In this paper, results of a set of numerical simulations applicable to the problem of particle acceleration by the beating of high‐energy laser waves are presented. The simulations have periodic or open‐ended boundary conditions. The growth rates of the parametric instabilities that are present in both situations are identical. In all cases they yield a destruction of the large amplitude plasma wave in a very short time. The amplitude of the saturation level is shown to be strongly dependent on initial conditions. Finally, some results in the term of the evolution of the distribution function of the background plasma in the context of strong turbulence are shown.