Nonlinear regime of electrostatic waves propagation in presence of electron-electron collisions

The effects are presented of including electron-electron collisions in self-consistent Eulerian simulations of electrostatic wave propagation in nonlinear regime. The electron-electron collisions are approximately modeled through the full three-dimensional Dougherty collisional operator [J. P. Dougherty, Phys. Fluids 7, 1788 (1964)]; this allows the elimination of unphysical byproducts due to reduced dimensionality in velocity space. The effects of non-zero collisionality are discussed in the nonlinear regime of the symmetric bump-on-tail instability and in the propagation of the so-called kinetic electrostatic electron nonlinear (KEEN) waves [T. W. Johnston et al., Phys. Plasmas 16, 042105 (2009)]. For both cases, it is shown how collisions work to destroy the phase-space structures created by particle trapping effects and to damp the wave amplitude, as the system returns to the thermal equilibrium. In particular, for the case of the KEEN waves, once collisions have smoothed out the trapped particle population which sustains the KEEN fluctuations, additional oscillations at the Langmuir frequency are observed on the fundamental electric field spectral component, whose amplitude decays in time at the usual collisionless linear Landau damping rate. (C) 2015 AIP Publishing LLC.