arXiv:2504.04826v2 Announce Type: replace Abstract: In this work, we propose a new numerical method for the Vlasov-Poisson system that is both asymptotically consistent and stable in the quasineutral regime, i.e. when the Debye length $\lambda$ is small compared to the characteristic spatial scale of the physical domain. Our approach consists in reformulating the Vlasov-Poisson system as a hyperbolic problem by applying a spectral expansion in the basis of Hermite functions in the velocity space and in designing a structure-preserving scheme for the time and spatial variables. Through this Hermite formulation, we establish a convergence result for the electric field toward its quasineutral limit together with explicit error estimates in $\lambda$. Following this path, we then propose a fully discrete numerical method for the Vlasov-Poisson system, inspired by the approach in arXiv:2306.14605, and rigorously prove that it is uniformly consistent in the quasineutral limit regime. Finally, we present several numerical simulations to illustrate the behavior of the proposed scheme. These results demonstrate the capability of our method to describe quasineutral plasmas, illustrate its stability and confirm its asymptotic preserving property.