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

Yongpeng Zhang; Guozhi Liu; Zhanfeng Yang; Qingzi Xing; Hao Shao; Renzhen Xiao; Huaqiang Zhong; Yuzheng Lin
April 2009
Physics of Plasmas;Apr2009, Vol. 16 Issue 4, p044511
Academic Journal
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.


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