Numerical Study of the Influence of Collisions on Oscillations of the Electric Field for the Vlasov-Poisson-Landau Kinetic Equation

The paper is devoted to the numerical study of solutions to the Vlasov-Poisson-Landau kinetic equations for distribution functions with typical length such that , where stands for the Debye radius. It is also assumed that the Knudsen number , where denotes the mean free path of electrons. We use the standard model of plasma of electrons with a spatially homogeneous neutralizing background of motionless heavy ions. We study numerically the one-dimensional (1D) in space kinetic equation with the two-dimensional in velocity space (in three-dimensional spherical coordinates with axial symmetry) Landau collisional operator for small and different . The numerical results are presented and compared with appropriate solutions obtained earlier for the simplified BGK model. The results confirm numerically the existence of high-frequency oscillations of the electric field, which slowly decline due to collisions.