Space-Charge-Limited Electron Flow in a Drift Space

The classical Child-Langmuir (CL) law predicts the maximum current density that can be obtained from a planar diode. Recently the 1D classical CL law has been extended to multi-dimensional models, quantum models and short pulse models. In this paper, we look beyond the accelerating stage (in the diode) and focus on the electron flows in the drift space at high power microwave devices, where space charge effects. In particular, we study the space-charge-limited (SCL) electron flows in drift space in classical, relativistic and quantum regimes, including the effects of finite emission and short pulse. The calculations are verified using particle-in-cell (PIC) simulation. The results are also compared to previous calculations on the SCL flows in a diode model.