Theory of ion-matrix-sheath dynamics

The time evolution of a one-dimensional, uni-polar ion sheath (an “ion matrix sheath”) is investigated. The analytical solutions for the ion-fluid and Poisson’s equations are found for an arbitrary time dependence of the wall-applied negative potential. In the case that the wall potential is large a...

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Bibliographic Details
Published inAIP advances Vol. 8; no. 1; pp. 015202 - 015202-13
Main Authors Kos, L., Tskhakaya, D. D.
Format Journal Article
LanguageEnglish
Published Melville American Institute of Physics 01.01.2018
AIP Publishing LLC
Subjects
Mathematical analysis
Sheaths
Time dependence
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Summary:The time evolution of a one-dimensional, uni-polar ion sheath (an “ion matrix sheath”) is investigated. The analytical solutions for the ion-fluid and Poisson’s equations are found for an arbitrary time dependence of the wall-applied negative potential. In the case that the wall potential is large and remains constant after its ramp-up application, the explicit time dependencies of the sheath’s parameters during the initial stage of the process are given. The characteristic rate of approaching the stationary state, satisfying the Child–Langmuir law, is determined.
ISSN:2158-3226
2158-3226
DOI:10.1063/1.5017654