Fractional-dimensional Child-Langmuir law for a rough cathode

M. Zubair, L. K. Ang

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


This work presents a self-consistent model of space charge limited current transport in a gap combined of free-space and fractional-dimensional space (Fα), where α is the fractional dimension in the range 0 < α ≤ 1. In this approach, a closed-form fractional-dimensional generalization of Child-Langmuir (CL) law is derived in classical regime which is then used to model the effect of cathode surface roughness in a vacuum diode by replacing the rough cathode with a smooth cathode placed in a layer of effective fractional-dimensional space. Smooth transition of CL law from the fractional-dimensional to integer-dimensional space is also demonstrated. The model has been validated by comparing results with an experiment.
Original languageEnglish (US)
Issue number7
StatePublished - Jul 1 2016
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-09-20

ASJC Scopus subject areas

  • Condensed Matter Physics


Dive into the research topics of 'Fractional-dimensional Child-Langmuir law for a rough cathode'. Together they form a unique fingerprint.

Cite this