| Recently, there has been a great deal interest in quantum plasmas because of theirpotential application, especially in ultra-small electron devices (e.g., metallic and semi-conductor nano-structures), in dense astrophysical systems and in laser plasmas. It is wellknown that, A lot of rich and particular physics phenomenon that are closely related tothe nonlinear interaction has been presented. Plasmas instabilities caused by the nonlin-ear interaction become a hot issue in recent years, including parametric instabilities havebeen induced by the nonlinear interaction between high frequency quantum Langmuirwaves and low frequency quantum ion-acoustic waves. Furthermore, the investigationof quantum plasmas has been greatly advanced in low-temperature and dense plasmas,in the circumstance, many novel and important physical efects have been found in theplasmas, such as, quantum efects, exchange-correlation efects, geometrical efects, etc..However, the influence of the efects on parameter instabilities in quantum plasmas isstill not very clear. Moreover, with the remarkable developments of the science and tech-nology, the electric devices gradually miniaturize and ultrasmall. The carbon nanotubesas a kind of ultrasmall electric device, parametric instability of regarding as plasma gasin the carbon nanotubes remains to be further studied. Therefore, in this paper, theinfluences of quantum efects, electron exchange-correlation efects and the geometricalefects (cylindrical) of the single carbon nanotubes have been studied in detail. The workcan provide some meaningful theoretical guiding values for deep-stated understanding thedynamical properties of quantum plasmas and how to choose the method of enhancingor suppressing instabilities for the demand of the occasion. The specific contents andconclusions of this paper are as follows:Firstly, the physical background and the related physical knowledge are briefly in-troduced, including quantum physics, high Langmuir wave, low ion-acoustic wave, Para-metric instability and so on.Secondly, Parametric instability in quantum plasmas are detailedly studied in thefollowing two chapters. In chapter II, By carrying out quantum Zakharov model, para-metric instabilities in quantum plasmas with the electron exchange-correlation efects arepresented. By using the quantum hydrodynamic equations with the electron exchange-correlation correction, we obtain an efective quantum Zaharov model, which is then usedto derive the modified dispersion relations and the growth rates of the decay and four-wave instabilities. The influences of the electron exchange-correlation efects and thequantum efects on the existence of quantum Langmuir waves and the parametric insta-bilities are discussed in detail. It is shown that the electron exchange-correlation efects and quantum efects are coupled strongly. The quantum Langmuir wave can propagatein quantum plasmas only when the electron exchange-correlation efects and the quan-tum efects satisfy a certain condition. The electron exchange-correlation efects tend toenhance the parametric instabilities, while quantum efects suppress the instabilities. Inchapter III, Parametric instabilities induced by the coupling excitation between the highfrequency quantum Langmuir waves and the low frequency quantum ion-acoustic wavesin single-walled carbon nanotubes are studied with quantum Zakharov model. Lineariz-ing the quantum hydrodynamic equations, we get the dispersion relations for the highfrequency quantum Langmuir wave and the low frequency quantum ion-acoustic wave,respectively. Using two time scale method, we obtain the quantum Zaharov model inthe cylindrical coordinates. Decay instability and four-wave instability are discussed indetail. It is shown that the carbon nanotubes’s radius, the equilibrium discrete azimuthalquantum number, the perturbed discrete azimuthal quantum number and the quantumparameter play the crucial role to the instabilities.Finally, we summarize the main results and give an outlook of the future in this field. |
