Modification of the ion background profile in the nonlinear electron-plasma oscillations

We give an approximate analytical solution, correct to the first order in m\M, the electron to ion mass ratio, for the ion background modification under the influence of the free non linear electron plasma oscillations driven by the initial unbalance between electron and ion density distribution, n(e)(x,0) = n0 and n(i)(x, 0) = n0(1 + alpha cos kx). When the electron plasma oscillations grow starting from a very small perturbation (alpha less-than-or-similar-to 0.02), we find a remarkable modification in the ion background profile before the electron oscillation wavebreaking takes place.