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

Abstract

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 2-5 keV using argon impurities.

High-performance plasmas after pellet injections in Wendelstein 7-X

“…The measurement chord of the dispersion interferometer is almost identical to the laser line of the Thomson scattering system; consequently, the latter can be conveniently cross-calibrated. Ion temperature profiles can be recovered from the XICS measurements of Ar +16 line widths along multiple lines of sight by using either a tomographic inversion with the known flux surface geometry [61] or a Bayesian modelling with Minerva framework [62]. In addition, high quality carbon ion temperature profiles can be measured with the CXRS diagnostic on the NBI, where the number of spatial channels varies between 30 and 70, depending on the diagnostic settings.…”

Charge exchange recombination spectroscopy at Wendelstein 7-X

“…However, the Ar XV I line at 436.5nm produced a good signal. Figure 11 shows the derived normalised concentration profiles (derived as in section IV D) compared to those determined from the XICS 38 . Agreement in the concentration profile shape can be seen despite the neglect of the charge exchange emission coefficients and their dependence on the plasma parameters, most likely due to lack of variation of those parameters over the profile in figure 11a and due to the dominance of the impurity peaking feature in 11b.…”

Accelerated Bayesian inference of plasma profiles with self-consistent MHD equilibria at W7-X via neural networks

“…To infer additional plasma parameters, more diagnostics can be included in the Minerva graph. A XICS can be used to constrain the ion temperature [43], and a spectrometer can be used to infer the effective charge 𝑍 eff [44].…”