Bayesian modelling of a thermal helium beam for measurement of electron density and temperature in the W7-X divertor plasma

In Greifswald/Germany W7-X, a new stellarator-type fusion plasma experiment, is currently being built. For the investigation of the divertor plasma two thermal helium beams are foreseen. This diagnostic is routinely used on several fusion plasma experiments and is capable of measuring radial profiles of electron density and temperature with good spatial and temporal resolution in the range of typical edge plasma parameters n e = 10 18 –10 19 m −3 and T e = 20–200 eV. The penetration depth of the beam is limited by electron collisional ionization of the helium atoms and amounts to 3–8 cm in this parameter range. In this paper we investigate the beam propagation for detached plasma conditions in the W7-X divertor region (based on a background plasma simulated with a 3D plasma and neutral transport code EMC3/EIRENE), in which the electron density in the divertor may well exceed 10 20 m −3 , as observed in the predecessor experiment W7-AS. In this regime the beam penetration drops to 1–2 cm. Through a Bayesian approach, we include uncertainties of all rate coefficients for electronic excitation and ionization used in the collisional–radiative model of atomic helium based on a steady-state approximation valid for a relaxed thermal or supersonic beam. Bayesian inversion of simulated signals for W7-X conditions provides a reliable quantitative estimation of the propagation of uncertainties of the atomic data to the n e and T e errors as well as input for potential improvements of the diagnostic setup. For example, the temperature error at T e = 5 eV and n e = 10 20 m −3 can be reduced from approximately 50% to 9% by absolute calibration of the observation system and fitting of three absolute line intensities instead of two line intensity ratios to the model.