Bayesian plasma model selection for Thomson scattering

Abstract

Laser Thomson scattering (LTS) is a measurement technique that can determine electron velocity distribution functions in plasma systems. However, accurately inferring quantities of interest from an LTS signal requires the selection of a plasma physics submodel, and comprehensive uncertainty quantification (UQ) is needed to interpret the results. Automated model selection, parameter estimation, and UQ are particularly challenging for low-density, low-temperature, potentially non-Maxwellian plasmas like those created in space electric propulsion devices. This paper applies Bayesian inference and model selection to a Raman-calibrated LTS diagnostic in the context of such plasmas. Synthetic data are used to explore the performance of the method across signal-to-noise ratios and model fidelity regimes. Plasmas with Maxwellian and non-Maxwellian velocity distributions are well characterized using priors that span a range of accuracy and specificity. The model selection framework is shown to accurately detect the type of plasmas generating the electron velocity distribution submodel for signal-to-noise ratios greater than around 5. In addition, the Bayesian framework validates the widespread use of 95% confidence intervals from least-squares inversion as a conservative estimate of the uncertainty bounds. However, epistemic posterior correlations between the variables diverge between least-squares and Bayesian estimates as the number of variable parameters increases. This divergence demonstrates the need for Bayesian inference in cases where accurate correlations between electron parameters are necessary. Bayesian model selection is then applied to experimental Thomson scattering data collected in a nanosecond pulsed plasma, generated with a discharge voltage of 5 and 10 kV at a neutral argon background pressure of 7 Torr-Ar. The Bayesian maximum a posteriori estimates of the electron temperature and number density are 1.98 and 2.38 eV and 2.6 × 1018 and 2.72 × 1018 m−3, using the Maxwellian and Druyvesteyn submodels, respectively. Furthermore, for this dataset, the model selection criterion indicates strong support for the Maxwellian distribution at 10 kV discharge voltage and no strong preference between Maxwellian and Druyvesteyn distributions at 5 kV. The logarithmic Bayes’ factors for these cases are −35.76 and 1.07, respectively.