基于库仑定律的二极管空间电荷限制效应研究

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.

Investigations of space charge limited effects in diode with Coulomb's law

Vacuum diode is a critical component of the apparatus which is the source of electron beams, the emitted electrons from the cathode of the diode have strong space charge limited effects. Based on Coulomb's law, the distributions of electric field in cathode-anode gap for different values of the ratio of radius to gap distance, R/D, are calculated numerically with the model of space charge limited effects in a planar vacuum diode. This method can avoid solving a non-linear differential equation which is used to yield the Child-Langmuir law from Poisson's equation. The results demonstrate that the only difference between the results from Coulomb's law and Child-Langmuir law is a modification factor, which is shown to be related to the potential difference across the gap. The results also show that one-dimensional space charge limited law will be a good approximation for the practical planar diode if the parameter R/D is beyond 10, but it can present a large error if the parameter R/D is small. Therefore it should be cautiously used.