This thesis is aimed toward developing a method to simulate ion thruster discharge chambers in a full three dimensional environment and to study the effect of discharge chamber size on ion thruster performance. The study focuses solely on ring-cusped thrusters that make use of Xenon for propellant and discharge cathode assembly for mean of propellant ionization. Commercial software is used in both the setup and analysis phases. Numerical simulation is handled by 3D Particle-In-Cell Monte-Carlo-Collision method. Simulation results are analyzed and compared with other works. It is concluded that the simulation methodology is validated and can be used to simulate different cases. Therefore, different simulation cases of varying chamber sizes are done and the results are used to develop a performance curve. This plot suggests that the most efficient case is the 30 cm thruster. The result further validates the simulation process since the operating parameters used for all of the cases are taken from a 30 cm thruster experiment. One of the obvious applications for such a simulation process is to determine a set of the most efficient operating parameters for a certain size thruster before actual fabrication and laboratory testing. / Master of Science