The finite Larmor radius approximation

The presence of a large external magnetic field in a plasma introduces an a dditional time-scale which is very constraining for the numerical simulatio n. Hence it is very useful to introduce averaged models which remove this t ime-scale. However, depending on other parameters of the plasma, different starting models for the asymptotic analysis may be considered. We introduce here a generic framework for our analysis which ts many of the possible re gimes and apply it in particular to justify the finite Larmor radius approx imation both in the linear case and in the nonlinear case in the plane tran sverse to the magnetic field.