Multi-dimensional effects in space-charge-limited emission: an improved voltage-current relation for parallel plate geometry

Summary form only given. Previous analysis (Luginsland, Yau, Gilgenbach, Phy. Rev. Lett., vol. 77, no. 2, p. 4668) of space-charge-limited emission in simple two-dimensional parallel plate geometry indicated that the current-voltage relationship in this geometry was not well approximated in all cases by the simple one-dimensional Child-Langmuir Law. This previous analysis used particle-in-cell code calculations to determine the limiting current for a given voltage and given beam width. This analysis assumed that the beam current density was uniform. A new analysis, based upon numerical solution of the Poisson equation, makes no assumption about the current density, but leaves the current density distribution as an unknown function to be determined. The numerical approach that has been developed to simultaneously determine the electrostatic potential and the beam current density will be described. The numerical method is used to generate a current-voltage relationship for the two-dimensional parallel plate geometry. These results are compared against particle-in-cell code calculations based upon two different approaches to modeling space-charge-limited emission.