We establish the global existence of Lagrangian solutions to the ionic Vlasov-Poisson system for a broad class of initial data. The key ingredient is a new decomposition of the electric potential for the Poisson-Boltzmann equation, which yields quantitative a priori estimates and stability properties under L^p physical densities with p>1, whereas previous approaches require p>d/2. Based on these estimates, we establish stability of the associated flows and construct global Lagrangian solutions. Based on a joint work with Young-Pil Choi and Sihyun Song (Yonsei University).