Kelvin-Helmholtz Instability at Proton Scales with an Exact Kinetic Equilibrium

The Kelvin-Helmholtz instability (KHI) is a ubiquitous physical process in ordinary fluids and plasmas, frequently observed also in space environments. In this paper, kinetic effects at proton scales in the nonlinear and turbulent stage of the KHI have been studied in magnetized collisionless plasmas by means of hybrid Vlasov-Maxwell simulations. The main goal of this work is to point out the back-reaction on particles triggered by the evolution of such instability, as energy reaches kinetic scales along the turbulent cascade. Interestingly, turbulence is inhibited when KHI develops over an initial state that is not an exact equilibrium state. On the other hand, when an initial equilibrium condition is considered, energy can be efficiently transferred toward short scales, reaches the typical proton wavelengths, and drives the dynamics of particles. As a consequence of the interaction of particles with the turbulent fluctuating fields, the proton velocity distribution deviates significantly from the local thermodynamic equilibrium, the degree of deviation increasing with the level of turbulence in the system and being located near regions of strong magnetic stresses. These numerical results support recent space observations from the Magnetospheric MultiScale mission of ion kinetic effects driven by the turbulent dynamics at Earth's magnetosheath and by the KHI in Earth's magnetosphere.