  Eulerian electrostatic kinetic simulations of unmagnetized plasmas (kinetic
electrons and motionless protons) with high-frequency equilibrium perturbations
have been employed to investigate the phase space free energy transfer across
spatial and velocity scales, associated with the resonant interaction of
electrons with the self-induced electric field. Numerical runs cover a wide
range of collisionless and weakly collisional plasma regimes. An analysis
technique based on the Fourier-Hermite transform of the particle distribution
function allows to point out how kinetic processes trigger the free energy
cascade, which is instead inhibited at finer scales when collisions are turned
on. Numerical results are presented and discussed for the cases of linear wave
Landau damping, nonlinear electron trapping, bump-on-tail and two-stream
instabilities. A more realistic situation of turbulent Langmuir fluctuations is
also discussed in detail. Fourier-Hermite transform shows a free energy spread,
highly conditioned by collisions, which involves velocity scales more quickly
than the spatial scales, even when nonlinear effects are dominant. This results
in anisotropic spectra whose slopes are compatible with theoretical
expectations. Finally, an exact conservation law has been derived, which
describes the time evolution of the free energy of the system, taking into
account the collisional dissipation.
