In this talk, we consider the global-in-time limits from the Vlasov-Poisson-Boltzmann system with cutoff Rutherford cross section to Vlasov-Poisson-Landau system with Coulomb potential near Maxwellians in the whole space. Precisely,

(i). we prove global well-posedness of the Vlasov-Poisson-Boltzmann system with cutoff Rutherford cross section which is perhaps the most singular kernel both in relative velocity and deviation angle.

(ii). we prove a global-in-time error estimate between solutions to the Vlasov-Poisson-Boltzmann system and the Vlasov-Poisson-Landau system with logarithm accuracy, which is consistent with the famous Coulomb logarithm. This is a joint work with Prof. Lingbing He from Tsinghua University.