Forward Modeling of X-Ray Imaging Crystal Spectrometers Within the Minerva Bayesian Analysis Framework

Two X-ray imaging crystal spectrometer systems are currently being prepared for commissioning at the stellarator Wendelstein 7-X (W7-X). Both are expected to be ready for the first plasma operation in 2015. The spectrometers will provide line-integrated measurements of basic plasma parameters like ion and electron temperatures (T_e,T_i), plasma rotation (v_rot), and argon impurity densities. A forward model based on the designed installation geometries of both spectrometers has been performed using the Minerva Bayesian analysis framework. This model allows us to create synthesized data given radial profiles of plasma parameters for a wide range of different scenarios. To simulate line-integrated spectra as measured by the (virtual) detector, the geometry and Gaussian detection noise are assumed. The line-integrated plasma parameters are inferred within the framework from noisy spectral data using the maximum posterior method. The capabilities and limitations of the model and method are discussed through examples of several synthesized data sets of different plasma parameter profiles.