Gaussian process tomography of the effective ion charge Z_eff from multiple line-integrated bremsstrahlung spectra

In magnetically confined fusion plasmas, the effective ion charge Z_eff, which is useful for determining impurity contaminations, power losses and transport, can be inferred from the plasma electron-ion bremsstrahlung, given the electron density n_e and temperature T_e. At the Wendelstein 7-X stellarator experiment, visible and infrared spectrometers collect the plasma bremsstrahlung spectra along multiple lines of sight which provide information on the spatial distribution of Z_eff over the plasma. To infer spatially resolved Z_eff profiles, a Bayesian model has been developed within the Minerva framework. Z_eff, n_e and T_e profiles are modelled as Gaussian processes whose hyperparameters constrain their smoothness. These profiles are mapped to Cartesian coordinates by assuming that physical quantities are constant on the poloidal magnetic flux surfaces. Given Z_eff, n_e and T_e, the predictive (forward) model, which takes into account the calibration of spectral responses and reflected stray lights, predicts the multiple line-integrated bremsstrahlung spectra observed by the visible and infrared spectrometers. Besides the spectrometers, the model additionally includes the interferometer and Thomson scattering system to infer n_e and T_e. The inferred Z_eff, n_e and T_e profiles are provided as the samples drawn from their posterior probability distribution. The smoothness (hyperparameters) of the profiles is determined by evidence optimisation based on the principle of Occam’s razor.