Coupling global and kinetic scales with the implicit Particle-in-Cell methods

The implicit moment Particle-in-Cell (PIC) method uses the mathematical formalism of the moment equations to help the kinetic PIC approach to tap into the fluid level. Of course, the fluid moment equations are exact, just integrals of the Vlasov equation. But they need closure of higher moments. Within a kinetic PIC approach that is no problem. The particles provide that, and allow the moment equations to talk directly with the Maxwell's equations without need for interpreters (integrals over phase space). This has three advantages. The first is well known and has been used since the implicit moment PIC method was invented: it allows implicit PIC simulations on larger and slower scales, by several orders of magnitude. We report here on two new advantages just made available within iPIC3D: the use of AMR that adapts the local PIC resolution to the desired scale (impossible without the implicit moment method because the resolution is limited by stability) and it allows to use the moments of the implicit moment PIC scheme to interface the fluid and kinetic descriptions. The issue of energy conservation in PIC methods is an additional topic of discussion.