Intense beam propagation is an active area of research and is at the center of various scientific studies, including heavy ion fusion, spallation neutron sources, high energy physics, nonlinear dynamics, and nuclear waste transmutation. The results presented here demonstrate that the Paul Trap Simulator Experiment (PTSX) is capable of simulating, in a compact cylindrical Paul trap, beams with intensities up to 80% of the space-charge limit and that propagate for equivalent distances of over 10 km. This allows the study of research topics such as: the conditions for quiescent beam propagation, collective mode excitation, generation and dynamics of halo particles, and distribution function effects. At the high beam intensities envisioned in present and next-generation facilities, a fundamental understanding of the influence of collective processes and self-field effects on beam transport and stability properties must be developed.