  The Kelvin-Helmholtz instability 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 Kelvin-Helmholtz instability 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 Kelvin-Helmholtz
instability develops over an initial state which is not an exact equilibrium
state. On the other hand, when an initial equilibrium condition is considered,
energy can be efficiently transferred towards 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
the Earth's magnetosheath (Perri et al., 2020, JPlPh, 86, 905860108) and by the
Kelvin-Helmholtz instability in the Earth's magnetosphere (Sorriso-Valvo et
al., 2019, PhRvL, 122, 035102).
