Theory of an Electrostatic Probe in a Strong Magnetic Field

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Abstract
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.

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