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

Chen, S. H.; Tai, L. C.; Liu, Y. L.; Ang, L. K.; Koh, W. S.
February 2011
Physics of Plasmas;Feb2011, Vol. 18 Issue 2, p023105
Academic Journal
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.


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