Asymmetry-induced transport of a non-neutral plasma within a coaxial Malmberg-Penning trap is analyzed using a single-particle simulation with collisional effects. Simulations of the case with standing wave asymmetry and periodic boundary conditions were studied. The relationship between the periods of oscillation for regular motion and the scaled radius matched between computer simulation and analysis of the scaled equations of motion: r vs t: Vz vs t: where A and B are constants. Poincaré sections were also used to gain more general knowledge regarding the boundary between regular and chaotic motion. It was discovered that particles can transition between the two states of motion, meaning they can become both trapped and untrapped over the duration of one simulation. The Poincaré sections also revealed that large radial excursions are possible over a greater number of velocity values, but axial trapping is what is truly required for regular motion.