Bayesian inference of spatially resolved Zeff profiles from line integrated bremsstrahlung spectra.

In nuclear fusion research, the effective ion charge Zeff, which characterizes the overall content of impurities, can be experimentally derived from the plasma electron-ion bremsstrahlung, given the electron density ne and temperature Te. At Wendelstein 7-X, a multichannel near-infrared spectrometer is installed to collect the plasma bremsstrahlung along 27 lines of sight covering more than half the plasma cross section, which provides information on Zeff over the entire plasma radius. To infer spatially resolved Zeff profiles, a Bayesian model is developed in the Minerva framework. Zeff, ne, and Te profiles are modeled as Gaussian processes, whose smoothness is determined by hyperparameters. These profiles are transformed to fields in Cartesian coordinates, given the poloidal magnetic flux surfaces calculated by the variational moments equilibrium code. Given all these physical quantities, the model predicts line-of-sight integrals of near-infrared bremsstrahlung spectra. The model includes the predictive (forward) models of the interferometer, Thomson scattering system, and visible and near-infrared spectrometers. Given the observations of all these diagnostics, the posterior probability distribution of Zeff profiles is calculated and shown as an inference solution. The smoothness (gradient) of the profiles is optimally chosen by Bayesian Occam's razor. Furthermore, wall reflections can significantly pollute the measurements of the plasma bremsstrahlung, which leads to over-estimation of Zeff values in the edge region. In the first results presented in this work, this problem does not appear, and the posterior samples of Zeff profiles are overall plausible and consistent with Zeff values inferred, given the data from the single-channel visible spectrometer.

Key results from the first plasma operation phase and outlook for future performance in Wendelstein 7-X.

The first physics operation phase on the stellarator experiment Wendelstein 7-X was successfully completed in March 2016 after about 10 weeks of operation. Experiments in this phase were conducted with five graphite limiters as the primary plasma-facing components. Overall, the results were beyond the expectations published shortly before the start of operation [Sunn Pedersen et al., Nucl. Fusion 55, 126001 (2015)] both with respect to parameters reached and with respect to physics themes addressed. We report here on some of the most important plasma experiments that were conducted. The importance of electric fields on global confinement will be discussed, and the obtained results will be compared and contrasted with results from other devices, quantified in terms of the fusion triple product. Expected values for the triple product in future operation phases will also be described and put into a broader fusion perspective.