  In this article, we design Asymptotic-Preserving Particle-In-Cell methods for
the Vlasov-Maxwell system in the quasi-neutral limit, this limit being
characterized by a Debye length negligible compared to the space scale of the
problem. These methods are consistent discretizations of the Vlasov-Maxwell
system which, in the quasi-neutral limit, remain stable and are consistent with
a quasi-neutral model (in this quasi-neutral model, the electric field is
computed by means of a generalized Ohm law). The derivation of
Asymptotic-Preserving methods is not straightforward since the quasi-neutral
model is a singular limit of the Vlasov-Maxwell model. The key step is a
reformulation of the Vlasov-Maxwell system which unifies the two models in a
single set of equations with a smooth transition from one to another. As
demonstrated in various and demanding numerical simulations, the
Asymptotic-Preserving methods are able to treat efficiently both quasi-neutral
plasmas and non-neutral plasmas, making them particularly well suited for
complex problems involving dense plasmas with localized non-neutral regions.
