Particle Methods for the One-Dimensional Vlasov–Poisson Equations

Abstract

We consider in this paper the numerical solution of the one-dimensional Vlasov-Poisson equations which describe the evolution of a noncollisional plasma when neglecting the magnetic effects. The numerical method, extensively used in plasma physics is based on a particle model where the distribution function of each species of charged particles is approximated by a sum of delta functions. The paper is devoted to the study of the convergence and the accuracy of the particle method in the periodic case.