Fractional-dimensional Child-Langmuir law for a rough cathode

Journal Article · Fri Jul 15 04:00:00 EDT 2016 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4958944· OSTI ID:22600017

This work presents a self-consistent model of space charge limited current transport in a gap combined of free-space and fractional-dimensional space (F{sup α}), 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.

• OSTI ID: 22600017
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 7 Vol. 23; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
CATHODES
COMPARATIVE EVALUATIONS
LANGMUIR FREQUENCY
LAYERS
ROUGHNESS
SPACE CHARGE
SURFACES
TRANSPORT THEORY