Time-dependent space-charge limited electron flow

Space charge limited current serves as a basic theoretical prediction for application of high current diodes and other vacuum electronics devices in field of non-neutral plasma physics. Classical Child-Langmuir law (CL law) analytically demonstrates maximum steady current density (space-charge-limited current density) transported before virtual cathode formation across a certain distance under a potential difference. In 2002, Á. Valfells et al. push edits boundary further by deriving a much higher density of electron beam than anticipated by CL law under short-pulse situation¹. However, both above only apply to temporally-steady status of electron flow and time-dependence of injection current density has not yet been investigated thoroughly.