2D Planar PIC Simulation of Space Charge Limited Current With Geometrical Parameters, Varying Temporal-Profile and Initial Velocities

In this paper, we simulated the space-charge effect current by the full electromagnetic particle-in-cell (PIC) code UNIPIC in a planar gap. Compared with Lau’s numerical work, we introduce the applied voltage
$U$
, gap separation
$D$
, suppression magnetic field
$B$
, electron-injection energy spectra
$f(E)$
and temporal profiles
$f(t)$
as the factors affecting the current densities and the particle distributions. It is shown that
$U$
and
$D$
could change the particle distribution significantly, causing the electrons’ escape, while they bring little impact on the ratio of 2-D Child-Langmuir current to the classical 1-D value
$J_{\mathrm {CL}}(2)/J_{\mathrm {CL}}$

(1)
. Considering the temporal profile, it is interesting that the transported current density is inversely going to decrease when the injection rise time is much smaller than the transit time, which explores the smaller temporal profile numerically compared with Valfells’s experiments. Last, the preliminary simulation of the combined effect of temporal profile and initial electron energy spectra is presented, and it is evident that the thermal electrons obeying the Boltzmann distribution generate a larger transported current density than the photoelectron under exponential distribution, which might be an inspiration to the engineering application.