Charge transport problem

In a recent report (UCID 17346, ''Relativistic Particle Beam in a Semi-Infinite Axially Symmetric conducting channel extending from a perfectly conducting plane,'' Dec. 13, 1976) Cooper and Neil demonstrate that the net charge transported by a beam pulse injected into a channel of finite conductivity equals the charge of the beam itself. The channel is taken to be infinite in the positive z direction, has finite radius and is terminated by a conducting ground plane at z =0. This result is not an obvious one, and it is restricted in its applicability by the special model assumed for the channel. It is the purpose to explain the result of Cooper and Neil in more qualitative terms and to make similar calculations using several other channel models. It must be emphasized that these calculations are not concerned with the fate of the transported charge after the pulse has stopped, but rather with how much charge leaves the ground plane assuming the pulse does not stop