In this paper, we establish the validity of the quasineutral limit for the ionic Vlasov-Poisson system for rough initial data that are exponentially small perturbations of analytic data. Exponential smallness is also required in the electron case, and it is essentially sharp due to the presence of instabilities if only polynomial smallness is assumed.
The nonlinear Poisson coupling leads to several new challenges compared to the electron case. To overcome them, we enhance the existing theory of the growth of characteristics for Vlasov systems with nonlinear couplings, and we combine stability estimates in kinetic-Wasserstein distances with improved regularity bounds on the elliptic coupling.
