Stability in Quasineutral Plasmas with Thermalized Electrons

We study the quasineutral limit for the ionic Vlasov-Poisson system with thermalized electrons (VPME) on the torus in dimensions one to three, for rough solutions with bounded spatial density. Our main result is a quantitative stability theorem showing that quasineutral convergence is robust under exponentially small perturbations of the initial data, as measured in Wasserstein distance: given a regular family of reference solutions for which the quasineutral limit is known to hold, we prove that the same limit remains valid for perturbed solutions on the same time interval. The proof combines a kinetic-Wasserstein stability framework with a refined analysis of the Poisson-Boltzmann coupling specific to VPME. A central new ingredient is an improved control of the characteristic flow: we obtain quantitative bounds on the growth of characteristics in the velocity coordinate, with only polynomial deterioration in the Debye length. This yields new locally-uniform-in-time bounds on the spatial density and provides the key input needed to complete the stability estimates. These results bring the stability theory for the ionic model in the quasineutral regime close to the known instability threshold and substantially relax the smallness conditions required in earlier works. As a byproduct, our approach improves the moment assumptions in the global well-posedness theory for bounded-density solutions to VPME on the torus.