中国物理B ›› 2010, Vol. 19 ›› Issue (7): 75207-075207.doi: 10.1088/1674-1056/19/7/075207

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Relation between space-charge-limiting current and electric field enhancement factor at curved surface cathode

刘国治, 杨占峰   

  1. Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi'an Jiaotong University, Xi'an 710049, China; Northwest Institute of Nuclear Technology, Xi'an 710024, China
  • 收稿日期:2009-09-01 出版日期:2010-07-15 发布日期:2010-07-15

Relation between space-charge-limiting current and electric field enhancement factor at curved surface cathode

Liu Guo-Zhi (刘国治), Yang Zhan-Feng (杨占峰)   

  1. Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi'an Jiaotong University, Xi'an 710049, China; Northwest Institute of Nuclear Technology, Xi'an 710024, China
  • Received:2009-09-01 Online:2010-07-15 Published:2010-07-15

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摘要： A two-dimensional solution of space-charge-limiting current for a high current vacuum diode with a spherical cathode is presented. The relation between space-charge-limiting current and electric field enhancement factor at the cathode surface for the diode with a curved surface cathode is also discussed. It is shown that compared with the current given by the conventional Child—Langmuir law, which describes the one-dimensional space-charege-limiting current, the two-dimensional space-charge-limiting current in such a diode is enhanced due to the electric-field enhancement along the cathode surface. Among practical parameter ranges, enhancement factor ηb approximately satisfies ηb ≈ Aβn, where β is the electric field enhancement factor at the cathode surface, and n is a constant between 1 and 2, which is confirmed to be universal for the diodes with curved surface cathodes.

Abstract: A two-dimensional solution of space-charge-limiting current for a high current vacuum diode with a spherical cathode is presented. The relation between space-charge-limiting current and electric field enhancement factor at the cathode surface for the diode with a curved surface cathode is also discussed. It is shown that compared with the current given by the conventional Child—Langmuir law, which describes the one-dimensional space-charege-limiting current, the two-dimensional space-charge-limiting current in such a diode is enhanced due to the electric-field enhancement along the cathode surface. Among practical parameter ranges, enhancement factor $\eta_{\rm b}$ approximately satisfies $\eta_{\rm b} \simeq A \beta^{n}$, where $\beta$ is the electric field enhancement factor at the cathode surface, and n is a constant between 1 and 2, which is confirmed to be universal for the diodes with curved surface cathodes.

Key words: diode, space-charge-limiting current, intense electron beam

中图分类号:  (Magnetohydrodynamic generators and thermionic convertors; plasma diodes)

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