2-DIMENSIONAL CHILD-LANGMUIR LAW

By considering uniform emission of electrons over a finite strip of wi dth W in a planar gap of gap separation D, we extend the classical one -dimensional Child-Langmuir law to two dimensions. The limiting curren t density in two dimensions J(CL)(2) in units of the classical one-dim ensional value J(CL)(1) is found to be a monotonically decreasing func tion of W/D. More surprisingly, it is virtually independent of the ext ernal magnetic field that is imposed along the mean flow. These result s were obtained from two different simulation codes, OOPIC and MAGIC.