Phase Transitions of Charged Particles in the Paul Trap

The Paul trap is an electrodynamic device that can be used to trap multiple particles simultaneously. The ensuing dynamics can be modeled classically by simply considering the different forces acting upon each particle and solving Newton's second law. This system however is highly nonlinear, and so even for two particles, numerical simulations must be employed in order to understand these dynamics. In this Thesis, we explore the three classical thermodynamic phases of matter (gas, liquid, solid) and how they manifest in the Paul trap. We also investigate the phase transitions that can occur between these phases, and through this work hope to both obtain a fuller understanding of the nonlinear dynamics that governs motion in this system, and inform future experiments that can test the results found here.