  This paper is concerned with the analysis of a mathematical model arising in
plasma physics, more specifically in fusion research. It directly follows
\cite{DHK1}, where the tri-dimensional analysis of a Vlasov-Poisson equation
with finite Larmor radius scaling was led, corresponding to the case of ions
with massless electrons whose density follows a linearized Maxwell-Boltzmann
law. We now consider the case of electrons in a background of fixed ions, which
was only sketched in \cite{DHK1}. Unfortunately, there is evidence that the
formal limit is false in general. Nevertheless, we formally derive a fluid
system for particular monokinetic data. We prove the local in time existence of
analytic solutions and rigorously study the limit (when the Debye length
vanishes) to a new anisotropic fluid system. This is achieved thanks to
Cauchy-Kovalevskaya type techniques, as introduced by Caflisch \cite{Caf} and
Grenier \cite{Gre1}.
