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同心球之间空间电荷限制电流的简单理论
Simple theory of space-charge-limited current between concentric sphere
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摘要: 在高功率微波二极管的设计中,空间电荷限制电流因其与二极管的特性及虚阴极形成关系密切而显得十分重要,虽然Langmuir和Blodgett给出的数值解十分有用,但是在实际的应用中一个简单的函数表达式还是更为方便,同时也可以避免当Rc/Ra很大时带来的级数发散问题.第一性原理已经应用在平行板和共轴圆柱之间二维空间电荷限制电流的推导,它的可靠性也已经得到了大量的验证.本文利用第一性原理推导出了同心球二极管空间电荷限制电流的解析表达式,其中的空间电荷场因子通过和经典的朗缪尔电流比较而得到.Abstract: In high-power microwave diode design, the space-charge-limited current is important because of its relation to the diode property and the formation of the virtual cathode. Although the Langmuir–Blodgett law, as a numerical solution, is helpful, a simple functional expression is more convenient for practical research and can avoide the divergence of the series for large Rc/Ra. First principle is used to generalize two-dimensional space-charge-limited current for planar plane capacitor and coaxial cylinders, and its reliability has been examined adequately. In this paper we obtain the functional expression of space-charge-limited current for concentric sphere, and the space-charge field factor in this expression by comparing the classical Langmuir current with the current from concentric sphere.
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