Phase Mixing of Nonlinear Plasma Oscillations in an Arbitrary Mass Ratio Cold Plasma

Nonlinear plasma oscillations in an arbitrary mass ratio cold plasma have been studied using 1-D particle-in-cell simulation. In contrast to earlier work for infinitely massive ion plasmas it has been found that the oscillations phase mix away at any amplitude and that the rate at which phase mixing occurs, depends on the mass ratio ($\Delta = m_{-}/m_{+}$) and the amplitude. A perturbation theoretic calculation carried upto third order predicts that the normalized phase mixing time $\omega_{p-} t_{mix}$ depends on the amplitude $A$ and the mass ratio $\Delta$ as $\sim [(A^{2}/24)(\Delta/\sqrt{1 + \Delta})]^{-1/3}$. We have confirmed this scaling in our simulations and conclude that stable non-linear oscillations which never phase mix, exist only for the ideal case with $\Delta = 0.0$ and $A < 0.5$. These cold plasma results may have direct relevance to recent experiments on superintense laser beam plasma interactions with applications to particle acceleration, fast ignitor concept etc.