A new class of variable-radii diffraction optics for high-resolution x-ray spectroscopy at the National Ignition Facility (invited).

A new class of crystal shapes has been developed for x-ray spectroscopy of point-like or small (a few mm) emission sources. These optics allow for dramatic improvement in both achievable energy resolution and total throughput of the spectrometer as compared with traditional designs. This class of crystal shapes, collectively referred to as the Variable-Radii Spiral (VR-Spiral), utilize crystal shapes in which both the major and minor radii are variable. A crystal using this novel VR-Spiral shape has now been fabricated for high-resolution Extended X-ray Absorption Fine Structure (EXAFS) experiments targeting the Pb-L3 (13.0 keV) absorption edge at the National Ignition Facility. The performance of this crystal has been characterized in the laboratory using a microfocus x-ray source, showing that high-resolution high-throughput EXAFS spectra can be acquired using this geometry. Importantly, these successful tests show that the complex three-dimensional crystal shape is manufacturable with the required precision needed to realize the expected performance of better than 5 eV energy resolution while using a 30 mm high crystal. An improved generalized mathematical form for VR-Spiral shapes is also presented allowing improved optimization as compared to the first sinusoidal-spiral based design. This new formulation allows VR-Spiral spectrometers to be designed at any magnification with optimized energy resolution at all energies within the spectrometer bandwidth.

Spatial calibration and synthetic diagnostic of a multi-energy hard x-ray camera at WEST tokamak.

WEST (tungsten environment in steady-state tokamak) is starting operation for the first time with a water-cooled full tungsten divertor, enabling long pulse operation. Heating is provided by radiofrequency systems, including lower hybrid current drive (LHCD). In this context, a compact multi-energy hard x-ray camera has been installed for energy and space-resolved measurements of the electron temperature, the fast electron tail density produced by LHCD and runaway electrons, and the beam-target emission of tungsten at the target due to fast electron losses interacting with the divertor plates. The diagnostic is a pinhole camera based on a 2D pixel array detector (Pilatus 3 CdTe CMOS Hybrid-Pixel detector produced by DECTRIS). The novelty of this diagnostic technique is the detector's capability of adjusting the threshold energy at pixel level. This innovation provides great flexibility in the energy configuration, allowing simultaneous space and energy-resolved x-ray measurements. This contribution details two important steps in the preparation of the diagnostic operation. First, the in-vessel spatial calibration that was carried out with a radioactive source. Second, the synthetic diagnostic is obtained by the suite of codes ALOHA/C3PO/LUKE/R5-X2, which simulates LH wave propagation and absorption, as well as the fast electron bremsstrahlung production.

Absolute calibration of the conical crystal configuration of the zinc spectrometer (ZSPEC) at the OMEGA laser facility.

In this study, we present the absolute calibration of the conical crystal for the zinc spectrometer (ZSPEC), an x-ray spectrometer at the OMEGA laser facility at the Laboratory for Laser Energetics. The ZSPEC was originally designed to measure x-ray Thomson scattering using flat or cylindrically curved highly oriented pyrolytic graphite crystals centered around Zn He-alpha emission at 9 keV. To improve the useful spectral range and collection efficiency of the ZSPEC, a conical highly annealed pyrolytic graphite crystal was fabricated for the ZSPEC. The conically bent crystal in the Hall geometry produces a line focus perpendicular to the spectrometer axis, corresponding to the detector plane of electronic detectors at large scale laser facilities such as OMEGA, extending the useful range of the spectrometer to 7-11 keV. Using data collected using a microfocus Mo x-ray source, we determine important characteristics of ZSPEC such as the dispersion, spatial resolution, and absolute sensitivity of the instrument. A ray-trace model of ZSPEC provides another point of agreement in calculations of the ZSPEC dispersion and crystal response.

Hot Spot Evolution Measured by High-Resolution X-Ray Spectroscopy at the National Ignition Facility.

Evolution of the hot spot plasma conditions was measured using high-resolution x-ray spectroscopy at the National Ignition Facility. The capsules were filled with DD gas with trace levels of Kr and had either a high-density-carbon (HDC) ablator or a tungsten (W)-doped HDC ablator. Time-resolved measurement of the Kr Heß spectra, absolutely calibrated by a simultaneous time-integrated measurement, allows inference of the electron density and temperature through observing Stark broadening and the relative intensities of dielectronic satellites. By matching the calculated hot spot emission using a collisional-radiative code to experimental observations, the hot spot size and areal density are determined. These advanced spectroscopy techniques further reveal the effect of W dopant in the ablator on the hot spot parameters for their improved implosion performance.

Impact of Magnetic Field Configuration on Heat Transport in Stellarators and Heliotrons.

We assess the magnetic field configuration in modern fusion devices by comparing experiments with the same heating power, between a stellarator and a heliotron. The key role of turbulence is evident in the optimized stellarator, while neoclassical processes largely determine the transport in the heliotron device. Gyrokinetic simulations elucidate the underlying mechanisms promoting stronger ion scale turbulence in the stellarator. Similar plasma performances in these experiments suggests that neoclassical and turbulent transport should both be optimized in next step reactor designs.

Design and expected performance of a variable-radii sinusoidal spiral x-ray spectrometer for the National Ignition Facility.

A novel high-resolution x-ray spectrometer for point-like emission sources has been developed using a crystal shape having both a variable major and a variable minor radius of curvature. This variable-radii sinusoidal spiral spectrometer (VR-Spiral) allows three common spectrometer design goals to be achieved simultaneously: 1. reduction of aberrations and improved spectral (energy) resolution, 2. reduction of source size broadening, and 3. use of large crystals to improve total throughput. The VR-Spiral concept and its application to practical spectrometer design are described in detail. This concept is then used to design a spectrometer for an extreme extended x-ray absorption fine structure experiment at the National Ignition Facility looking at the Pb L3 absorption edge at 13.0352 keV. The expected performance of this VR-Spiral spectrometer, both in terms of energy resolution and spatial resolution, is evaluated through the use of a newly developed raytracing tool, xicsrt. Finally, the expected performance of the VR-Spiral concept is compared to that of spectrometers based on conventional toroidal and variable-radii toroidal crystal geometries showing a greatly improved energy resolution.

Multi-energy reconstructions, central electron temperature measurements, and early detection of the birth and growth of runaway electrons using a versatile soft x-ray pinhole camera at MST.

A multi-energy soft x-ray pinhole camera has been designed, built, and deployed at the Madison Symmetric Torus to aid the study of particle and thermal transport, as well as MHD stability physics. This novel imaging diagnostic technique employs a pixelated x-ray detector in which the lower energy threshold for photon detection can be adjusted independently on each pixel. The detector of choice is a PILATUS3 100 K with a 450 µm thick silicon sensor and nearly 100 000 pixels sensitive to photon energies between 1.6 and 30 keV. An ensemble of cubic spline smoothing functions has been applied to the line-integrated data for each time-frame and energy-range, obtaining a reduced standard-deviation when compared to that dominated by photon-noise. The multi-energy local emissivity profiles are obtained from a 1D matrix-based Abel-inversion procedure. Central values of Te can be obtained by modeling the slope of the continuum radiation from ratios of the inverted radial emissivity profiles over multiple energy ranges with no a priori assumptions of plasma profiles, magnetic field reconstruction constraints, high-density limitations, or need of shot-to-shot reproducibility. In tokamak plasmas, a novel application has recently been tested for early detection, 1D imaging, and study of the birth, exponential growth, and saturation of runaway electrons at energies comparable to 100 × Te,0; thus, early results are also presented.

Demonstration of reduced neoclassical energy transport in Wendelstein 7-X.

Research on magnetic confinement of high-temperature plasmas has the ultimate goal of harnessing nuclear fusion for the production of electricity. Although the tokamak1 is the leading toroidal magnetic-confinement concept, it is not without shortcomings and the fusion community has therefore also pursued alternative concepts such as the stellarator. Unlike axisymmetric tokamaks, stellarators possess a three-dimensional (3D) magnetic field geometry. The availability of this additional dimension opens up an extensive configuration space for computational optimization of both the field geometry itself and the current-carrying coils that produce it. Such an optimization was undertaken in designing Wendelstein 7-X (W7-X)2, a large helical-axis advanced stellarator (HELIAS), which began operation in 2015 at Greifswald, Germany. A major drawback of 3D magnetic field geometry, however, is that it introduces a strong temperature dependence into the stellarator's non-turbulent 'neoclassical' energy transport. Indeed, such energy losses will become prohibitive in high-temperature reactor plasmas unless a strong reduction of the geometrical factor associated with this transport can be achieved; such a reduction was therefore a principal goal of the design of W7-X. In spite of the modest heating power currently available, W7-X has already been able to achieve high-temperature plasma conditions during its 2017 and 2018 experimental campaigns, producing record values of the fusion triple product for such stellarator plasmas3,4. The triple product of plasma density, ion temperature and energy confinement time is used in fusion research as a figure of merit, as it must attain a certain threshold value before net-energy-producing operation of a reactor becomes possible1,5. Here we demonstrate that such record values provide evidence for reduced neoclassical energy transport in W7-X, as the plasma profiles that produced these results could not have been obtained in stellarators lacking a comparably high level of neoclassical optimization.

A new class of focusing crystal shapes for Bragg spectroscopy of small, point-like, x-ray sources in laser produced plasmas.

This paper describes a new class of focusing crystal forms for the x-ray Bragg crystal spectroscopy of small, point-like, x-ray sources. These new crystal forms are designed with the aid of sinusoidal spirals, a family of curves, whose shapes are defined by only one parameter, which can assume any real value. The potential of the sinusoidal spirals for the design x-ray crystal spectrometers is demonstrated with the design of a toroidally bent crystal of varying major and minor radii for measurements of the extended x-ray absorption fine structure near the Ta-L3 absorption edge at the National Ignition Facility.

Correction and verification of x-ray imaging crystal spectrometer analysis on Wendelstein 7-X through x-ray ray tracing.

X-ray ray tracing is used to develop ion-temperature corrections for the analysis of the X-ray Imaging Crystal Spectrometer (XICS) used at Wendelstein 7-X (W7-X) and perform verification on the analysis methods. The XICS is a powerful diagnostic able to measure ion-temperature, electron-temperature, plasma flow, and impurity charge state densities. While these systems are relatively simple in design, accurate characterization of the instrumental response and validation of analysis techniques are difficult to perform experimentally due to the requirement of extended x-ray sources. For this reason, a ray tracing model has been developed that allows characterization of the spectrometer and verification of the analysis methods while fully considering the real geometry of the XICS system and W7-X plasma. Through the use of ray tracing, several important corrections have been found that must be accounted for in order to accurately reconstruct the ion-temperature profiles. The sources of these corrections are described along with their effect on the analyzed profiles. The implemented corrections stem from three effects: (1) effect of sub-pixel intensity distribution during de-curving and spatial binning, (2) effect of sub-pixel intensity distribution during forward model evaluation and generation of residuals, and (3) effect of defocus and spherical aberrations on the instrumental response. Possible improvements to the forward model and analysis procedures are explored, along with a discussion of trade-offs in terms of computational complexity. Finally, the accuracy of the tomographic inversion technique in stellarator geometry is investigated, providing for the first time a verification exercise for inversion accuracy in stellarator geometry and a complete XICS analysis tool-chain.

Calibration of a versatile multi-energy soft x-ray diagnostic for WEST long pulse plasmas.

A compact multi-energy soft x-ray diagnostic is being installed on the W Environment in Steady-state Tokamak (WEST), which was designed and built to test ITER-like tungsten plasma facing components in a long pulse (∼1000 s) scenario. The diagnostic consists of a pinhole camera fielded with the PILATUS3 photon-counting Si-based detector (≲100 kpixel). The detector has sensitivity in the range 1.6-30 keV and enables energy discrimination, providing a higher energy resolution than conventional systems with metal foils and diodes with adequate space and time resolution (≲1 cm and 2 ms). The lower-absorption cut-off energy is set independently on each one of the ∼100 kpixels, providing a unique opportunity to measure simultaneously the plasma emissivity in multiple energy ranges and deduce a variety of plasma parameters (e.g., Te, nZ, and ΔZeff). The energy dependence of each pixel is calibrated here over the range 3-22 keV. The detector is exposed to a variety of monochromatic sources-fluorescence emission from metallic targets-and for each pixel, the lower energy threshold is scanned to calibrate the energy dependence. The data are fit to a responsivity curve ("S-curve") that determines the mapping between the possible detector settings and the energy response for each pixel. Here, the calibration is performed for three energy ranges: low (2.3-6 keV), medium (4.5-13.5 keV), and high (5.4-21 keV). We determine the achievable energy resolutions for the low, medium, and high energy ranges as 330 eV, 640 eV, and 950 eV, respectively. The main limitation for the energy resolution is found to be the finite width of the S-curve.

Multi-energy calibration of a PILATUS3 CdTe detector for hard x-ray measurements of magnetically confined fusion plasmas.

A multi-energy hard x-ray pin-hole camera based on the PILATUS3 X 100K-M CdTe detector has been developed at the Princeton Plasma Physics Laboratory for installation on the Tungsten Environment in Steady State Tokamak. This camera will be employed to study thermal plasma features such as electron temperature as well as non-thermal effects such as fast electron tails produced by a lower hybrid radiofrequency current drive and the birth of runaway electrons. The innovative aspect of the system lies in the possibility of setting the threshold energy independently for each of the ∼100k pixels of the detector. This feature allows for the measurement of the x-ray emission in multiple energy ranges with adequate space and time resolution (∼1 cm, 2 ms) and coarse energy resolution. In this work, the energy dependence of each pixel was calibrated within the range 15 keV-100 keV using a tungsten x-ray tube and emission from a variety of fluorescence targets (from yttrium to uranium). The data corresponding to pairs of Kα emission lines are fit to the characteristic responsivity ("S-curve"), which describes the detector sensitivity across the 64 possible energy threshold values for each pixel; this novel capability is explored by fine-tuning the voltage of a six-bit digital-analog converter after the charge-sensitive amplifier for each of the ∼100k pixels. This work presents the results of the calibration including a statistical analysis. It was found that the achievable energy resolution is mainly limited by the width of the S-curve to 3 keV-10 keV for threshold energies up to 50 keV, and to ≥20 keV for energies above 60 keV.

Charge exchange recombination spectroscopy at Wendelstein 7-X.

The Charge Exchange Recombination Spectroscopy (CXRS) diagnostic has become a routine diagnostic on almost all major high temperature fusion experimental devices. For the optimized stellarator Wendelstein 7-X (W7-X), a highly flexible and extensive CXRS diagnostic has been built to provide high-resolution local measurements of several important plasma parameters using the recently commissioned neutral beam heating. This paper outlines the design specifics of the W7-X CXRS system and gives examples of the initial results obtained, including typical ion temperature profiles for several common heating scenarios, toroidal flow and radial electric field derived from velocity measurements, beam attenuation via beam emission spectra, and normalized impurity density profiles under some typical plasma conditions.

First Observation of a Stable Highly Dissipative Divertor Plasma Regime on the Wendelstein 7-X Stellarator.

For the first time, the optimized stellarator Wendelstein 7-X has operated with an island divertor. An operation regime in hydrogen was found in which the total plasma radiation approached the absorbed heating power without noticeable loss of stored energy. The divertor thermography recorded simultaneously a strong reduction of the heat load on all divertor targets, indicating almost complete power detachment. This operation regime was stably sustained over several energy confinement times until the preprogrammed end of the discharge. The plasma radiation is mainly due to oxygen and is located at the plasma edge. This plasma scenario is reproducible and robust at various heating powers, plasma densities, and gas fueling locations. These experimental results show that the island divertor concept actually works and displays good power dissipation potential, producing a promising exhaust concept for the stellarator reactor line.

Inference of temperature and density profiles via forward modeling of an x-ray imaging crystal spectrometer within the Minerva Bayesian analysis framework.

At the Wendelstein 7-X stellarator, the X-ray imaging crystal spectrometer provides line integrated measurements of ion and electron temperatures, plasma flows, as well as impurity densities from a spectroscopic analysis of tracer impurity radiation. In order to infer the actual profiles from line integrated data, a forward modeling approach has been developed within the Minerva Bayesian analysis framework. In this framework, the inversion is realized on the basis of a complete forward model of the diagnostic, including error propagation and utilizing Gaussian processes for generation and inference of arbitrary shaped plasma parameter profiles. For modeling of line integrated data as measured by the detector, the installation geometry of the spectrometer, imaging properties of the crystal, and Gaussian detection noise are considered. The inversion of line integrated data is achieved using the maximum posterior method for plasma parameter profile inference and a Markov chain Monte Carlo sampling of the posterior distribution for calculating uncertainties of the inference process. The inversion method shows a correct and reliable inference of temperature and impurity density profiles from synthesized data within the estimated uncertainties along the whole plasma radius. The application to measured data yields a good match of derived electron temperature profiles to data of the Thomson scattering diagnostic for central electron temperatures between 2 and 5 keV using argon impurities.

Stellarators Resist Turbulent Transport on the Electron Larmor Scale.

Electron temperature gradient (ETG)-driven turbulence, despite its ultrafine scale, is thought to drive significant thermal losses in magnetic fusion devices-but what role does it play in stellarators? The first numerical simulations of ETG turbulence for the Wendelstein 7-X stellarator, together with power balance analysis from its initial experimental operation phase, suggest that the associated transport should be negligible compared to other channels. The effect, we argue, originates essentially from the geometric constraint of multiple field periods, a generic feature of stellarators.

Design of tangential x-ray crystal spectrometer for Aditya-U tokamak.

A tangential soft x-ray crystal spectrometer has been designed to measure the x-ray spectrum of He-like argon for the Aditya-U tokamak plasma. The system enables to measure electron temperature using the intensity ratio of the resonance line to the satellite line. For this purpose, an x-ray spectral line at 3.9494 Å from He-like argon, Ar16+, is considered. The spectrometer consists of a cylindrically bent silicon (111) crystal and a CCD detector to measure the resonance spectral line and its satellite lines in the wavelength region of 3.94-4.0 Å, viewing the plasma tangentially at an angle of 26° with respect to the toroidal direction in the magnetic axis. Considering Aditya-U tokamak plasma parameters and its geometrical constraints, plasma to crystal and crystal to detector distances have been kept at 1.47 m and 0.5 m, respectively, to detect a sufficient signal. The engineering design has been optimized after adequately addressing the issues related to port geometry and machine accessibility. Details on the design of the crystal spectrometer are presented in this paper.

Plasma impurities observed by a pulse height analysis diagnostic during the divertor campaign of the Wendelstein 7-X stellarator.

The paper reports on the optimization process of the soft X-ray pulse height analyzer installed on the Wendelstein 7-X (W7-X) stellarator. It is a 3-channel system that records X-ray spectra in the range from 0.6 to 19.6 keV. X-ray spectra, with a temporal and spatial resolution of 100 ms and 2.5 cm (depending on selected slit sizes), respectively, are line integrated along a line-of-sight that crosses near to the plasma center. In the second W7-X operation phase with a carbon test divertor unit, light impurities, e.g., carbon and oxygen, were observed as well as mid- to high-Z elements, e.g., sulfur, chlorine, chromium, manganese, iron, and nickel. In addition, X-ray lines from several tracer elements have been observed after the laser blow-off injection of different impurities, e.g., silicon, titanium, and iron, and during discharges with prefill or a gas puff of neon or argon. These measurements were achieved by optimizing light absorber-foil selection, which defines the detected energy range, and remotely controlled pinhole size, which defines photon flux. The identification of X-ray lines was confirmed by other spectroscopic diagnostics, e.g., by the High-Efficiency XUV Overview Spectrometer, HEXOS, and high-resolution X-ray imaging spectrometer, HR-XIS.

A new toroidal x-ray crystal spectrometer for the diagnosis of high energy density plasmas at the National Ignition Facility.

The here-described spectrometer was developed for the extended x-ray absorption fine structure spectroscopy of high-density plasmas at the National Ignition Facility. It employs as the Bragg reflecting element a new type of toroidally bent crystal with a constant and very large major radius R and a much smaller, locally varying, minor radius r. The focusing properties of this crystal and the experimental arrangement of the source and detector make it possible to (a) fulfill the conditions for a perfect imaging of an ideal point source for each wavelength, (b) obtain a high photon throughput, (c) obtain a high spectral resolution by eliminating the effects of source-size broadening, and (d) obtain a one-dimensional spatial resolution with a high magnification perpendicular to the main dispersion plane.