从空间电荷限制流假设、Poisson方程及电子正则动量守恒关系出发,推导了平板形、同轴圆柱和共顶点同轴圆锥三种导体构形的空间电荷流随传导电流变化的广义Poisson方程,给出了求解方法及解的基本特征,分析比较了三种导体构形空间电荷限制流的基本性质.通过推导,计算和分析可得:各种电压条件下传导电流对空间电荷限制(SCL) 流的作用效果不一样,电压越高传导电流提高磁绝缘程度的作用越显著;当几何因子(即高阻抗)较小时其它两种导体的SCL流与平板形相差较大,几何因子较大时与平板形十分接近;同样电压条件下负极性的SCL流比平板形小、正极形正好相反,而相同几何因子条件下同轴圆筒的SCL流比共顶点同轴圆锥的小;在分析研究低阻抗MITL时,采用SCL流的平板近似不会带来大的误差.在描述时变脉冲作用于MITL时,可以通过对SCL流随电压、传导电流变化的曲面函数插值的方法确定各个时刻的磁绝缘状态.

A generalized equation, which governs the dependence of space charge current flow on conducting current in three relativistic configurations, is deduced from Poisson's equation with assumption of space-charge-limited flow and electrons' canonical momentum conservation. A method for solution to the equation is introduced and the characteristic of the solution for the three configurations is discussed. It is concluded that for these configurations the effect of conducting current on magnetic insulation is much significant with increase of anode voltage, and that for the same anode voltage their SCL flows will behave differently when their geometrical factors become small, with the SCL flow of the two non-plane conductors smaller than that of the plane conductor for negative polarity and larger for positive polarity. However, for those non-plane conductors with great geometrical factors it is reasonable to directly adopt plane's SCL flow considering the little difference between each other. In practice, the magnetic insulation state of conductor carrying time-varying pulse,can be determined conveniently by interpolating from a surface which is formed by SCL flows for various conducting currents and voltages.