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

摘要

Summary form only given. Previous analysis (Luginsland, Yau,Gilgenbach, Phy. Rev. Lett., vol. 77, no. 2, p. 4668) ofspace-charge-limited emission in simple two-dimensional parallel plategeometry indicated that the current-voltage relationship in thisgeometry was not well approximated in all cases by the simpleone-dimensional Child-Langmuir Law. This previous analysis usedparticle-in-cell code calculations to determine the limiting current fora given voltage and given beam width. This analysis assumed that thebeam current density was uniform. A new analysis, based upon numericalsolution of the Poisson equation, makes no assumption about the currentdensity, but leaves the current density distribution as an unknownfunction to be determined. The numerical approach that has beendeveloped to simultaneously determine the electrostatic potential andthe beam current density will be described. The numerical method is usedto generate a current-voltage relationship for the two-dimensionalparallel plate geometry. These results are compared againstparticle-in-cell code calculations based upon two different approachesto modeling space-charge-limited emission