Modulational Instability of Electron Plasma and Ion Plasma Waves

抄録

Through application of the reductive perturbation method to the fluid equations for electrons and ions, a nonlinear Schrödinger equation is derived. For the electron plasma wave, the assumption of the uniform background of ions is not used. Then exact properties of the equation are obtained for all wave numbers, including a modulationally unstable region predicted by Zakharov. For the ion-acoustic mode, the assumptions of the Boltzmann distribution for electrons and of cold ions are not used. Then a modulationally unstable region for the ion plasma wave exists for wavelengths shorter than the electron Debye length, and the growth rate of the instability is appreciably large even at low ion temperatures.