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A general solution condition for collisionless sheaths

Published online by Cambridge University Press:  13 March 2009

Geoffrey L. Main  and
S. H. Lam
Geoffrey L. Main
Affiliation:
School of Mechanical Engineering, Georgia Institute of Technolog, Atlanta, Georgia 30332
S. H. Lam
Affiliation:
Mechanical and Aerospace Engineering Department, Princeton University, Princeton, New Jersey 08544
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Abstract

A general solution condition for collisionless sheaths is developed. Previous work has assumed that the Bohm criterion or the generalized Bohm criterion ensures a self-consistent sheath solution. This paper shows that for nonmonotonic collisionless sheath structures, such as double sheaths containing trapped ions, the generalized Bohm criterion is a necessary but not a sufficient condition. The general solution condition developed is always sufficient and the generalized Bohm criterion is shown to be special case of it. The general solution condition is applied to a double emitter sheath containing trapped ions. First, it is shown that the low-energy part of the plasma ion distribution coming into the sheath cannot be neglected as claimed in some analyses, because the shift in mean ion velocity through the pre-sheath (generalized Bohm speed) depends strongly on low-energy ions. Second, it is shown that the presence of trapped ions moves the point of critical self-consistency away from the collisionless sheath-neutral plasma asymptotic match and into the collisionless sheath. Consequently, both the sheath structure and the generalized Bohm speed depend on the amount of trapped ions. Thus collisional effects may dominate the structure of a presumably collisionless sheath through the trapping mechanism and the collisional pre-sheath which determines the low-energy ion component entering the collisionless sheath.

Type
Research Article
Information
Journal of Plasma Physics , Volume 38 , Issue 2 , October 1987 , pp. 287 - 300
Copyright
Copyright © Cambridge University Press 1987

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References

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