Potential buildup on an electron-emitting ionospheric satellite

An experiment in which a continuous beam of high-energy electrons is emitted from a satellite (e.g. to produce an artificial aurora or to map the geomagnetic field) will be jeopardized if the satellite potential becomes so high that the beam electrons cannot escape. The potential acquired by the satellite is determined by the condition that it collect from the ambient ionosphere a current equal to the emitted current. The geomagnetic field severely limits the current that may be emitted. For example, a spherical satellite of radius 1.5 meters in the F layer cannot emit more than about 40 ma of kilovolt electrons.