Numerical study of asymptotic damping of electric field long-wave oscillations for the Vlasov equation

Plasma consisting of electrons on neutralizing background of infinitely heavy ions is considered. The Vlasov kinetic equation with initial temperature gradient is numerically simulated in 1D1V space by finite differences for typical lengths of the order of mean free path $r_D\ll L_0\leqslant\lambda_{ei}$. A comparison with the asymptotic formula for an electric field in the linearized case is made [1]. An exponentially weak damping of the oscillating electric field in nonlinear case is shown. Damping rates depend on the parameter $\varepsilon=r_D/L_0$. This circumstance must be taken into account in the kinetic simulation of weakly collision plasmas.