Ion pseudoheating by low-frequency Alfv\'en waves revisited

Pseudoheating of ions in the presence of Alfv\'en waves is studied. We show that this process can be explained by $E\times B$ drift. The analytic solution obtained in this paper are quantitatively in accordance with previous results. Our simulation results show that the Maxwellian distribution is broadened during the pseudoheating; however, the shape of the broadening distribution function depends on the number of wave modes (i.e., a wave spectrum or a monochromatic dispersionless wave) and the initial thermal speed of ions ($v_{p}$). It is of particular interests to find that the Maxwellian shape is more likely to maintain during the pseudoheating under a wave spectrum compared with a monochromatic wave. It significantly improves our understanding of heating processes in interplanetary space where Alfv\'enic turbulences exist pervasively. Compared with a monochromatic Alfv\'en wave, $E\times B$ drift produces more energetic particles in a broad spectrum of Alfv\'en waves, especially when the Alfv\'enic turbulence with phase coherent wave modes is given. Such particles may escape from the region of interaction with the Alfv\'en waves and can contribute to fast particle population in astrophysical and space plasmas.