When a positively charged beam enters a plasma, plasma electrons are drawn in toward the beam axis, creating a region of extremely large charge-density with complicated, nonlinear fields. Few analytic solutions exist to describe these fields, and this necessitates the use of simulations to model positively charged beam-plasma interactions. In this paper, we study the evolution of a positron beam as an analogous model for the proton driven plasma wakefield experiment proposed by Caldwell.