Simple solutions for relativistic generalizations of the Child-Langmuir law and the Langmuir-Blodgett law

Journal Article · Wed Apr 15 00:00:00 EDT 2009 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.3124135· OSTI ID:21277058

Yongpeng, Zhang ^[1]; Guozhi, Liu; Zhanfeng, Yang; Hao, Shao; Renzhen, Xiao ^[2]; Qingzi, Xing; Huaqiang, Zhong; Yuzheng, Lin ^[1]

---

1. Department of Engineering Physics, Key Laboratory of High Energy Radiation Imaging Fundamental Science for National Defense, Tsinghua University, Beijing 100084 (China)
2. Northwest Institute of Nuclear Technology, P.O. Box 69-13, Xi'an 710024 (China)

In this paper, the Child-Langmuir law and Langmuir-Blodgett law are generalized to the relativistic regime by a simple method. Two classical laws suitable for the nonrelativistic regime are modified to simple approximate expressions applicable for calculating the space-charge-limited currents of one-dimensional steady-state planar diodes and coaxial diodes under the relativistic regime. The simple approximate expressions, extending the Child-Langmuir law and Langmuir-Blodgett law to fit the full range of voltage, have small relative errors less than 1% for one-dimensional planar diodes and less than 5% for coaxial diodes.

• OSTI ID: 21277058
• Journal Information: Physics of Plasmas, Vol. 16, Issue 4; Other Information: DOI: 10.1063/1.3124135; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ELECTRIC CURRENTS
ONE-DIMENSIONAL CALCULATIONS
SPACE CHARGE
STEADY-STATE CONDITIONS
THERMIONIC DIODES