Quasi-Neutral Limit for Euler-Poisson System

Summary.

This paper provides a rigorous proof of the quasi-neutral limit for the Euler-Poisson system on a bounded domain in one space dimension. The most general case is being considered when the plasma is sustained by ionization. A wide range of plasmas, from collisionless to highly collisional, is permitted. At the plasma center, the ions are assumed to be at rest, and essentially quasi-neutral initial data are prescribed. The theorem asserts that the quasi-neutral limit is obtained until the ion velocity reaches the ion-sound speed. In addition, formal matched asymptotic expansions are given which describe the solution in its passage from the plasma center to the wall.