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Analytic expression for the electric potential in the plasma sheath

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2 Author(s)
Sheridan, T.E., Jr. ; Dept. of Phys. & Astron., Iowa Univ., Iowa City, IA, USA ; Goree, J.A.

An expression for the spatial dependence of the electric potential in a collisionless and source-free planar plasma sheath is presented. This expression is derived by analogy with Child's law and approaches Child's law asymptotically as the potential drop φW across the sheath becomes large, |eφW/kTe|>104. Here k is Boltzmann's constant, Te is the electron temperature, and e is the electronic charge. Comparison with numerical solutions of the model equations indicates that the sheath thickness and potential variation predicted by this improved Child's law are accurate for |eφW/kTe|>10. In contrast, the authors find that Child's law is accurate only when |e φW/kTe|>104

Published in:

Plasma Science, IEEE Transactions on  (Volume:17 ,  Issue: 6 )