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真空二极管是电子束源装置中的一个关键部件,其阴极发射的电子束进入二极管阴阳极间隙区会产生很强的空间电荷限制效应.本文针对平板真空二极管中的空间电荷限制效应物理模型,从库仑定律的积分形式出发,选取了不同参数的阴极半径与阴阳极间隙距离之比,计算得到了真空二极管阴阳极间隙区的电场分布情况,从而避免了采用Poisson方程求解时需要处理复杂的非线性偏微分方程这一问题.结果表明,基于库仑定律的计算结果与从Child-Langmuir定律分析得到的结果仅相差一个与二极管极板边界条件有关的修正量.当二极管阴极半径与阴阳极间隙距离之比R/D>10时,一维空间电荷限制定律将是一个较好的近似结果,当R/D较小时,用该定律计算误差较大,在实际物理问题中需要谨慎使用.
The vacuum diode is a key component in the electron beam source device, and its cathode emits electron beam into the cathode-anode gap region of the diode to produce a strong space charge limiting effect.In this paper, the physical model of the space charge limiting effect in the flat-panel vacuum diode Coulomb’s law, we choose the ratio of the cathode radius to the distance between the cathode and the anode. The distribution of the electric field in the gap between the anode and the cathode of the vacuum diode is calculated, which avoids the need to deal with complex nonlinearity Partial differential equations.The results show that the calculated results based on Coulomb’s law differ from the results obtained from Child-Langmuir’s law only by a correction amount related to the diode plate boundary conditions.When the diode cathode radius and the anode-cathode gap distance When R / D> 10, the one-dimensional space charge limitation law will be a good approximation. When the R / D is small, the law is used to calculate the error and need to be used with caution in practical physics.