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 current 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 maximal amount of limited current density under certain conditions. Our simulations show that it is unlikely that a time-varying injection emitted from the cathode exceeds the known SC limits, in either the classical or relativistic regime.