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Over three decades of in-situ observations illustrate that the Kelvin–Helmholtz (KH) instability driven by the sheared flow between the magnetosheath and magnetospheric plasma often occurs on the magnetopause of Earth and other planets under various interplanetary magnetic field (IMF) conditions. It has been well demonstrated that the KH instability plays an important role for energy, momentum, and mass transport during the solar-wind-magnetosphere coupling process. Particularly, the KH instability is an important mechanism to trigger secondary small scale (i.e., often kinetic-scale) physical processes, such as magnetic reconnection, kinetic Alfvén waves, ion-acoustic waves, and turbulence, providing the bridge for the coupling of cross scale physical processes. From the simulation perspective, to fully investigate the role of the KH instability on the cross-scale process requires a numerical modeling that can describe the physical scales from a few Earth radii to a few ion (even electron) inertial lengths in three dimensions, which is often computationally expensive. Thus, different simulation methods are required to explore physical processes on different length scales, and cross validate the physical processes which occur on the overlapping length scales. Test particle simulation provides such a bridge to connect the MHD scale to the kinetic scale. This study applies different test particle approaches and cross validates the different results against one another to investigate the behavior of different ion species (i.e., H+ and O+), which include particle distributions, mixing and heating. It shows that the ion transport rate is about 10 25  particles/s, and mixing diffusion coefficient is about 10 10  m 2  s −1 regardless of the ion species. Magnetic field lines change their topology via the magnetic reconnection process driven by the three-dimensional KH instability, connecting two flux tubes with different temperature, which eventually causes anisotropic temperature in the newly reconnected flux. 

As space plasmas are highly collisionless and involve several temporal and spatial scales, understanding the physical mechanisms responsible for energy transport between these scales is a challenge. Ideally, to study cross-scale space plasma processes, simultaneous multi-spacecraft measurements in three different scales (fluid, ion and electron) would be required together with adequate instrumental temporal resolution. In this chapter we discuss cross-scale energy transport mechanisms mainly focusing on velocity shear driven Kelvin-Helmholtz instability and resulting secondary instabilities and processes, e.g, magnetic reconnection, kinetic magnetosonic waves and kinetic Alfven waves/mode conversion. 

The Magnetospheric Multiscale (MMS) mission has presented a new opportunity to study the fine scale structures and phenomena of the Earth’s magnetosphere, including cross scale processes associated with the Kelvin–Helmholtz Instability (KHI), but such studies of the KHI and its secondary processes will require a database of MMS encounters with Kelvin–Helmholtz (KH) waves. Here, we present an overview of 45 MMS observations of the KHI from September 2015 to March 2020. Growth rates and unstable solid angles for each of the 45 events were calculated using a new technique to automatically detect plasma regions on either side of the magnetopause boundary. There was no apparent correlation between solar wind conditions during the KHI and its growth rate and unstable solid angle, which is not surprising as KH waves were observed downstream of their source region. We note all KHI were observed for solar wind flow speeds between 295 and 610 km/s, possibly due to a filtering effect of the instability onset criteria and plasma compressibility. Two‐dimensional Magnetohydrodynamic (2D MHD) simulations were compared with two of the observed MMS events. Comparison of the observations with the 2D MHD simulations indicates that the new region sorting method is reliable and robust. The ability to automatically detect separate plasma regions on either side of a moving boundary and determine the KHI growth rate may prove useful for future work identifying and studying secondary processes associated with the KHI.

 

We present a case study of the Magnetospheric Multiscale (MMS) observations of the Southern Hemispheric dayside magnetospheric boundaries under southward interplanetary magnetic field direction with strongB_ycomponent. During this event MMS encountered several magnetic field depressions characterized by enhanced plasma beta and high fluxes of high‐energy electrons and ions at the dusk sector of the southern cusp region that resemble previous Cluster and Polar observations of cusp diamagnetic cavities. Based on the expected maximum magnetic shear model and magnetohydrodynamic simulations, we show that for the present event the diamagnetic cavity‐like structures were formed in an unusual location. Analysis of the composition measurements of ion velocity distribution functions and magnetohydrodynamics simulations show clear evidence of the creation of a new kind of magnetic bottle structures by component reconnection occurring at lower latitudes. We propose that the high‐energy particles trapped in these cavities can sometimes end up in the loss cone and leak out, providing a likely explanation for recent high‐energy particle leakage events observed in the magnetosheath.