L. M. Reusch

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.

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.

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.

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.

Incorporating Beam Attenuation Calculations into an Integrated Data Analysis Model for Ion Effective Charge

Abstract We have created a forward model for charge-exchange impurity density measurements that incorporates neutral beam attenuation measurements self-consistently for the purpose of determining the ion-effective charge Zeff. The model is constructed within an integrated data analysis framework to include a self-consistent calculation of neutral beam attenuation due to multiple impurity species into the measurement of a single impurity density. The model includes measurements of the beam Doppler-shift spectrum and shine-through particle flux to determine the neutral beam particle density which is attenuated by ion collisions. Synthetic data are generated from the diagnostic forward model using statistical and calibration uncertainties. These “noisy” data are used in the analysis to evaluate how accurately Zeff is determined. Methods of experimental design are employed to calculate the information gained from different diagnostic combinations. The analysis shows that while attenuation measurements alone do not provide a unique impurity density measurement in the case of a multispecies inhomogeneous plasma, they do provide an effective measurement of the Zeff profile and place constraints on the impurity density profiles.

Model Validation for Quantitative X-Ray Measurements

Abstract Soft–X-ray (SXR) brightness measurements contain information on a number of physics parameters in fusion plasmas; however, it is nearly impossible to extract the information without modeling. A validated forward model is therefore necessary for the accurate interpretation of SXR measurements and will be critical in the burning plasma era, where medium- and high-Z impurities are ever present. The Atomic Data and Analysis Structure (ADAS) database is a powerful interpretive tool that is extensively used to model and predict atomic spectra, level populations, and ionization balance for fusion plasmas. These predictions are in good agreement with experimental measurements. However, continuum radiation in the X-ray range, while also modeled in ADAS, has not been rigorously verified or tested against experimental data. We therefore performed a systematic comparison of ADAS to a simplified model called PFM. PFM only calculates continuum radiation but shows good agreement with experimental data when only continuum radiation is present. ADAS and the simplified model agree to within 1% to 2% indicating that ADAS is calculating continuum radiation correctly. We have also begun a validation of SXR brightness calculations from ADAS. The SXR brightness measurements modeled by ADAS agree well with experimental measurements from an extreme where the signal is dominated by line radiation continuously through another extreme where the signal is dominated by continuum emission. While this validation work is preliminary, it strongly suggests that ADAS accurately models the physics that lead to SXR radiation.

Using integrated data analysis to extend measurement capability (invited)

The analysis approach called integrated data analysis (IDA) provides a means to exploit all information present in multiple streams of raw data to produce the best inference of a plasma parameter. This contrasts with the typical approach in which information (data) from a single diagnostic is used to measure a given parameter, e.g., visible bremsstrahlung → Z eff. Data from a given diagnostic usually contain information on many parameters. For example, a Thomson scattering diagnostic is sensitive to bremsstrahlung and line emission in addition to electron temperature. This background light is typically subtracted off and discarded but could be used to improve knowledge of Z eff. IDA encourages explicit awareness of such information and provides the quantitative framework to exploit it. This gives IDA the ability to increase spatial and temporal resolution, increase precision and accuracy of inferences, and measure plasma parameters that are difficult or impossible to measure using single diagnostic techniques. One example is the measurement of Z eff on Madison symmetric torus using IDA since no single diagnostic can provide a robust measurement. As we enter the burning plasma era, application of IDA will be critical to the measurement of certain parameters, as diagnostic access in the harsh fusion environment will be extremely limited.

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.