  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.
