Statistical inference of higher-order moments of electron velocity distribution functions from incoherent Thomson scattering spectra

Noninvasive direct measurements of higher-order moments of the electron velocity distribution function (EVDF) are needed to improve the understanding of non-Maxwellian electron behavior in various plasmas. This work presents a Bayesian inference method with Monte Carlo sampling to infer the electron heat flux and excess kurtosis from ILTS spectra, which also improves the inferences of the lower-order moments. The method assumes that the EVDFs are described by the sum of at most four super-Gaussians and is tested against synthetic spectra that are representative of ITLS measurements in low-temperature plasmas. Fifteen synthetic spectra are considered that include Maxwellian, Druyvesteyn, and Kappa distributions and their skewed counterparts. For all synthetic spectra considered, the true value of the heat flux is within the uncertainty bounds of the inference. Regarding the excess kurtosis, the true value of the excess kurtosis is within the uncertainty bounds of the inference for all cases except for the Kappa distributions with no or low skewness. At the signal-to-noise ratio of the synthetic spectra, the minimum detectable skewness and excess kurtosis are around ±0.006 and ±0.07, respectively. When the heat flux and excess kurtosis are significantly above their minimum detectable values, relative uncertainties range between 40% and 5%. Finally, in terms of symmetric or low-skewness EVDFs, we find that ILTS is best suited for EVDFs with negative excess kurtosis, suggesting that ILTS can accurately and precisely measure nonequilibrium electron properties in many low-temperature plasmas.