Short-pulse space-charge-limited electron flows in a drift space

In this paper, the space-charge-limited (SCL) electron flows in a drift space is studied by including the effect of finite electron pulse length, which is smaller than the gap transit time. Analytical formulas are derived to calculate the maximum SCL current density that can be transported across a drift space under the short-pulse injection condition. For a given voltage or injection energy, the maximum current density that can be transported is enhanced by a large factor (as compared to the long-pulse or steady-state case), and the enhancement is inversely proportional to the electron pulse length. In drift space, the effect of pulse expansion is important at very short-pulse length, and the short-pulse enhancement factor is smaller as compared to a diode. The enhancement factor will be suppressed when the injection energy is larger than the electron rest mass, and effect of pulse expansion is less critical at relativistic energy. The analytical formulas have been verified by performing a particle-in-cell simulation in the electrostatic mode.