  It is shown that two circularly polarised Alfv\'en waves that propagate along
the ambient magnetic field in an uniform plasma trigger non oscillating
electromagnetic field components when they cross each other. The
non-oscilliating field components can accelerate ions and electrons with great
efficiency. This work is based on particle-in-cell (PIC) numerical simulations
and on analytical non-linear computations. The analytical computations are done
for two counter-propagating monochromatic waves. The simulations are done with
monochromatic waves and with wave packets. The simulations show parallel
electromagnetic fields consistent with the theory, and they show that the
particle acceleration result in plasma cavities and, if the waves amplitudes
are high enough, in ion beams. These acceleration processes could be relevant
in space plasmas. For instance, they could be at work in the auroral zone and
in the radiation belts of the Earth magnetosphere. In particular, they may
explain the origin of the deep plasma cavities observed in the Earth auroral
zone.
