Fractional-dimensional Child-Langmuir law for a rough cathode
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 01, 2016
- Source ID
- 10.1063/1.4958944
Entities
People
- Lay Kee Ang
- Muhammad Zubair
Organizations
- Air Force Office of Scientific Research
- Ministry of Education
- Singapore University of Technology and Design