Phase Mixing of Large Amplitude Relativistic Electron Plasma Oscillation With Inhomogeneous Ion Background

Phase mixing of relativistic large amplitude nonlinear plasma wave in presence of a time independent space periodic ion density profile has been investigated. Inhomogeneous ion along with the relativistic variation of electron mass make the characteristic frequency of the wave to acquire a space dependency and thereby it breaks at arbitrarily small amplitude due to phase mixing. An approximate space time dependent solution is obtained in the weakly relativistic limit by Bogoliuboff and Kryloff method of averaging. We find that the change in the ion density perturbation and also the relativistic electron mass variation have significant effect in modifying the time at which phase mixing occurs.