## Analysis and asymptotics of a one-dimensional ion extraction model.(English)Zbl 0829.76096

Summary: A one-dimensional model for ion extraction from a plasma is investigated. The analysis is made using by a singular perturbation of the transport equations based on the smallness of 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.

### MSC:

 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 82D10 Statistical mechanics of plasmas