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.
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