The problem of space-charge limited current flow between two electrodes with a finite particle injection velocity is revisited theoretically, and numerically with particle-in-cell (PIC) simulations. Using an Eulerian approach, we obtain a complete analytical solution for both the space-charge limited (SCL) current (which agrees with previously derived expressions), as well as the spatial profiles of all physical quantities. These analytical solutions are unique in that they apply to both fluid, and kinetic particle descriptions of the system, and we demonstrate how they can be used to verify the accuracy and correctness of certain aspects of numerical simulation codes. For injection currents above the SCL limit, the PIC simulations show that the system becomes unstable, and self-excited space charge oscillations are generated with a period of the order of the particle transit time between the electrodes. In this oscillatory regime, the maximum time-averaged current that can be t...

中文翻译：

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重新探究有限注入速度下的空间电荷限制电流

理论上重新讨论了空间注入受限电流在两个电极之间以有限的粒子注入速度流动的问题，并通过单元内粒子（PIC）仿真在数值上进行了重新讨论。使用欧拉方法，我们可以获得空间电荷受限（SCL）电流（与先前得出的表达式一致）以及所有物理量的空间分布的完整解析解决方案。这些分析解决方案的独特之处在于它们既适用于系统的流体描述，也适用于动力学粒子描述，并且我们演示了如何将其用于验证数值模拟代码某些方面的准确性和正确性。对于高于SCL极限的注入电流，PIC仿真表明系统变得不稳定，并且自激空间电荷振荡以电极之间的粒子渡越时间的周期产生。在这种振荡状态下，最大时间平均电流可以达到...