This article is concerned with the kinetic modeling, by means of the Vlasov
equation, of charged particles under the influence of a strong external
electromagnetic field, i.e. when epsilon^2, the dimensionless cyclotron period,
tends to zero. This leads us to split the velocity variable in the Vlasov
equation into fluid and random components. The latter is supposed to have a
large magnitude of order 1/epsilon (which corresponds to the low Mach number
regime). In the limit epsilon -> 0, the resulting model is a hybrid model which
couples a kinetic description of the microscopic random motion of the particles
to a fluid description of the macroscopic behavior of the plasma. The
microscopic model is a first-order partial differential system for the
distribution function, which is averaged over the ultra-fast Larmor gyration
and the fast parallel motion along the magnetic field lines. The perpendicular
component (with respect to the magnetic field lines) of the bulk velocity is
governed by the classical relations describing the E X B and diamagnetic
drifts, while its parallel component satisfies an elliptic equation along the
magnetic field lines.