The dissertation presents the computational technique Particle-In-Cell, or PIC for short, and its applications in studying the magnetospheres of neutron stars, modeled as conducting rotators with strong magnetic fields. Pigeon, an open-source PIC simulator written by the author in modern C++, is anatomically examined as an instrument to illustrate the principles, algorithms and engineering difficulties of the PIC technique. Two types of rotators are studied using Pigeon. The monopolar rotator, which has an exact solution in the force free limit, serves as a tester for the code, as well as an example of the PIC's capability. The main application of Pigeon is on the ab initio simulation of an (axisymmetric) dipolar rotator with self-consistent gamma ray photon emission and pair creation, the study of which could reveal valuable information of the mechanism of the pulsars. Thanks to the performance boost brought by Pigeon's dynamic load balancing functionality, we are able to perform the simulation with a 4096x4096 high resolution grid.

The high resolution is critical in obtaining a Lorentz factor of 10000 of the polar cap potential drop, which in turn enables good separations of energy levels and hence makes the simulation closer to representing the real-life pulsars. With the high resolution, we are also able to study the Y point more closely, where we find that the angular momentum conservation dictates the process of magnetic flux surface crossing that is responsible for the release of electromagnetic energies into the plasma.