Bayesian inference of excited state population densities and equilibrium temperatures in argon plasmas using emission spectroscopy

Emission spectroscopy is a powerful tool to extract chemical and thermodynamic state information from light emitting substances. Specifically, in the case of plasmas, one can extract excited state populations and temperatures. However, the accuracy of emission spectroscopic measurements suffers from the fact that several approximations and uncertain parameters are required to invert the measurement model for the quantities of interest. For some of these parameters, uncertainties are relatively well quantified, e.g. for spontaneous emission coefficients; for others, auxiliary measurements have to be performed which introduce their own uncertainties. We present a Bayesian framework to infer plasma state information from emission spectroscopic measurements coupled with a measurement model for argon and apply it to two cases. In the first, we infer excited state population densities of argon in a non-equilibrium capacitively coupled glow discharge plasma. In the second, we infer temperatures in a near-equilibrium argon plasma in an inductively coupled plasma torch. The approach accounts for uncertainties in spontaneous emission coefficients, the plasma slab depth and the line shape width. First results show the promise of this approach to propagate uncertainties to the final quantities of interest in a consistent fashion, to include prior knowledge in the data evaluation, and to extend it to more complex measurement models. The methodology supports the integration of experimental data and model predictions and increases the fidelity of emission spectroscopic measurements.