Short-wavelength electrostatic fluctuations in the solar wind

Hybrid Vlasov–Maxwell simulations have been used recently to investigate the dynamics of the solar-wind plasma in the tail at short wavelengths of the energy cascade. These simulations have shown that a significant level of electrostatic activity is detected at wavelengths smaller than the proton inertial scale in the longitudinal direction with respect to the ambient magnetic field. In this paper, we describe the results of a new series of hybrid Vlasov–Maxwell simulations that allow us to investigate in more detail the generation process of these electrostatic fluctuations in terms of the electron-to-proton temperature ratio Te/Tp. This analysis gives evidence for the first time that even in the case of cold electrons, Te of the order of Tp (the appropriate condition for solar-wind plasmas), the resonant interaction of protons with large-scale left-hand polarized ion-cyclotron waves is responsible for the excitation of short-scale electrostatic fluctuations with an acoustic dispersion relation. Moreover, through our numerical results we propose a physical mechanism to explain the generation of longitudinal proton-beam distributions in typical conditions of the solar-wind environment.