An Existence Result for a Stationary Vlasov–Poisson Model with Source Term

Abstract

In the low energy part of an ion accelerator, the ion beam reaches the first accelerating device through a drift tube where a residual neutral gas is present. A process of ionization takes place and secondary electrons and ions are created. We analyze the coupling between these secondary particles, the beam density and the electrical potential.In a previous article, 2 we proved that a stationary Vlasov-Poisson problem with ionization source terms, which, at first sight, seems the natural model for this system, does not admit solutions. To overcome this difficulty, we propose here a heuristic model which consists of modifying the electron source term. In this new frame, we prove that the problem can be solved and we give numerical examples.