We study the expansion of a cold, non-neutral ion plasma into the vacuum. The plasma is made from cold rubidium atoms in a magneto-optical trap (MOT) and is formed via ultraviolet photoionization. We employ time-delayed plasma extraction and imaging onto a position-and time-sensitive micro-channel plate detector to analyze the plasma. We report on the formation and persistence of plasma shock shells, pair correlations in the plasma, and external-field-induced plasma focusing effects. We also develop trajectory and fluid descriptions to model the data and to gain further insight. The simulations verify the formation of shock shells and correlations, and allow us to model time-and position-dependent density, temperature, and Coulomb coupling parameter, Γ(r, t). This analysis both reaffirms the presence of shock shells and verifies that the experimental plasma is strongly coupled.