Abstract
A unified radial model of the collisionless sheath for both cylindrical and spherical Langmuir probes is developed. The I–V characteristics are obtained and analytically fitted, taking into account both the probe radius and the probe biasing potential as parameters of the model. This parameterization allowed us to obtain an analytical approach for the potential profile, the floating potential and the sheath edge according to the Nachmann and Tahn criterion [M. Nachmann and P. C. Tahn, IEEE Trans. Plasma Sci. 19, 423 (1991)]. An alternative criterion for the sheath edge is established. This is referred to as the curvature criterion and it matches the Bohm criterion in the limiting case of planar Langmuir probes. The case of a planar sheath is obtained as a limiting case of the model when the probe radius is large enough.
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