The Paul Trap Simulator Experiment (PTSX) is a linear Paul trap whose purpose is to simulate the nonlinear transverse dynamics of intense charged particle beam propagation in periodic-focusing quadrupole magnetic transport systems. Externally created cesium ions are injected and trapped in the long central electrodes of the PTSX device. In order to have well-matched one-component plasma equilibria for various beam physics experiments, it is important to optimize the ion injection. From the experimental studies reported in this paper, it is found that the injection process can be optimized by minimizing the beam mismatch between the source and the focusing lattice, and by minimizing the number of particles present in the vicinity of the injection electrodes when the injection electrodes are switched from the fully oscillating voltage waveform to their static trapping voltage.