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.

Robust analysis of space-, time-, and energy-resolved soft x-ray measurements of magnetically confined fusion plasmas (invited).

A novel compact multi-energy soft x-ray (ME-SXR) diagnostic based on the PILATUS3 100K x-ray detector has been developed in collaboration between the Princeton Plasma Physics Laboratory and the University of Wisconsin-Madison and tested on the Madison Symmetric Torus (MST) reversed-field pinch. This solid-state photon-counting detector consists of a two-dimensional array of ∼100 000 pixels for which the lower photon absorption cutoff energy can be independently set, allowing it to be configured for a unique combination of simultaneous spatial, spectral, and temporal resolution of ∼1 cm, 100 eV, and 500 Hz, respectively. The diagnostic is highly versatile and can be readily adapted to diverse plasma operating conditions and scientific needs without any required downtime. New results from improved-confinement and quasi-single helicity plasmas in the MST demonstrate how the detector can be applied to study multiple aspects of the evolution of magnetically confined fusion-grade plasmas. These include observing the evolution of thermal emissivity, characterizing the energy of mid-Z excitation lines, extracting the Te profile, and observing the evolution of non-thermal populations. A technique for integrating the ME-SXR diagnostic into an integrated data analysis framework based on Bayesian inference is also presented. This allows ME-SXR measurements to be combined with data for complementary diagnostics in order to simultaneously infer Te and nZ from all available information.

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.

Simulation, design, and first test of a multi-energy soft x-ray (SXR) pinhole camera in the Madison Symmetric Torus (MST).

A multi-energy soft x-ray pinhole camera has been designed and built for the Madison Symmetric Torus reversed field pinch to aid the study of particle and thermal-transport, as well as MHD stability physics. This novel imaging diagnostic technique combines the best features from both pulse-height-analysis and multi-foil methods employing a PILATUS3 x-ray detector in which the lower energy threshold for photon detection can be adjusted independently on each pixel. Further improvements implemented on the new cooled systems allow a maximum count rate of 10 MHz per pixel and sensitivity to the strong Al and Ar emission between 1.5 and 4 keV. The local x-ray emissivity will be measured in multiple energy ranges simultaneously, from which it is possible to infer 1D and 2D simultaneous profile measurements of core electron temperature and impurity density profiles with no a priori assumptions of plasma profiles, magnetic field reconstruction constraints, high-density limitations, or need of shot-to-shot reproducibility. The expected time and space resolutions will be 2 ms and <1 cm, respectively.

Pixel-to-pixel variation on a calibrated PILATUS3-based multi-energy soft x-ray detector.

A multi-energy soft x-ray pin-hole camera based on the PILATUS3 100 K x-ray detector has recently been installed on the Madison Symmetric Torus. This photon-counting detector consists of a two-dimensional array of ∼100 000 pixels for which the photon lower-threshold cutoff energy E c can be independently set for each pixel. This capability allows the measurement of plasma x-ray emissivity in multiple energy ranges with a unique combination of spatial and spectral resolution and the inference of a variety of important plasma properties (e.g., T e, n Z, Z eff). The energy dependence of each pixel is calibrated for the 1.6-6 keV range by scanning individual trimbit settings, while the detector is exposed to fluorescence emission from Ag, In, Mo, Ti, V, and Zr targets. The resulting data for each line are then fit to a characteristic "S-curve" which determines the mapping between the 64 possible trimbit settings for each pixel. The statistical variation of this calibration from pixel-to-pixel was explored, and it was found that the discreteness of trimbit settings results in an effective threshold resolution of ΔE < 100 eV. A separate calibration was performed for the 4-14 keV range, with a resolution of ΔE < 200 eV.

A comparison between soft x-ray and magnetic phase data on the Madison symmetric torus.

The Soft X-Ray (SXR) tomography system on the Madison Symmetric Torus uses four cameras to determine the emissivity structure of the plasma. This structure should directly correspond to the structure of the magnetic field; however, there is an apparent phase difference between the emissivity reconstructions and magnetic field reconstructions when using a cylindrical approximation. The difference between the phase of the dominant rotating helical mode of the magnetic field and the motion of the brightest line of sight for each SXR camera is dependent on both the camera viewing angle and the plasma conditions. Holding these parameters fixed, this phase difference is shown to be consistent over multiple measurements when only toroidal or poloidal magnetic field components are considered. These differences emerge from physical effects of the toroidal geometry which are not captured in the cylindrical approximation.