Studying Charged Particle Interaction Modeling with Theoretical Computational Field Solvers

     In the field of physics, biology, chemistry, and engineering, the question of how many particle systems interact with each other is often pondered. Now, with the strength of computer science and our knowledge of physics, we can now approach this question fully by developing methods that integrate these two fields. Specifically, there are several ways in which this can be accomplished. In general, we want to understand how charged particles interact with each other given their own intrinsic properties and how they affect their surroundings, i.e. charged particles generate electric fields which act as forces that draw and/or pull. Often, you are examining this physical phenomena for a number of particles in the billions. Obviously, this is a large quantity of particles, and has thus provided motivation for developing field solvers. The field solvers in question are Particle in Cell (PIC) and the Fast Multipole Method (FMM), along with the most naive approach, direct calculation. The basis of this project on which these field solvers will be constructed consists of developing a simulation of particles, generally called source particles, on a grid composed of evenly spaced nodes. These grid nodes will be used as a reference when considering what effect these particles have on its surroundings. Furthermore, High Performance Computing (HPC) will also be used to further investigate the efficiency and accuracy of these methods. This research can impact the field of nuclear physics as we can now further examine beam quality, which is used to probe the nucleus of atoms. Additionally, the development of these field solves can be applied to many body problems in nuclear physics, as well.