Particle simulations of space weather

We review the application of particle simulation techniques to the full kinetic study of space weather events. We focus especially on the methods designed to overcome the difficulties created by the tremendous range of time and space scales present in the physical systems. We review the aspects of the derivation of the particle in cell (PIC) method relevant to the discussion. We consider first the explicit formulation highlighting its severe limitations due to the presence of stability constraints. Next we introduce implicit methods designed to remove such constraints. We describe both fully implicit methods based on the use of non-linear iteration solvers and semi-implicit methods based on the linearization of the coupling and on simpler linear solvers. We focus the discussion on the implicit moment method but remark its differences from the direct implicit method. The application of adaptive methods within PIC is discussed. Finally practical considerations about the implementation of the implicit PIC method on massively parallel computers to conduct studies of space weather events are given.