystal spectrometer for high-resolution x-ray measurements on electron beam ion traps and tokamaks.

We describe a crystal spectrometer implemented on the Livermore electron beam ion traps that employ two spherically bent quartz crystals and a cryogenically cooled back-illuminated charge-coupled device detector to measure x rays with a nominal resolving power of λ/Δλ ≥ 10 000. Its focusing properties allow us to record x rays either with the plane of dispersion perpendicular or parallel to the electron beam and, thus, to preferentially select one of the two linear x-ray polarization components. Moreover, by choice of dispersion plane and focussing conditions, we use the instrument either to image the distribution of the ions within the 2 cm long trap region, or to concentrate x rays of a given energy to a point on the detector, which optimizes the signal-to-noise ratio. We demonstrate the operation and utility of the new instrument by presenting spectra of Mo34+, which prepares the instrument for use as a core impurity diagnostic on the NSTX-U spherical torus and other magnetic fusion devices that employ molybdenum as plasma facing components.

Experimentally determining the relative efficiency of spherically bent germanium and quartz crystals.

We have used the EBIT-I electron beam ion trap at the Lawrence Livermore National Laboratory and a duplicate Orion High Resolution X-ray Spectrometer (OHREX) to measure the relative efficiency of a spherically bent quartz (101̄1) crystal (2d = 6.687 Å) and a spherically bent germanium (111) crystal (2d = 6.532 Å). L-shell X-ray photons from highly charged molybdenum ions generated in EBIT-I were simultaneously focussed and Bragg reflected by each crystal, both housed in a single spectrometer, onto a single CCD X-ray detector. The flux from each crystal was then directly compared. Our results show that the germanium crystal has a reflection efficiency significantly better than the quartz crystal, however, the energy resolution is significantly worse. Moreover, we find that the spatial focussing properties of the germanium crystal are worse than those of the quartz crystal. Details of the experiment are presented, and we discuss the advantages of using either crystal on a streak-camera equipped OHREX spectrometer.

Calibration of the microcalorimeter spectrometer on-board the Hitomi (Astro-H) observatory (invited).

The Hitomi Soft X-ray Spectrometer (SXS) was a pioneering non-dispersive imaging x-ray spectrometer with 5 eV FWHM energy resolution, consisting of an array of 36 silicon-thermistor microcalorimeters at the focus of a high-throughput soft x-ray telescope. The instrument enabled astrophysical plasma diagnostics in the 0.3-12 keV band. We introduce the SXS calibration strategy and corresponding ground calibration measurements that took place from 2012-2015, including both the characterization of the microcalorimeter array and measurements of the x-ray transmission of optical blocking filters.

Lineshape spectroscopy with a very high resolution, very high signal-to-noise crystal spectrometer.

We have developed a high-resolution x-ray spectrometer for measuring the shapes of spectral lines produced from laser-irradiated targets on the Orion laser facility. The instrument utilizes a spherically bent crystal geometry to spatially focus and spectrally analyze photons from foil or microdot targets. The high photon collection efficiency resulting from its imaging properties allows the instrument to be mounted outside the Orion chamber, where it is far less sensitive to particles, hard x-rays, or electromagnetic pulses than instruments housed close to the target chamber center in ten-inch manipulators. Moreover, Bragg angles above 50° are possible, which provide greatly improved spectral resolution compared to radially viewing, near grazing-incidence crystal spectrometers. These properties make the new instrument an ideal lineshape diagnostic for determining plasma temperature and density. We describe its calibration on the Livermore electron beam ion trap facility and present spectral data of the K-shell emission from highly charged sulfur produced by long-pulse as well as short-pulse beams on the Orion laser in the United Kingdom.

Use of a priori spectral information in the measurement of x-ray flux with filtered diode arrays.

Filtered x-ray diode (XRD) arrays are often used to measure x-ray spectra vs. time from spectrally continuous x-ray sources such as hohlraums. A priori models of the incident x-ray spectrum enable a more accurate unfolding of the x-ray flux as compared to the standard technique of modifying a thermal Planckian with spectral peaks or dips at the response energy of each filtered XRD channel. A model x-ray spectrum consisting of a thermal Planckian, a Gaussian at higher energy, and (in some cases) a high energy background provides an excellent fit to XRD-array measurements of x-ray emission from laser heated hohlraums. If high-resolution measurements of part of the x-ray emission spectrum are available, that information can be included in the a priori model. In cases where the x-ray emission spectrum is not Planckian, candidate x-ray spectra can be allowed or excluded by fitting them to measured XRD voltages. Examples are presented from the filtered XRD arrays, named Dante, at the National Ignition Facility and the Laboratory for Laser Energetics.

Development of a ten inch manipulators-based, flexible, broadband two-crystal spectrometer.

We have developed and implemented a broadband X-ray spectrometer with a variable energy range for use at the Atomic Weapons Establishment's Orion Laser. The spectrometer covers an energy bandwidth of ∼1-2 keV using two independently mounted, movable Bragg diffraction crystals. Using combinations of cesium hydrogen pthlate, ammonium dihydrogen phosphate, and pentaerythritol crystals, spectra covering the 1.4-2.5, 1.85-3.15, or 3.55-5.1 keV energy bands have been measured. Image plate is used for detection owing to its high dynamic range. Background signals caused by high energy X-rays and particles commonly produced in high energy laser experiments are reduced by a series of tantalum baffles and filters installed between the source and crystal and also between the crystals and detector.

System for calibrating the energy-dependent response of an elliptical Bragg-crystal spectrometer.

A multipurpose spectrometer (MSPEC) with elliptical crystals is in routine use to obtain x-ray spectra from laser produced plasmas in the energy range 1.0-9.0 keV. Knowledge of the energy-dependent response of the spectrometer is required for an accurate comparison of the intensities of x-ray lines of different energy. The energy-dependent response of the MSPEC has now been derived from the spectrometer geometry and calibration information on the response of its components, including two different types of detectors. Measurements of the spectrometer response with a laboratory x-ray source are used to test the calculated response and provide information on crystal reflectivity and uniformity.