Simulation of collisionless plasma with the Vlasov method

Space plasma is a collisionless, multi-scale, and highly nonlinear medium. There are numerous types of selfconsistent computer simulations that treat space plasma according to various approximations. The global-scale dynamics are commonly described by magneto-hydrodynamic (MHD), Hall-MHD and multi-fluid models, while electron-scale processes are described by the kinetic model, i.e., the Maxwell equations and either the Newton-Lorentz equation for charged particles or the Vlasov (collisionless Boltzmann) equation. Hybrid methods treat ions as particles and electrons as a fluid for ion-scale processes. Conventionally, MHD simulations have been used for numerical modeling of global-scale problems such as magnetospheres of stars and planets. However, the MHD simulations need diffusion coefficients, which are essentially due to kinetic processes that are eliminated in the framework of the MHD approximation. Recent high-resolution in-situ observations have also suggested that fluid scale and kinetic scale in space plasma are strongly coupled with each other, which is called cross-scale coupling. To understand the cross-scale coupling in space plasma, it is important to include full kinetics in global-scale simulations, which is the goal of this study.