Description
At Wendelstein 7-X (W7-X), the world’s largest superconducting stellarator, three thermal helium beam systems are used to infer edge plasma electron density and temperature applying the spectral line intensity ratio method [1]. In this contribution, we present a Bayesian forward model of the helium beam emission in W7-X. In contrast to conventional approaches based on line intensity ratios, the proposed model directly employs absolute line intensities at 667.9 nm, 706.7 nm, and 728.3 nm to infer the electron density and temperature.
The full three-dimensional geometry of the helium gas valve and diagnostic lines of sight (LOS) is taken into account, enabling beam divergence effects to be included in the calculation of LOS-integrated intensities. Beam attenuation due to electron-impact ionization losses is explicitly incorporated. This provides an additional constraint on electron density by exploiting information contained in the attenuation, particularly at high densities where line ratios show only weak sensitivity to density and temperature.
Local emissivities per helium atom are modeled using photon emissivity coefficients (PECs) obtained from a collisional-radiative model (CRM) of atomic helium. The ionization loss rates from the same CRM are used to compute beam attenuation along its trajectory. Preliminaryanalysis of absolute line intensities measured in W7-X plasmas does not provide a consistent fit to line ratios and absolute intensities, which may indicate inaccuracies in the CRM ionization rates. Nevertheless, we investigate whether including beam attenuation in the inference reduces the final uncertainties in the derived electron density and temperature.
The model is implemented within the Minerva Bayesian framework [2], enabling efficient specification of the forward model and Bayesian inference. Markov Chain Monte Carlo (MCMC) sampling of the posterior probability density function provides quantitative uncertainty estimates for the inferred electron density and temperature, which are not accessible in conventional line-ratio-based analyses.
[1] T. Barbui et. al., Rev. Sci. Instrum. 87, 11E554 (2016)
[2] J. Svensson and A. Werner, IEEE Int. Symp. Intell. Signal Process. 2007 (2007) 1