On a penalization of the Child–Langmuir emission condition for the one-dimensional Vlasov–Poisson equation

Article type: Research Article

Authors: Degond, P. | Raviart, P.A.

Affiliations: Centre de Mathématiques et Leurs Applications (CMLA), Ecole Normale Supérieure de Cachan, 61, avenue du Président Wilson, 94235 Cachan Cedex, France | Centre de Mathématiques Appliquées, Ecole Poly technique, 91128 Palaiseau Cedex, France

Abstract: In a preceding paper, an asymptotic analysis of the one dimensional Vlasov–Poisson was presented. That analysis accounted for the “Child–Langmuir regime”, when the injected particle energy is small compared with the applied external bias. In the present paper, we propose a numerical algorithm for solving the Vlasov-Poisson equations in the “Child–Langmuir regime”. The crucial step of the algorithm is a penalization of the “Child–Langmuir emission condition”, which is proved to converge in the one-dimensional case.

DOI: 10.3233/ASY-1992-6101

Journal: Asymptotic Analysis, vol. 6, no. 1, pp. 1-27, 1992