Transverse deections in a cavity due to the short-range longitudinal wake

This note documents a set of expressions used to explore the issue of whether or not it is reasonable to consider a conventional positron source for a Tesla formatted beam. The critical issue is that of energy deposition in the conversion target and the comparison of the induced stress with the ultimate tensile strength of the target material. Since the length of the incident beam pulse is large in comparison to the ratio of beam size to the speed of sound, the concurrent pressure pulse dissipates in a time short compared to the overall pulse duration and one is left with only the