Plasma–wall interaction in an oblique magnetic field: Model of the space-charge sheath for large potentials and small Debye lengths

Abstract

An analytical model of the space-charge sheath around a planar wall is derived for the case of (i) uniform magnetic field B incident at any angle into the wall, (ii) large wall potentials (relative to the plasma temperature): φW≫1, and (iii) Debye length, λd, much smaller than thermal Larmor radius of the attracted species, λm. It is found that, irrespective of the angle of incidence: (i) The potential threshold for a magnetized sheath is φW=O(λd4/λm4); (ii) the characteristic magnetic length in the sheath is λm3/λd2, much larger than λm and proportional to |B|−3 and the plasma flow into the sheath; (iii) the electric field E increases towards the wall and produces a noncycloidal plasma drift that breaks down magnetic insulation. Plasma dynamics in a magnetized sheath consists of an E-aligned region, a drift region, and a B-aligned region. The drift region is relevant only for angles far from normal incidence and the density profile presents spatial oscillations there; for grazing incidence, the B-aligned region is not found. Different scaling laws of the sheath thickness versus wall potential and incidence angle are obtained; in particular, the thickness of a magnetized sheath at parallel incidence is the local Larmor radius at the wall. The applicability of the model to experiments in the ionosphere is commented.