A volume of fluid method for a two-dimensional plasma expansion problem

This paper is devoted to the numerical study of a two-dimensional model for plasma expansion in vacuum. The plasma, constituted of ions and electrons, is injected from a part of the cathode and undergoes a thermal expansion. Due to the positive anode potential, electrons are emitted from the plasma–vacuum interface, forming an electron beam. Moreover, electron emission produces a reaction-pressure force which slows down the plasma expansion. Previous works [P. Degond, C. Parzani, M.H. Vignal, Un modéle d’expansion de plasma dans le vide, C. R. Acad. Sci. Paris 335 (2002) 399; P. Degond, C. Parzani, M.H. Vignal, Plasma expansion in vacuum: modeling the breakdown of quasineutrality, SIAM, Multiscale Model. Simul. 2 (2003) 158; P. Degond, C. Parzani, M. H. Vignal, A model for plasma expansion in the vacuum, in: Proceedings of the Conference “Free Boundary Problems 2002”, Trento, June 2002] have been realized to describe this process in the one-dimensional case. One of the main goal is to get a precise description of the interface motion. The aim of the present work is to explore more realistic cases investigating a two-dimensional model. However, considering upper dimensions yields to new difficulties essentially from a numerical point of view. Indeed, in the 2D space case, the plasma–vacuum interface is no more a point but a curve. Therefore, in this work, after proposing a two-dimensional model, we focus on the interface tracking using a volume of fluid method. We perform numerical simulations on two test cases. The first test case consists in a two-dimensional fluid compression for which an analytic solution is known. The second test case is the plasma bubble expansion between two electrodes.