M.B. McGarry

A new double-foil soft x-ray array to measure Te on the MST reversed field pincha)

A soft x-ray (SXR) diagnostic to measure electron temperature on the Madison Symmetric Torus using two complementary methods is presented. Both methods are based on the double-foil technique, which calculates electron temperature via the ratio of SXR bremsstrahlung emission from the plasma in two different energy ranges. The tomographic emissivity method applies the double-foil technique to a tomographic reconstruction of SXR emissivity, creating a two-dimensional map of temperature throughout the plasma. In contrast, the direct brightness method applies the double-foil technique directly to the measured brightness and generates vertical and horizontal radial profiles. Extensive modeling demonstrates advantages and limitations in both techniques. For example, although the emissivity technique provides a two-dimensional mapping of temperature, its reliance on multiple tomographic inversions introduces some artifacts into the results. On the other hand, the more direct brightness technique avoids these artifacts but is only able to provide a radial profile of electron temperature.

Determination of Z eff by integrating measurements from x-ray tomography and charge exchange recombination spectroscopy

The effective ionic charge, Zeff, is determined through the integration of soft x-ray tomography and charge exchange recombination spectroscopy impurity density measurements in the Madison Symmetric Torus. Zeff is found is be 2.3 ± 0.1 in the core of high temperature, high current, improved confinement discharges, with a slightly hollow profile peaking near mid-radius. A Bayesian probability framework, developed as part of an on-going effort in Integrated Data Analysis, was used to incorporate these two measurements. This framework provides a method to address different systematic and statistical uncertainties associated with each diagnostic and to test hypothetical contributions to Zeff against the existing data set. The combined analysis provides much higher confidence in the result than previous single-diagnostic attempts to characterize Zeff using near-infrared bremsstrahlung or x-ray spectroscopy.

High-performance double-filter soft x-ray diagnostic for measurement of electron temperature structure and dynamics.

A new soft x-ray (SXR) T(e) and tomography diagnostic has been developed for MST that can be used for simultaneous SXR spectrum measurement, tomographically reconstructed emissivity, and reconstructed and line-of-sight electron temperature. The diagnostic utilizes high-performance differential transimpedance amplifiers (gain 10(5)-10(9)) to provide fast time response (up to 125 kHz), allowing for the study of plasma structure dynamics. SXR double-foil T(e) measurements are consistent with Thomson scattering. SXR brightness through a variety of filter thicknesses has been combined with charge exchange recombination spectroscopy (CHERS) impurity density measurements to determine the plasma energy spectrum. Magnetic pickup from the fluctuating magnetic fields in the plasma (B̃∼20 gauss at 10-20 kHz) has been dramatically reduced by improving the detector and housing design, so that nanoampere diode currents are now measured without interference from the substantial fluctuating magnetic field incident on the plasma facing surface of the probe.

An integrated data analysis tool for improving measurements on the MST RFP.

Many plasma diagnostics contain complementary information. For example, the double-foil soft x-ray system (SXR) and the Thomson Scattering diagnostic (TS) on the Madison Symmetric Torus both measure electron temperature. The complementary information from these diagnostics can be combined using a systematic method based on integrated data analysis techniques, leading to more accurate and sensitive results. An integrated data analysis tool based on Bayesian probability theory was able to estimate electron temperatures that are consistent with both the SXR and TS diagnostics and more precise than either. A Markov Chain Monte Carlo analysis to increase the flexibility of the tool was implemented and benchmarked against a grid search method.

Calibration of a two-color soft x-ray diagnostic for electron temperature measurement

The two-color soft x-ray (SXR) tomography diagnostic on the Madison Symmetric Torus is capable of making electron temperature measurements via the double-filter technique; however, there has been a 15% systematic discrepancy between the SXR double-filter (SXRDF) temperature and Thomson scattering (TS) temperature. Here we discuss calibration of the Be filters used in the SXRDF measurement using empirical measurements of the transmission function versus energy at the BESSY II electron storage ring, electron microprobe analysis of filter contaminants, and measurement of the effective density. The calibration does not account for the TS and SXRDF discrepancy, and evidence from experiments indicates that this discrepancy is due to physics missing from the SXRDF analysis rather than instrumentation effects.

Note: Effect of photodiode aluminum cathode frame on spectral sensitivity in the soft x-ray energy band

Silicon photodiodes used for soft x-ray detection typically have a thin metal electrode partially covering the active area of the photodiode, which subtly alters the spectral sensitivity of the photodiode. As a specific example, AXUV4BST photodiodes from International Radiation Detectors have a 1.0 μm thick aluminum frame covering 19% of the active area of the photodiode, which attenuates the measured x-ray signal below ~6 keV. This effect has a small systematic impact on the electron temperature calculated from measurements of soft x-ray bremsstrahlung emission from a high-temperature plasma. Although the systematic error introduced by the aluminum frame is only a few percent in typical experimental conditions on the Madison Symmetric Torus, it may be more significant for other instruments that use similar detectors.

Three dimensional equilibrium solutions for a current-carrying reversed-field pinch plasma with a close-fitting conducting shell

In order to characterize the Madison Symmetric Torus (MST) reversed-field pinch (RFP) plasmas that bifurcate to a helical equilibrium, the V3FIT equilibrium reconstruction code was modified to include a conducting boundary. RFP plasmas become helical at a high plasma current, which induces large eddy currents in MSTs thick aluminum shell. The V3FIT conducting boundary accounts for the contribution from these eddy currents to external magnetic diagnostic coil signals. This implementation of V3FIT was benchmarked against MSTFit, a 2D Grad-Shafranov solver, for axisymmetric plasmas. The two codes both fit Bθ measurement loops around the plasma minor diameter with qualitative agreement between each other and the measured field. Fits in the 3D case converge well, with q-profile and plasma shape agreement between two distinct toroidal locking phases. Greater than 60% of the measured n = 5 component of Bθ at r = a is due to eddy currents in the shell, as calculated by the conducting boundary model.

Effect of beryllium filter purity on x-ray emission measurements

Beryllium foils of the purity grade typically specified for use as filters in soft x-ray (SXR) diagnostics may contain sufficient heavy element impurities to distort the energy transmission response of the filter. Electron microprobe analysis of the foils used in the Madison Symmetric Torus (MST) SXR tomography diagnostic revealed an impurity content of ~0.3% fractional abundance by weight, comprised primarily of iron, zirconium, chromium, and nickel. These impurities lower the peak filter transmission in the energy range of the detector and alter the shape of the transmission curve. As a result, foil impurities introduce errors in any general measurement where radiation is being filtered. For example, neglecting the effect of impurities on filter transmission leads to large systematic errors (50%) in the electron temperature measured using the SXR double-filter technique on MST.