Amplitude modulation of electron plasma waves in a quantum plasma

Using the one dimensional quantum hydrodynamic model for a two-component electron-ion dense quantum plasma the linear and nonlinear properties of electron plasma waves are studied including ion motion. By using the standard method of multiple scales perturbation technique a nonlinear Schrödinger equation containing quantum effects is derived. From this equation it is shown that with immobile ions an electron plasma wave becomes modulationally unstable in two distinct regions of the wavenumber. Numerical calculation shows that the stability domain of the wavevector shrinks with the increase in quantum diffraction effect. It is also found that the growth rate of instability in the high wavenumber region increases with the increase in quantum effect. Ion motion is found to have significant effect in changing the stability/instability domains of the wavenumber in the low k-region.