Electrostatic Probe in a Collisionless Plasma

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Abstract
The theory developed differs from classical Langmuir theory in that the potential at the sheath's edge need not be the ambient potential and the velocity distribution function for each species is determined for all points in space, rather than at the probe surface only. The range of validity of the classical theory is discussed quantitatively by presentation of several solutions for the spatial distributions of potential. Examination of an earlier result given for a moderately negative probe and mono-energetic ions reveals an inconsistent formulation; an exact result is presented. A solution for the infinite collisionless field of arbitrary potential distribution is derived, and an approximate form of this solution is compared with numerical results.

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