Classical model of two electrons interacting in a saddle-shaped electric potential, and a constant perpendicular magnetic field

Abstract

Electron collisions are fundamental phenomena in modern physics with diverse applications ranging from collision ionization to quantum computing and high-energy plasma studies. This paper focuses on the intricate dynamics of electron collisions within a saddle-shaped electric potential and a constant magnetic field, mimicking the conditions found in beam splitters (and particle accelerators). While existing studies often employ a quantum framework to model these interactions and actually perform the experiment, we adopt a classical approach to provide a more intuitive understanding of the phenomena involved. The transition from quantum to classical representation eliminates probabilistic elements, allowing for precise and deterministic simulations. We utilized a self-programmed python script based on mathematical expressions for the situation, which are also self-derived in the paper. We have managed to replicate 2/4 results simply by altering the starting positions of the electrons and have added further functionality within the python simulations for further research and development i.e., a softening factor controlling the relative screening effect of the material of the constriction, and a time delay feature to be able to offset the starting time of one of the particles relative to the other. Our hope with this paper is for people to be able to take our results, and the model used to derive them, and use it for the purposes of further research and exploration.