Current-voltage characteristics of an electron-emitting, satellite in the ionosphere

Abstract

The limitation on the current that a sphere at a large positive potential ϕ can draw from a surrounding collisionless plasma in a magnetic field is investigated. The model assumes that for eϕ ≫ kTe the ions are excluded from the region of high potential surrounding the sphere. This region increases in size as ϕ increases, thus presenting an increased cross-sectional area through which electrons can be collected from the plasma along magnetic field lines. We suggest that there is a critical density at which the electron cloud surrounding the positive body is sufficiently turbulent that the electrons are free to diffuse radially across magnetic field lines and thereby reach the sphere. This model yields a saturation current I ∝ ϕ/lnϕ, which scales directly with the density, thermal velocity, and square of the body size. At high background electron concentrations a space-charge-limited flow model that predicts I ∝ ϕ6/7 is more applicable, whereas the more pessimistic limit of I ∝ ϕ1/2, which follows from the conservation of the single particle constants of motion in time invariant electric and magnetic fields, is appropriate when the background electron concentration is low.