In this talk, we will investigate the incompressible limit from Euler-Poisson equations in nonthermal plasma to incompressible Euler equations with an  ill-prepared initial data, which will lead to the initial layer effect. The  strong convergence result will be obtained with convergence rate  via nonlinear asymptotic stability analysis of the approximate solution constructed by an initial layer expansion. This is joint work with Prof. Tao Luo and Prof. Shu Wang.