Collisional effects in weakly collisional plasmas: nonlinear electrostatic waves and recurrence phenomena

Abstract:

The longstanding problem of collisions in plasmas is a very fascinating and huge topic in plasma physics. The ‘natural’ operator that describes the Coulombian interactions between charged particles is the Landau (LAN) integral operator. The LAN operator is a nonlinear, integro-differential and Fokker-Planck type operator which satisfies the H theorem for the entropy growth. Due to its nonlinear nature and multi-dimensionality, any approach to the solution of the Landau integral is almost prohibitive. Therefore collisions are usually modeled by simplified collisional operators. Here collisional effects are modeled by i) the one-dimensional Lenard-Bernstein (LB) operator and ii) the three-dimensional Dougherty (DG) operator.

In the first case i), by focusing on a 1D-1V phase space, we study recurrence effects in a weakly collisional plasma, being collisions modeled by the LB operator. By decomposing the linear Vlasov-Poisson system in the Fourier-Hermite space, the recurrence problem is investigated in the linear regime of the damping of a Langmuir wave and of the onset of the bump-on-tail instability. The analysis is then confirmed and extended to the nonlinear regime through a Eulerian collisional Vlasov-Poisson code. Despite being routinely used, an artificial collisionality is not in general a viable way of preventing recurrence in numerical simulations. Moreover, recursive phenomena affect both the linear exponential growth and the nonlinear saturation of a linear instability by producing a fake growth in the electric field, thus showing that, although the filamentation is usually associated with low amplitude fluctuations contexts, it can occur also in nonlinear phenomena.

On the other hand ii), the effects of electron-electron collisions on the propagation of nonlinear electrostatic waves are shown by means of Eulerian simulations in a 1D-3V (one dimension in physical space, three dimensions in velocity space) phase space. The nonlinear regime of the symmetric bump-on-tail instability and the propagation of KEEN waves are discussed in detail. 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. Moreover, collisional effects are much stronger when the system exhibits nonlinear features.