Parametric instabilities in quantum plasmas with electron exchange—correlation effects

Abstract

Parametric instabilities induced by the nonlinear interaction between high frequency quantum Langmuir waves and low frequency quantum ion-acoustic waves in quantum plasmas with the electron exchange—correlation effects are presented. By using the quantum hydrodynamic equations with the electron exchange—correlation correction, we obtain an effective quantum Zaharov model, which is then used to derive the modified dispersion relations and the growth rates of the decay and four-wave instabilities. The influences of the electron exchange—correlation effects and the quantum effects on the existence of quantum Langmuir waves and the parametric instabilities are discussed in detail. It is shown that the electron exchange—correlation effects and quantum effects are strongly coupled. The quantum Langmuir wave can propagate in quantum plasmas only when the electron exchange—correlation effects and the quantum effects satisfy a certain condition. The electron exchange—correlation effects tend to enhance the parametric instabilities, while quantum effects suppress the instabilities.