Numerical matching of the sheath and presheath solutions for a spherical probe in radial-motion theory

Journal Article · Wed Oct 15 04:00:00 EDT 2014 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4897385· OSTI ID:22299721

Din, Alif ^[1]; Kuhn, Siegbert ^[2]

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1. Theoretical Physics Division, PINSTECH, P.O. Nilore, 44000 Islamabad (Pakistan)
2. Association EURATOM-ÖAW, Institute for Theoretical Physics, University of Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria)

The theory of positive-ion collection by a probe immersed in a low-pressure plasma was reviewed and extended by Allen, Boyd, and Reynolds [Proc. Phys. Soc. 70, 297 (1957)]. For a given value of the ion current, the boundary values of the matched “nonneutral” or “sheath” solution V{sup ~}{sub nn}{sup (m)}(r; r{sub m}) were obtained from the “quasineutral” or “presheath” solution V{sup ~}{sub qn}(r) by choosing the small potential and electric-field values corresponding to some large “matching radius” r{sub m}. Here, a straightforward but efficient numerical method is presented for systematically determining an optimal value of the matching radius at which the presheath and sheath solutions are joined to yield the “matched” potential profile. Some suitable initial matching radius r{sub m1} is chosen and the related potential and electric-field values of the quasineutral solution are calculated. Using these as boundary conditions, Poisson's equation is integrated to yield the matched nonneutral solution including the corresponding potential at the probe surface. This procedure is repeated for increasing values r{sub m2}, r{sub m3},…. until the resulting potential at the probe surface becomes practically constant. The corresponding value of r{sub m} is taken as the “optimal” matching radius r{sub mo} at which the presheath and sheath solutions are ultimately joined to yield the “optimal” matched potential profile in the entire plasma-probe transition region. It is also shown that the Bohm criterion is inapplicable in the present problem.

• OSTI ID: 22299721
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 10 Vol. 21; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MATHEMATICAL SOLUTIONS
POISSON EQUATION
POTENTIALS
PROBES
SPHERICAL CONFIGURATION