Time-resolved Bayesian analysis of low-pressure misty plasmas using optical emission spectroscopy and collisional-radiative modeling

Optical emission spectroscopy (OES) is widely used for non-invasive, real-time plasma characterisation. OES data is often coupled with sophisticated collisional-radiative modelling (CRM) to get in-depth insight on the fundamental properties of the plasma. The CRM comes with a number of adjustable parameters, whose values must provide the best agreement between the measured and simulated spectra. This work presents an OES/CRM method with a twist: the search for the best-matching spectrum is framed in terms of probability, to take full advantage of the principles of Bayesian inference. Some of the tools provided by Bayesian analysis are illustrated in the specific case of OES/CRM diagnostics. Both experimental and modelling uncertainties are taken into account in a rigorous mathematical framework, and results are expressed as probability distributions rather than single error-minimizing values. Time-resolved data is used to define proper prior distributions. The question of model selection is addressed through the estimation of the Bayesian evidence of each candidate CRM, so that the Bayes factor can be used as a quantitative metric to filter out superfluous adjustable parameters. Low-pressure "misty" plasmas, in which liquid droplets are injected as aerosols, are used as an adequate case study: they are complex in nature, subject to time-dependent changes, and require non-invasive diagnostics as they are usually employed for thin film deposition. Results include the temporal evolution of the electron temperature, electron density, and quenching frequency of metastable species during the pulsed injection of liquids in an argon plasma, all extracted from OES measurements.