Unified Theory for the Langmuir Probe in a Collisionless Plasma

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Abstract
An asymptotic analysis is presented of the Langmuir‐probe problem in a quiescent, collisionless plasma in the limit of large body dimension to Debye length ratio. The structures of the electric potential distribution about spheres and cylinders are analyzed and discussed in detail. It is shown that when the probe potential is smaller than a certain well defined value, there exists no sheath adjacent to the solid surface. At large body potentials, for which a sheath is present, the electric potential distribution is given in terms of several universal functions. Master current‐voltage characteristic diagrams are given which exhibit clearly the effects of all the pertinent parameters in the problem. An explicit trapped‐ion criterion is presented. The general problem with an arbitrary body dimension to Debye length ratio is qualitatively discussed.