This work deals with the numerical resolution of the Fokker-Planck-Maxwell system in the quasi-neutral regime. In this regime the sti ness of the stability constraints of classic schemes causes huge calculation times. That is why, we introduce a new stable numerical scheme consistent with the transitional and limit models. Such schemes are called Asymptotic-Preserving (AP) schemes in literature. This new scheme is able to handle the quasi-neutrality limit regime without any restrictions on time and space steps. This approach can be easily applied to angular moment models by using a moments extraction. Finally, two physically relevant numerical test cases are presented for the Asymptotic-Preserving scheme in di erent regimes. The rst one shows the e ciency of the Asymptotic-Preserving scheme in the quasi-neutral regime whereas the second one on the contrary corresponds to a regime where electromagnetic e ects are predominant.
