Characterization of back-streaming proton VDFs in the Earth's bowshock using a Gaussian Mixture Model.

The ion foreshock is the region of space where solar wind ions interacting with Earth’s bowshock can reach after being reflected in the bowshock instead of penetrating into the megnetosheath. The foreshock forms wherever the interplanetary magnetic field is quasit parallel to the bowshock’s normal and connected to it. In the foreshock, the ions reflected at the bowshock form a population that propagates in the upstream direction and make the Velocity Distribution Function (VDF) unstable, giving rise to Ultra Low Frequency (ULF) waves.

 

 

The Magnetospheric Multiscale Mission (MMS) in it orbit around the earth periodically probes the ion foreshock. The on-board Fast Plasma Investigation (FPI) instrument provides full ion VDFs of this region, a velocity distribution function comprised of the contributions of all ion populations present, including different ion species and the back-streaming protons characteristic of the ion foreshock. Here we present a method based on Gaussian Mixture Models (GMM) that we use to decompose full ion VDF into partial VDFS corresponding to the different ion populations. In this way, we can isolate the VDF of only the back-propagating foreshock protons, that can be used to study how they contribute to the instability of the full VDF and the excitation of propagation of ULF waves throughout the foreshock.

 

We demonstrate the ability of this method to find separate population-specific VDFs and apply it to a case study where ULF waves are observed in association to a diffuse back-streaming proton distribution function.