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Kinetic Alfv\'en waves represent an important subject in space plasmaphysics, since they are thought to play a crucial role in the development ofthe turbulent energy cascade in the solar wind plasma at short wavelengths (ofthe order of the proton inertial length $d_p$ and beyond). A full understandingof the physical mechanisms which govern the kinetic plasma dynamics at thesescales can provide important clues on the problem of the turbulent dissipationand heating in collisionless systems. In this paper, hybrid Vlasov-Maxwellsimulations are employed to analyze in detail the features of the kineticAlfv\'en waves at proton kinetic scales, in typical conditions of the solarwind environment. In particular, linear and nonlinear regimes of propagation ofthese fluctuations have been investigated in a single-wave situation, focusingon the physical processes of collisionless Landau damping and wave-particleresonant interaction. Interestingly, since for wavelengths close to $d_p$ andproton plasma beta $\beta$ of order unity the kinetic Alfv\'en waves have smallphase speed compared to the proton thermal velocity, wave-particle interactionprocesses produce significant deformations in the core of the particle velocitydistribution, appearing as phase space vortices and resulting in flat-topvelocity profiles. Moreover, as the Eulerian hybrid Vlasov-Maxwell algorithmallows for a clean almost noise-free description of the velocity space,three-dimensional plots of the proton velocity distribution help to emphasizehow the plasma departs from the Maxwellian configuration of thermodynamicequilibrium due to nonlinear kinetic effects.

Vlasov simulations of Kinetic Alfv\'en Waves at proton kinetic scales