Macroparticles

Macroparticles are a computational representation used in kinetic simulations to model many physical particles with a single tracked entity. Each macroparticle stands for a group of real particles and carries a statistical weight that scales its charge and mass relative to a single particle. In common formulations, the macroparticle’s position and velocity describe the center of its group in phase space, while the macroparticle charge q and mass m are given by q = w q0 and m = w m0, where w is the weight and q0, m0 are the charge and mass of the species being modeled.

In particle-in-cell and related methods, the simulation domain is discretized on a spatial grid. Macroparticles move under the Lorentz force calculated from the grid-based fields, while their charges and currents are deposited onto the grid to update the fields. This cycle advances the system in time, frequently alternating field solves with particle pushes. Deposition uses shape functions to reduce numerical noise and avoid self-force effects.

Macroparticles enable efficient modeling of plasmas, charged beams, and other collective systems where full tracking of all real particles would be computationally prohibitive. They are sometimes called superparticles and are central to PIC, Vlasov–Poisson, and related kinetic schemes. The approach trades exact microscopic resolution for tractable sampling of distribution functions.

Limitations include statistical noise from finite sampling, numerical heating, and weight-induced inconsistencies if not managed carefully. Techniques such as particle splitting and merging, adaptive weighting, and improved deposition schemes are used to mitigate these issues.