  We study the non-linear interaction of three parallel Alfv\'en wave packets
(AWP) in an initially uniform plasma using 2.5D particle-in-a-cell (PIC)
numerical simulations. We aim to help to explain the observation of
suprathermal electrons by multiple Alfv\'en waves collision in regions where
these waves are trapped like IAR (Ionospheric Alfv\'en Resonator), Earth
radiation belts or coronal magnetic loops. In the context of APAWI process that
have been described by Mottez (2012, 2015), the interaction of two parallel
Alfv\'en waves (AW) generates longitudinal density modulations and parallel
electric field at the APAWI crossing region that can accelerate particles
effectively in the direction of the background magnetic field. Our simulations
show that when a third parallel AWP of different initial position arrives at
the APAWI crossing region, it gives rise to a strong parallel electron beams
($V \sim 5--7VTe$) at longitudinal cavity density gradients. We suggest that
velocity drift from outgoing AW generates interface waves in the transverse
direction, which allows propagating waves to develop parallel electric fields
by phase mixing process when the transverse scale of the wavy density gradient
(oblique gradient) is in the range of the electron inertial length.
