Beyond the child-langmuir limit

R. E. Caflisch, M. S. Rosin

Research output: Contribution to journalArticlepeer-review


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
Issue number5
StatePublished - May 18 2012

ASJC Scopus subject areas

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


Dive into the research topics of 'Beyond the child-langmuir limit'. Together they form a unique fingerprint.

Cite this