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Continuum theory of spherical electrostatic probes (frozen chemistry)

Published online by Cambridge University Press:  13 March 2009

William B. Bush  and
Francis E. Fendell
William B. Bush
Affiliation:
University of Southern California, Los Angeles, California
Francis E. Fendell
Affiliation:
TRW Systems, Redondo Beach, California
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Abstract

Continuum theory is adopted to describe the steady, spherically symmetric flow of an unbounded expanse of quiescent, slightly ionized fluid about a perfectly catalytic conductor. The negative charge carrier is taken to be an electron, the potential bias of the probe φP is taken to be negative, and recombination and ionization effects are taken to be negligible. Matched asymptotic expansions are used to study the limit of small Debye number ∈, where ∈ is the ratio of Debye length to conductor radius. The current collected at the probe is found for three ranges of applied potential: small bias, including φp = O(1); moderate bias in which φP = O(log(1/∈)); and large bias in which φP = O(log(1/∈);). The current collected does not saturate (become independent of φP) for the range of c studied here; however, for φP, the current collected remains of order unity while the potential bias varies over several orders of magnitude. The previous asymptotic treatments of this problem, principally due to Su & Lam and to Cohen, are critically reviewed and compared with the results developed here.

Type
Research Article
Information
Journal of Plasma Physics , Volume 4 , Issue 2 , May 1970 , pp. 317 - 334
Copyright
Copyright © Cambridge University Press 1970

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References

REFERENCES

Antosiewicz, H. A. 1964 Bessel functions of fractional order, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, edited by Abramowitz, M. and Stegun, I. A.. Applied Mathematics Series Number 55, U.S. Govern. ment Printing Office, Washington, D.C.Google Scholar
Baum, E. & Chapkis, R. L. 1968 Theory of a spherical electrostatic probe in a continuum gas: au exact solution. Report 06488-6242-RO-00. TRW Systems Group, Rcdondo Beach, California.Google ScholarPubMed
Ciceroni, R. J. & Bowhill, S. A. 1967 Positive ion collection by a spherical probe in a collision-dominated plasma. Report 21, Aeronomy Laboratory, Department of Electrical Engineering, University of Illinois, Urbana, Illinois.Google Scholar
Cohen, I. M. 1963 Phys. Fluids 6, 1492.CrossRefGoogle Scholar
Cohen, I. M. 1967 AIAA J. 5, 78.CrossRefGoogle Scholar
Cohen, I. M. 1968 Ion and electron saturation currents to ellipsoidal Langmuir probes in a slightly ionized, collision-dominated plasma with uniform magnetic field. Report 2281/1, Towno School of Civil and Mechanical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania.Google ScholarPubMed
Lyddon, Thomas D. 1969 Phys. Fluids 12, 356Google Scholar
McAssey, E. V. Jr & Yeh, H. 1969 Electron heat transfer and probe characteristics in a moving non-equilibrium plasma. AIAA paper 69–699 (presented at the 2nd AIAA Plasma and Fluid Dynamics Conference, San Francisco, California).CrossRefGoogle Scholar
Radbill, J. R. 1966 AIAA J. 4, 1195.CrossRefGoogle Scholar
Su, C. H. & Kiel, R. E. 1966 J. Appl. Phys. 37, 4907.CrossRefGoogle Scholar
Su, C. H. & Lam, S. H. 1963 Phys. Fluids 6, 1479.CrossRefGoogle Scholar
Toba, K. & Sayano, S. 1967 J. Plasma Phys. 1, 407.CrossRefGoogle Scholar