  In this paper, we build a Two-Scale Macro-Micro decomposition of the Vlasov
equation with a strong magnetic field. This consists in writing the solution of
this equation as a sum of two oscillating functions with circonscribed
oscillations. The first of these functions has a shape which is close to the
shape of the Two-Scale limit of the solution and the second one is a correction
built to offset this imposed shape. The aim of such a decomposition is to be
the starting point for the construction of Two-Scale Asymptotic-Preserving
Schemes.
