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1、 Parametric instabilities in quantum plasmas He Caixia 西北师范大学研究生学位论文作者信息 论文题目量子等离子体中参量不稳定性研究 姓名何彩霞学号2010210838 专业名称理论物理答辩日期2013 年 5 月 26 日 联系电话15095397302E_mailhecaixiatext 通信地址(邮编)：甘肃省定西市安定区凤翔镇响河村（743000） 备注： ? Cc5du?f?lfN?d3Ac?AO3?f?(X?7!? NB?(?)! p?UN?n9-1?lfN?2?A f?A9%B?+?A?A(G)?lfN?5?K?“T ?g/n)
2、?f?lfN?A59X?|?I?J?*? ?Jn?d?“ ?N?SN?(?Xe? k?0?n?9?)?f?lfN! p“KD?! $“lf(!Zakharov ?!?5“ ?g ?f?lfN?5“ 1?|?fZakharov? .?A?f?lfN?5?K?“l6N?u! (?m”?k?fZakharov?.,?|d?.?P? 5?o?5?X?O?A!?f?AKD ?39?5?K?“(JL?A?f?AUr?/? ?u?5“?k?A?f?A?v?KD?U3 ?f?lfND“?A“?u*?5?f?A“?u? ?5“1n?|?fZakharov?.?9%B?+dp“KD? $“lf(?m?-u?)?5
3、“L?5?f6N? ?p“KD?$lf(?X“2|?m”?4?Ie? fZakharov?.“ ?%B?+?P?5?o?5“ (JL %B ?+?!l?f!l?6?f?f?%B?+? 5?“ ?o(?9“T+?c?“ ?c?f?A?AA?Ap“KD?$“lf( Zakharov?. ?5 i Abstract Recently, there has been a great deal interest in quantum plasmas because of their potential application, especially in ultra-small electron dev
4、ices (e.g., metallic and semi- conductor nano-structures), in dense astrophysical systems and in laser plasmas. It is well known that, A lot of rich and particular physics phenomenon that are closely related to the nonlinear interaction has been presented. Plasmas instabilities caused by the nonlin-
5、 ear interaction become a hot issue in recent years, including parametric instabilities have been induced by the nonlinear interaction between high frequency quantum Langmuir waves and low frequency quantum ion-acoustic waves. Furthermore, the investigation of quantum plasmas has been greatly advanc
6、ed in low-temperature and dense plasmas, in the circumstance, many novel and important physical eff ects have been found in the plasmas, such as, quantum eff ects, exchange-correlation eff ects, geometrical eff ects, etc However, the infl uence of the eff ects on parameter instabilities in quantum p
7、lasmas is still not very clear. Moreover, with the remarkable developments of the science and tech- nology, the electric devices gradually miniaturize and ultrasmall. The carbon nanotubes as a kind of ultrasmall electric device, parametric instability of regarding as plasma gas in the carbon nanotub
8、es remains to be further studied. Therefore, in this paper, the infl uences of quantum eff ects, electron exchange-correlation eff ects and the geometrical eff ects (cylindrical) of the single carbon nanotubes have been studied in detail. The work can provide some meaningful theoretical guiding valu
9、es for deep-stated understanding the dynamical properties of quantum plasmas and how to choose the method of enhancing or suppressing instabilities for the demand of the occasion. The specifi c contents and conclusions of this paper are as follows: Firstly, the physical background and the related ph
10、ysical knowledge are briefl y 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 the following two chapters. In chapter II, By carrying out quantum Zakha
11、rov model, para- metric instabilities in quantum plasmas with the electron exchange-correlation eff ects are presented. By using the quantum hydrodynamic equations with the electron exchange- correlation correction, we obtain an eff ective quantum Zaharov model, which is then used to derive the modi
12、fi ed dispersion relations and the growth rates of the decay and four- wave instabilities. The infl uences of the electron exchange-correlation eff ects and the quantum eff ects on the existence of quantum Langmuir waves and the parametric insta- bilities are discussed in detail. It is shown that th
13、e electron exchange-correlation eff ects ii Abstract and quantum eff ects are coupled strongly. The quantum Langmuir wave can propagate in quantum plasmas only when the electron exchange-correlation eff ects and the quan- tum eff ects satisfy a certain condition. The electron exchange-correlation ef
14、f ects tend to enhance the parametric instabilities, while quantum eff ects suppress the instabilities. In chapter III, Parametric instabilities induced by the coupling excitation between the high frequency quantum Langmuir waves and the low frequency quantum ion-acoustic waves in single-walled carb
15、on nanotubes are studied with quantum Zakharov model. Lineariz- ing the quantum hydrodynamic equations, we get the dispersion relations for the high frequency quantum Langmuir wave and the low frequency quantum ion-acoustic wave, respectively. Using two time scale method, we obtain the quantum Zaharov model in the cylindrical coordinates. Decay instability and four-wave instability are discussed in detail. It is shown that the carbon nanotubess radius, the equilibrium discrete azimuthal quant
