Space-charge effect of the time-varying electron injection in a diode: classical and relativistic regimes

Conventionally, space-charge (SC) limited current density is defined as the maximal cur- rent density allowed to traverse a diode under a DC voltage when a time-invariant flow is injected from the cathode. In this work, we study the SC limited current density under a time-varying injection for both classical and relativistic regimes and determine the maxi- mal amount of limited current density under certain conditions. Our simulations show that it is unlikely that a time-varying injection emitted from cathode exceeds the known SC limits, in either classical or relativistic regime.