Numerical analysis of the Vlasov equation preliminary results

We numerically solve a Vlasov equation in two dimensions using the semi-Lagrangian method with a bi-linear interpolation before each advection. We apply this method to a particular case of systems with long-range interactions and two-stream instability. We use the initial conditions as a Maxwellian distribution with perturbations to explore the evolution through the quasi-stationary states to the stability. We analyze this evolution through the electron density, potential, and electric field, where we find the damped oscillations of the two-stream instability. We also explore the behavior of the mainstream affected by the perturbation stream by using the phase space added to the distribution function graphic.