  In many physical contexts, evolution convection equations may present some
very large amplitude convective terms. As an example, in the context of
magnetic confinement fusion, the distribution function that describes the
plasma satisfies the Vlasov equation in which some terms are of the same order
as $\epsilon^{-1}$, $\epsilon \ll 1$ being the characteristic gyrokinetic
period of the particles around the magnetic lines. In this paper, we aim to
present a model hierarchy for modeling the distribution function for any value
of $\epsilon$ by using some two-scale convergence tools. Following Fr\'enod \\&
Sonnendr\"ucker's recent work, we choose the framework of a singularly
perturbed convection equation where the convective terms admit either a high
amplitude part or a an oscillating part with high frequency $\epsilon^{-1} \gg
1$. In this abstract framework, we derive an expansion with respect to the
small parameter $\epsilon$ and we recursively identify each term of this
expansion. Finally, we apply this new model hierarchy to the context of a
linear Vlasov equation in three physical contexts linked to the magnetic
confinement fusion and the evolution of charged particle beams.
