摘要
尘埃等离子体由普通的电子-离子等离子体和沉浸其中的带电尘埃颗粒组成，它广泛存在于宇宙空间和实验室中。理论分析和空间观测的结果表明，尘埃等离子体中常存在一种服从幂律分布而非麦克斯韦分布的超热粒子；不同的尘埃等离子体团相互并不独立，而是经常在相对运动中交会并相互穿越。基于上述事实，本论文一方面在非广延统计框架下，推广了尘埃等离子体的理论研究成果，另一方面建立了相互穿越的尘埃等离子体模型，并初步探讨了其中的线性尘埃声波及其稳定性。
本论文在非广延统计框架下研究了尘埃等离子体中尘埃颗粒的基本充电过程，包括电子离子附着以及电子致二次电子辐射。研究中假设电子、离子均服从非广延幂律分布，且各自有着不同的非广延参数，在此基础上得到了由电子、离子非广延参数修正的尘埃充电电流，包括电子流、离子流和二次电子流。考虑不同的尘埃充电过程，文中通过理论推导和数值计算，分析了电子和离子的非广延性质对尘埃表面电性和电量的影响。
本论文在非广延统计框架下研究了尘埃等离子体中所特有的尘埃声孤波。研究基于两种不同的假设：尘埃电量恒定和尘埃电量扰动。在尘埃电量恒定假设下，根据约化摄动法和赝势法分别求得小振幅和任意振幅的尘埃声孤波，并通过理论推导和数值计算，分析了非广延性质对尘埃声孤波的影响。在尘埃电量扰动假设下，本论文只讨论了小振幅的尘埃声孤波。在这两种不同的假设下，非广延性质对尘埃声孤波的影响不同，通过分析可知：电子非广延性直接作用于尘埃电量扰动，从而间接影响尘埃声孤波性质；离子非广延性则直接影响尘埃声孤波性质。
本论文建立了由快尘埃等离子体与靶尘埃等离子体共同构成的相互穿越尘埃等离子体模型，分别在经典统计力学和非广延统计力学的框架下研究了模型中的线性尘埃声波，并进一步分析了其稳定性及稳定性条件。文中考虑了两种极限情况。在靶尘埃等离子体中的尘埃热速度远小于尘埃声波的相速度情况下，经典统计和非广延统计的结果均表明尘埃声波总是不稳定的；在靶尘埃等离子体中的尘埃热速度远大于尘埃声波的相速度情况下，尘埃声波有可能稳定传播，其稳定性受到相互穿越尘埃等离子体中某些组分的性质包括其非广延性质的直接影响。
Dusty plasmas, which can be loosely defined as normal electron-ion plasmaswith additional charged components of dust grains, are rather ubiquitous in space andlaboratory. According to the theoretical analyses and space observations, it should bepointed out that suprathermal particles in the dusty plasma obey the power-lawdistribution instead of the Maxwell distribution, and moreover, the space plasmas aregenerally in motion and thus an permeating plasma physical phenomenon mayfrequently occur if two or more space plasmas encounter in the same space region.Consequently, the theoretical achievements in the dusty plasmas is generalized in theframework of nonextensive statistics, additionally, the dust-acoustic waves is studiedin the interpenetrating dusty plasma.
Firstly, some elemental dust charging processes in the dusty plasma isinvestigated on the basis of nonextensive statistics, including the collection of plasmaparticles and the secondary electron emission induced by the impact of electrons. Theelectrons and ions are assumed to be described by the nonextensive power-lawdistribution with q-parameters different from each other. Therefore, the dust chargingcurrents, including electron current, ion current and secondary electron current arederived. For different dust charging processes, according to the theoretical analysisand numerical calculation, the influnce of the electrons' and ions' nonextensivecharacters on the dust charge is analyzed.
Then, the nonextensive statistics is applied to study the nonlinear properties ofdust-acoustic solitary waves in the dusty plasmas. The investigation is based on twodifferent assumptions. The dust charge is either unvariable or variable. If the dustcharge is kept constant, according to the reductive erturbation method and theSagdeev potential method, the dust-acoustic solitary solution with small amplitudeand arbitary amplitude are derived. The influnces of the nonextensive parameters onthe solitary waves are identical by analysis. Therefore, if the dust charge is variable,only the small-amplitude dust-acoustic solitary waves are studied. With these twodifferent assumptions, the nonextensive characters have different effects on thesolitary waves. The nonextensive character of electrons affects on the dust chargefluctuation and thus affects on the solitary waves indirectly, on the other hand, thenonextensive character of ions affects on the solitary waves directly.
At last, the model of the permeating dusty plasma is established, which consists of two parts, i.e., the fast flowing dusty plasma and the target dusty plasma. In theframeworks of the classical and nonextensive statistics, the dust-acoustic waves andtheir stability in the permeating dusty plasma are investigated. It has been found thatthe stability of the waves depends strongly on the velocity of the fast flowing dustyplasma. There are two limiting physical cases that the thermal velocity of the flowingdusty plasma is much larger than or much smaller than the phase velocity of thewaves. In the former case, the dust acoustic waves are always instable, while in thelatter case, the dust acoustic waves may be stable and the stability is affected by thecharacters and nonextensive parameters of some components.
引文
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