A discrete approximation to the one-dimensional vlasov-poisson system

Abstract

In its simplest form the kinetic equation of plasma is the one-dimensional Vlasov-Poisson system

This system describes the motion of a plasma in one space dimension under the electrostatic approximation of zero magnetic field. The function f is the phase space distribution function (for electrons), f₀ is the initial distribution and b is the fixed background distribution of opposite charge. In this paper we develop a discrete approximation to (1.1). The system is first discretized in x and v, but not in t and the trajectories of (1.1) are approximated by the trajectories of this discretized problem. Time discretization is then introduced and the space discretized system is approximated by the space-time discretization which then becomes the final approximation to (1.1).