This paper is devoted to the electronic polarization effect of dielectric materials in plasma physics. Using the two-scale convergence method introduced by G. Nguetseng and G. Allaire, we study the electronic polarization effect induced by two-scale homogenization. The microscopic properties of electrons in dielectric materials are characterized by Vlasov-Poisson system. The homogenized equations describing the mean behaviors of the microscopic equations are obtained. We also derive the modified Gauss law through the polarization effect. From the homogenized Poisson equation, the dielectric function is also acquired.
"Homogenization and Electronic Polarization Effects in Dielectric Materials." Taiwanese J. Math. 21 (2) 319 - 339, 2017. https://doi.org/10.11650/tjm/7783