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Two-dimensional electromagnetic (EM) 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...
The one-dimensional Child-Langmuir law has been extended to two dimensions by numerical simulation in planar geometries . The space charge limit in two dimensions is examined. Simulations were done with no applied magnetic field as well as with a large longitudinal magnetic field to restrict motion of particles to 1D. The ratio of the observed current density limit JCL2 to the theoretical one-dimensional...
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