Beyond the child-langmuir limit

Russel Caflisch, M. S. Rosin

Research output: Contribution to journalArticle

Abstract

This article presents a new formulation of the solution for fully nonlinear and unsteady planar flow of an electron beam in a diode. Using characteristic variables (i.e., variables that follow particle paths) the solution is expressed through an exact analytic, but implicit, formula for any choice of incoming velocity v 0, electric field E 0, and current J 0. For steady solutions, this approach clarifies the origin of the maximal current J max, derived by Child and Langmuir for v 0=0 and by Jaffe for v 0>0. The implicit formulation is used to find (1) unsteady solutions having constant incoming flux J 0>J max, which leads to formation of a virtual cathode, and (2) time-periodic solutions whose average flux exceeds the adiabatic average of J max.

Original languageEnglish (US)
Article number056408
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume85
Issue number5
DOIs
StatePublished - May 18 2012

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Time-periodic Solutions
Formulation
Fully Nonlinear
Electron Beam
Diode
formulations
Electric Field
Exceed
Path
cathodes
diodes
electron beams
electric fields
Children

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Beyond the child-langmuir limit. / Caflisch, Russel; Rosin, M. S.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 85, No. 5, 056408, 18.05.2012.

Research output: Contribution to journalArticle

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