Phase space dynamics of unmagnetized plasmas: collisionless and collisional regimes

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.