Fractional-dimensional Child-Langmuir law for a rough cathode
- SUTD-MIT International Design Centre, Singapore University of Technology and Design, Singapore 487372 and Engineering Product Development, Singapore University of Technology and Design, Singapore 487372 (Singapore)
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, Vol. 23, Issue 7; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
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