Two-dimensional electromagnetic Child–Langmuir law of a short-pulse electron flow

Abstract

Two-dimensional electromagnetic particle-in-cell simulations were performed to study the effect of the displacement current and the self-magnetic field on the space charge limited current density or the Child–Langmuir law of a short-pulse electron flow with a propagation distance of ζ and an emitting width of W from the classical regime to the relativistic regime. Numerical scaling of the two-dimensional electromagnetic Child–Langmuir law was constructed and it scales with (ζ/W) and (ζ/W)2 at the classical and relativistic regimes, respectively. Our findings reveal that the displacement current can considerably enhance the space charge limited current density as compared to the well-known two-dimensional electrostatic Child–Langmuir law even at the classical regime.