Three-dimensional Child-Langmuir law for uniform hot electron emission

Journal Article · Sun May 15 04:00:00 EDT 2005 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.1913612· OSTI ID:20722111

Koh, W S; Ang, L K; Kwan, T J.T. ^[1]

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1. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (Singapore)

This paper presents a three-dimensional (3D) model of Child-Langmuir (CL) law for uniform hot electron emission in planar and cylindrical gap, including the effects of finite emission energy. It is found that the enhancement of 3D CL law (in terms of 1D CL law) can be written in a general form of J{sub C}[3D]/J{sub C}[1D]=1+FxG, where F is the normalized mean position of 1D electron flow in classical, weakly relativistic, and quantum regime, and G is the geometrical correction factor depending on the geometrical properties of the finite emitting patches on the cathode. In particular, we present the analytical solutions for various emitting patches, such as rectangle, ellipse, square, circle, triangle, and polygon, which agree very well with 3D particle-in-cell simulation. For a cylindrical gap of finite width, it is also found that the convergent flow (cathode outside) has larger enhancement than the divergent flow (cathode inside) at a given aspect ratio of outer radius to inner radius of the gap. Smooth transition from various operating regimes is demonstrated.

• OSTI ID: 20722111
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 5 Vol. 12; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
COMPUTERIZED SIMULATION
ELECTRON EMISSION
PLASMA SIMULATION
RELATIVISTIC PLASMA
THREE-DIMENSIONAL CALCULATIONS