Relativistic electron plasma oscillations in an inhomogeneous ion background

The combined effect of relativistic electron mass variation and background ion inhomogeneity on the phase mixing process of large amplitude electron oscillations in cold plasmas have been analyzed by using Lagrangian coordinates. An inhomogeneity in the ion density is assumed to be time-independent but spatially periodic, and a periodic perturbation in the electron density is considered as well. An approximate space-time dependent solution is obtained in the weakly-relativistic limit by employing the Bogolyubov and Krylov method of averaging. It is shown that the phase mixing process of relativistically corrected electron oscillations is strongly influenced by the presence of a pre-existing ion density ripple in the plasma background.