On the self-force problem of point-like charged particles in classical electrodynamics
The problem of a point-like charged particle's self-interaction force has been a long-standing problem in the field of classical electrodynamics. For over a century, physicists have unsuccessfully developed a satisfactory solution until recently. We expand on the work done by Gralla et. al. in order to establish a smooth and relativistically correct formulation of point-like charged particles in motion and shed light on related problems and applications, particularly the motion of elementary particles with magnetic dipoles through non-uniform static magnetic fields. We conduct numerical simulations in order to quantify the magnitude of the perturbations from this self-force due to the new equations of motion relative to the Lorentz force. These results will be utilized in single particle dynamics experiments in accelerator rings.