CONCENTRATIONS IN THE ONE-DIMENSIONAL VLASOV-POISSON EQUATIONS - ADDITIONAL REGULARIZATIONS

We consider the one component Vlasov-Poisson equations in one dimensio n. These equations model a collisionless plasma of electrons moving th rough a uniform background of ions, and serve as a simpler analog of t he two-dimensional incompressible Euler equations in vorticity form. W e study the behavior of weak solutions to the Vlasov-Poisson equations which arise from non-smooth electron sheet initial data (an electron sheet describes a concentrated beam of electrons). We regularize the V lasov-Poisson equations with electron sheet initial data in two differ ent ways, smoothing the initial condition and by including collisions modeled by the Fokker-Planck equations. We perform numerical simulatio ns with a finite difference method to examine the solution of the Vlas ov-Poisson equations obtained in the limit of vanishing regularization . (C) 1998 Elsevier Science B.V.