In this paper, we present some new results about the approximation of the
Vlasov-Poisson system with a strong external magnetic field by the 2D finite
Larmor radius model. The proofs within the present work are built by using
two-scale convergence tools, and can be viewed as a new slant on previous works
of Fr\'enod and Sonnendr\"ucker and Bostan on the 2D finite Larmor Radius
model. In a first part, we recall the physical and mathematical contexts. We
also recall two main results from previous papers of Fr\'enod and
Sonnendr\"ucker and Bostan.