A one-dimensional model of plasma expansion

We consider a system consisting of a vacuum gap separated by two electrodes. A plasma is injected at the cathode and expands. From the sharp plasma boundary, electrons are accelerated towards the anode, forming an electron beam. In this paper, from a two-fluid isentropic Euler system for each species of particles coupled with the Poisson equation, we perform a formal asymptotic analysis, yielding a quasi-neutral model for the plasma region and a Child-Langmuir law for the beam region. These two models are connected through a transmission layer problem. Finally, a numerical validation of this asymptotic model against the original two-fluid model is given.