The mechanism of laser plasma generation and heating by the impinging laser beam occurs mostly by the way of oscillatory motion of electrons in the electric field of the light wave, which is damped by the electron–ion collisions, dissipating thus the energy of the coherent laser wave, the so-called inverse bremsstrahlung mechanism. However, in the external part of the corona the laser plasma is only weakly collisional and the evolution of the electron distribution function in the electron phase space is far from remaining a Maxwellian one. The predominant mechanism causing deviations from a Maxwell distribution is the particle trapping in electrostatic waves. The electrostatic waves turn up in the plasma as daughter wave in the nonlinear processes of wave transformations, the typical example of which is the Raman scattering when the heating laser wave decays in a scattered electromagnetic wave and a forward directed electrostatic electron plasma wave. The potential troughs of this electrostatic wave are trapping the electrons which travel at nearly the same speed as the wave phase velocity and later start to oscillate around the wave potential minima. The scattered Raman wave may grow strong enough to undergo a secondary scattering, which leads to a Raman cascade. The oscillating electrons have their own dynamics separate from that of the bulk thermal electrons, which gives rise to additional wave modes. One of them is the trapped particle instability, which broadens the electrostatic spectrum and leads to an intermittency. The electron phase space is hardly accessible to a direct measurement of the electron distribution function, which is changing fast on a time scale of order of picoseconds, it therefore makes sense to resort to a numerical modelling of the phase space evolution. This is effected by a solution of the Vlasov equation (including a weak collision term) simultaneously with the Maxwell equations in a 1D periodic slab model by a transform method. The parameters of the computation were chosen to be compatible with the plasma in the laser corona typically generated by the nanosecond Prague Asterix Laser System (PALS) system at the high flux end attainable by a tight focusing ∼1016 W/cm2. The results of the modelling are presented and the physically interesting points highlighted.