Proton energization by phase-steepening of parallel propagating Alfv\'enic fluctuations

Proton energization at magnetic discontinuities generated by phase-steepened fronts of parallel propagating, large-amplitude Alfv\'enic fluctuation is studied using hybrid simulations. We find that dispersive effects yield to the collapse of the wave via phase steepening and the subsequent generation of compressible fluctuations that mediate an efficient local energy transfer from the wave to the protons. Proton scattering at the steepened edges causes non-adiabatic proton perpendicular heating. Furthermore, the parallel electric field at the propagating fronts mediates the acceleration of protons along the mean field. A steady-state is achieved where proton distribution function displays a field-aligned beam at the Alfv\'en speed, and compressible fluctuations are largely damped. We discuss the implications of our results in the context of Alfv\'enic solar wind.