Analysis of Electron Distribution Functions From the Magnetospheric Multiscale (MMS) Mission Using the Gaussian Mixture Model

Abstract Velocity distribution functions (VDFs) measured by the Magnetospheric Multiscale (MMS) mission are complex 3D data sets that can be represented as a superposition of multiple beams. Recent work proposed the use of the Gaussian Mixture Model (GMM) to identify different populations. Here we investigate the approach by considering first synthetic distributions made by synthetically creating beams of either Maxwellian distributions or kappa distributions with varying power law index. By varying the inter‐beam average difference and the beam standard deviation we evaluate the ability of the GMM in recognizing correctly the beam. We then apply the method systematically to MMS data in the tail and in the dayside of the Earth's magnetosphere. The approach relies on a GMM algorithm to detect and characterize the number of distinct clusters within a VDF, and a model selection approach based on the Bayesian Information Criterion to determine the optimal number of clusters. The conclusion of the analysis is that the GMM can estimate the complexity of a VDF in terms of the number of optimal beams provided by information theory criteria. By evaluating the complexity of VDFs, we can identify regions of interest within the plasma where significant physical phenomena may be present.