Diffusion Limit with Optimal Convergence Rate of Classical Solutions to the modified Vlasov-Poisson-Boltzmann System

In the present paper, we study the diffusion limit of the classical solution to the modified Vlasov-Poisson-Boltzmann (mVPB) System with initial data near a global Maxwellian. Based on the spectral analysis, weprove the convergence and establish the convergence rate of the global strong solution to the mVPB system towards the solution to an incompressible Navier-Stokes-Poisson-Fourier system with the precise estimation on the initial layer.