  The purpose of this paper is to bridge kinetic plasma descriptions and low
frequency single fluid models. More specifically, the asymptotics leading to
Magneto-Hydro-Dynamic (MHD) regimes starting from the Vlasov-Maxwell system are
investigated. The analogy with the derivation, from the Vlasov-Poisson system,
of a fluid representation for the ions coupled to the Boltzmann relation for
electrons is also outlined. The aim is to identify asymptotic parameters
explaining the transitions from one microscopic description to a macroscopic
low frequency model. These investigations provide ground work for the
derivation of multi-scale numerical methods, model coupling or physics based
preconditioning.
