Transition to kinetic turbulence at proton scales driven by large-amplitude Kinetic Alfv'en fluctuations

Space plasmas are dominated by the presence of large-amplitude waves, large-scale inhomogeneities, kinetic effects and turbulence. Beside the homogeneous turbulence, the generation of small scale fluctuations can take place also in other realistic configurations, namely, when perturbations superpose to an inhomogeneous background magnetic field. When an Alfvén wave propagates in a medium where the Alfvén speed varies in a direction transverse to the mean field, it undergoes phase-mixing, which progressively bends wavefronts, generating small scales in the transverse direction. As soon as transverse scales become of the order of the proton inertial length dp, kinetic Alfvén waves (KAWs) are naturally generated. KAWs belong to the branch of Alfvén waves and propagate almost perpendicularly to the ambient magnetic field, at scales close to dp. Many numerical, observational and theoretical works have suggested that these fluctuations may play a determinant role in the development of the solar-wind turbulent cascade. In the present paper, the generation of large amplitude KAW fluctuations in inhomogeneous background, as well as their effect on the protons, have been investigated by means of hybrid Vlasov-Maxwell direct numerical simulations. Imposing a pressure balanced magnetic shear, the kinetic dynamics of protons has been investigated by varying both the magnetic configuration and the amplitude of the initial perturbations. Of particular interest here is the transition from quasi-linear to turbulent regimes, focusing in particular on the development of important non-Maxwellian features in the proton distribution function driven by KAW fluctuations. Several indicators to quantify the deviations of the protons from thermodynamic equilibrium are presented. These numerical results might help to explain the complex dynamics of inhomogeneous and turbulent astrophysical plasmas, such as the heliospheric current sheet, the magnetospheric boundary layer, and the solar corona.