Characterizing Satellite Path Through Kelvin-Helmholtz Instability Using a Mixing Parameter

We introduce the mixing parameter to analyze the in situ measurements of a Kelvin-Helmholtz event observed by the Magnetospheric Multiscale mission. We define the mixing parameter, for both ions and electrons, using the well distinct particle energies which characterize the magnetosphere and magnetosheath plasmas. This parameter nicely identifies the different populations which are interacting at the Earth's magnetopause and the boundaries of Kelvin-Helmholtz vortices. Thus, we analyze the crossing of each structure into a parameter space defined as the space of the electron mixing versus the ion mixing, where specific shapes occur according to the evolutionary phase of the Kelvin-Helmholtz instability. All along the event, we observe three different types of shapes, namely a straight line, a simple loop, and a complex loop, which likely corresponds to linear waves, steepened waves, and rolled-up vortices, respectively. The most complex shape (rolled-up vortex) is observed mostly at the end of the interval, owing to fast growth of the instability which is connected to variations of the solar wind magnetic field orientation.