Analysis and asymptotics of a one-dimensional ion extraction model

Article type: Research Article

Authors: Abdallah, Naoufel Ben | Mas-Gallic, Sylvie | Raviart, Pierre-Arnaud

Affiliations: CMAP (URA CNRS 756), Ecole Poly technique, 91128 Palaiseau Cedex, France

Abstract: In this paper a one-dimensional model for ion extraction from a plasma is investigated. The analysis is achieved thanks to a singular perturbation of the transport equations based on the smallness of both, the Debye length and the thermal voltage. The convergence of the perturbed problems to a limit problem, where a “free surface” appears, is proved (in one dimension the free surface reduces to a single point). The analysis is first done for finite temperature ions. For cold ions, the analysis can be carried out further: a boundary layer lying at the free surface is exhibited and analyzed.

DOI: 10.3233/ASY-1995-10101

Journal: Asymptotic Analysis, vol. 10, no. 1, pp. 1-28, 1995