  Here we present the mathematical and numerical details of a general hybrid
model for plasmas. All grid quantities are stored at cell centers on the grid.
The most common discretization of the fields in PIC solvers is to have the
electric and magnetic fields staggered, introduced by Yee. This automatically
ensures that div(B)=0, down to round-off errors. Here we instead present a cell
centered discretization of the magnetic field. That the standard cell centered
second order stencil for rot(E) in Faraday's law will preserve div(B)=0 was
noted by Toth. The advantage of a cell centered discretization is ease of
implementation, and the possibility to use available solvers that only handle
cell centered variables. We also show that the proposed method has very good
energy conservation for a simple test problem in three dimensions, when
compared to a commonly used algorithm.
