An electromagnetic particle-particle method for relativistic particle 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 particle 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 the transport of a many-particle charged bunch under the Earth's prescribed geomagnetic field. The formulation is applicable to charged particles with either charge sign, and positrons are used as the representative example in the present simulations. 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 particle bunches when short-range electromagnetic interaction is important.