Velocity-Space Proton Diffusion in the Solar Wind Turbulence

We study the velocity-space quasi-linear diffusion of the solar wind protons driven by oblique Alfvén turbulence at proton kinetic scales. Turbulent fluctuations at these scales possess the properties of kinetic Alfvén waves (KAWs) that are efficient in Cherenkov-resonant interactions. The proton diffusion proceeds via Cherenkov kicks and forms a quasi-linear plateau – the nonthermal proton tail in the velocity distribution function (VDF). The tails extend in velocity space along the mean magnetic field from 1 to (1.5 – 3) VA, depending on the spectral break position, on the turbulence amplitude at the spectral break, and on the spectral slope after the break. The most favorable conditions for the tail generation occur in the regions where the proton thermal and Alfvén velocities are about equal, VTp/VA ≈ 1. The estimated formation times are within 1 – 2 h for typical tails at 1 AU, which is much shorter than the solar wind expansion time. Our results suggest that the nonthermal proton tails, observed in situ at all heliocentric distances >0.3 AU, are formed locally in the solar wind by the KAW turbulence. We also suggest that the bump-on-tail features – proton beams, often seen in the proton VDFs, can be formed at a later evolutional stage of the nonthermal tails by the time-of-flight effects