A singular perturbation problem arising in the modelling of plasma sheaths ∗

Consider the interaction of a flowing plasma with a planar Langmuir probe [2]. Assume that the plasma flows in the plane of the probe surface and that the plasma consists solely of positive ions with density n+ and electrons with density ne. Downstream of the probe, the ions are moving with a velocity of u = (ui, uv +uF) and (u0, uF) is the constant flow velocity of the ion