Particle-in-cell simulation of plasmas - A tutorial

This chapter serves as a tutorial introduction to the field of particle-in-cell (PIC) simulation of plasmas. The full particle version of these models, in which both the electrons and ions are treated as particles, makes no approximations to the basic laws of mechanics and electricity and magnetism, and thus the full range of collisionless plasma physics is included in such a model. The basic techniques involved in a PIC model are illustrated: accumulation of the charge and current densities on a spatial grid, time integration of the field and particle equations, and limitations imposed by the underlying kinetic physics of a plasma. Various approximations to the full set of Maxwell's equations are described as well as the case of hybrid models (particle ions, fluid electrons) in which fluid equations are used to model the slow time evolution of high frequency phenomena, thus allowing a study of lower frequency kinetic phenomena on longer temporal and larger spatial scales. Examples of PIC simulations of magnetic reconnection are discussed.