Theory of cylindrical and spherical Langmuir probes in the limit of vanishing Debye number

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Abstract
A theory has been developed for cylindrical and spherical probes and other collectors in collisionless plasmas, in the limit where the ratio of Debye length to probe radius (the Debye number λD) vanishes. Results are presented for the case of equal electron and ion temperatures. On the scale of the probe radius, the distributions of potential and density in the presheath appear to have infinite slope at the probe surface. The dimensionless current–voltage characteristic is the same for the cylinder as for the sphere, within the limits of error of the numerical results, although no physical reason for this is evident. As the magnitude of probe potential (relative to space) increases, the current does not saturate abruptly but only asymptotically; its limiting value is about 45% larger than at space potential. Probe currents for small nonzero λD approach those for zero λD only very slowly, showing power-law behavior as function of λD in the limit as λD → 0, with power-law exponents less than unity, resulting in infinite limiting derivatives with respect to λD.