An Electromagnetic Particle-Particle Method for Relativistic Electron Bunch Dynamics from Early Expansion to Long-Range Transport

Particle-mesh methods, such as the particle-in-cell (PIC) method, cannot retain exact pairwise interaction at sub-cell scales. For dense nonneutral relativistic electron bunches, this makes it difficult to accurately capture the inter-particle electromagnetic interaction and the associated bunch divergence. In this work, the previously developed electromagnetic particle-particle (EM-PP) model for relativistic two-particle interaction is extended to many-particle electron bunch transport in the Earth's magnetosphere. The method combines the Li\'enard--Wiechert fields, an improved retarded-time evaluation procedure, and a relativistic particle pusher, and adopts a two-stage strategy to couple the dense early self-field-dominated evolution to the later long-range geomagnetic-field-controlled transport. The method provides a practical mesh-free approach for accurately simulating long-range transport of relativistic electron bunches when short-range electromagnetic interaction is important.