Relation between space-charge-limiting current and electric field enhancement factor at curved surface cathode |
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Authors: | Liu Guo-Zhi and Yang Zhan-Feng |
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Institution: | 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 |
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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 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. |
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Keywords: | diode space-charge-limiting current intense electron beam |
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