Theory of an Electrostatic Probe in a Strong Magnetic Field

If the magnetic field is so strong as to impair collective transverse drifts, all the charges supplied to the probe come mainly from a long tube of force, whose section is about one Larmor radius larger than the probe; while a diffusion process, more efficient than ordinary drifts, continuously exchanges particles between the inside and the rest of the plasma. A one-dimensional model of this process is proposed, leading to an integro-differential Poisson's equation, which has been studied for the case in which the collected particles are very fast. The solution consists of a chargeless, slowly decaying potential which describes the geometrical screening effect of the probe; while in the sheath an approximate boundary-layer solution matches with the probe's potential.