磁化尘埃等离子体中波的不稳定性研究
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摘要
尘埃等离子体物理是近十年里等离子体学科中一个活跃的分支领域之一,带电尘埃广泛存在于空间等离子体、实验室聚变装置、低温等离子体工业应用等众多不同的环境中,并且呈现出相同或相似的性质。这是一种部分或完全电离的等离子体,其基本成分除了电子和离子外,还有(通常)带负电的、且电荷不是常数的微粒。带电颗粒有着与电子和离子完全不同的动力学行为,其与等离子体的相互作用呈现出许多新的物理现象。例如,这些大质量、强带电的尘埃颗粒的出现激发像尘埃声波和尘埃离子声波等等新的波动模式。目前,尘埃声波的研究已经成为低温等离子体研究的热门课题之一。
本文以涡旋状离子分布的磁化尘埃等离子体中尘埃声波为研究对象,详细就磁化尘埃等离子体中尘埃声波模型的得来、波的不稳定性进行了分析和讨论。其中分别考虑了等离子体波传播方向与磁场方向平行以及不与磁场方向平行(即斜传播)两种情况。在前一种情况下,分析了尘埃参数对波的不稳定性的影响;在后一种情况下,不仅分析了尘埃大小和尘埃电荷量的影响,还分析了扰动波的波数、方向对波的不稳定性的影响。值的一提的是,本文试图提出一种新的尘埃大小分布——多项式分布,通过这个分布可以更有效的分析实验室中实际的尘埃大小分布,对进一步研究尘埃大小分布对尘埃声波的影响具有重要的意义。
The physics of dusty plasmas has been an active branch of plasma science during the past decade. Charged dust particles exists widely in diverse environments as space plasmas, laboratory fusion devices, and low-temperature plasma applications in industry. Nevertheless, they exhibit the same or similar characteristics. Dusty plasma is defined as partially or fully ionized plasma consisting of, besides electrons and ions, (usually) negatively charged micron-sized dust particles with variable charges. The grains have completely different dynamic behavior compared with electrons and ions. Many unique self-organization phenomena in the complex plasma are affected by or originate due to the openness of the system. Take an example, the presence of dust particles, with their large inertia and small charge-to-mass ratios, give rise to new, and very low frequency modes. One example is the so-called dust acoustic wave(DAW), which attracts great attention.
In this thesis, a modified Zakharov - Kuznetsov equation for small but finite amplitude dust acoustic waves in a magnetized vortex-like ion distribution dusty plasma is obtained. It seems that there is instability for a soliton under higher-order transverse perturbations in this system. There is a certain critical value 4λ_0. If the ratio of the wave length of the higher-order perturbations to the width of the soliton is larger than this critical value, the solitary wave is unstable, otherwise it is stable. The growth rate of disturbances to a solitary waves is also obtained by using multiple-scale perturbation method. The effects of the parameters of both the dusty plasma and the disturbances have been numerically discussed as well. Finally, the obliquely-propagating waves in magnetized vortex-like ion distribution dusty plasmas are investigated. A plane solitary traveling-wave solution propagating at an angleα(0≤α≤π) to the magnetic field has been considered. The effects of the parameters of both the dusty plasma and the perturbations have been numerically discussed.
本文以涡旋状离子分布的磁化尘埃等离子体中尘埃声波为研究对象,详细就磁化尘埃等离子体中尘埃声波模型的得来、波的不稳定性进行了分析和讨论。其中分别考虑了等离子体波传播方向与磁场方向平行以及不与磁场方向平行(即斜传播)两种情况。在前一种情况下,分析了尘埃参数对波的不稳定性的影响;在后一种情况下,不仅分析了尘埃大小和尘埃电荷量的影响,还分析了扰动波的波数、方向对波的不稳定性的影响。值的一提的是,本文试图提出一种新的尘埃大小分布——多项式分布,通过这个分布可以更有效的分析实验室中实际的尘埃大小分布,对进一步研究尘埃大小分布对尘埃声波的影响具有重要的意义。
The physics of dusty plasmas has been an active branch of plasma science during the past decade. Charged dust particles exists widely in diverse environments as space plasmas, laboratory fusion devices, and low-temperature plasma applications in industry. Nevertheless, they exhibit the same or similar characteristics. Dusty plasma is defined as partially or fully ionized plasma consisting of, besides electrons and ions, (usually) negatively charged micron-sized dust particles with variable charges. The grains have completely different dynamic behavior compared with electrons and ions. Many unique self-organization phenomena in the complex plasma are affected by or originate due to the openness of the system. Take an example, the presence of dust particles, with their large inertia and small charge-to-mass ratios, give rise to new, and very low frequency modes. One example is the so-called dust acoustic wave(DAW), which attracts great attention.
In this thesis, a modified Zakharov - Kuznetsov equation for small but finite amplitude dust acoustic waves in a magnetized vortex-like ion distribution dusty plasma is obtained. It seems that there is instability for a soliton under higher-order transverse perturbations in this system. There is a certain critical value 4λ_0. If the ratio of the wave length of the higher-order perturbations to the width of the soliton is larger than this critical value, the solitary wave is unstable, otherwise it is stable. The growth rate of disturbances to a solitary waves is also obtained by using multiple-scale perturbation method. The effects of the parameters of both the dusty plasma and the disturbances have been numerically discussed as well. Finally, the obliquely-propagating waves in magnetized vortex-like ion distribution dusty plasmas are investigated. A plane solitary traveling-wave solution propagating at an angleα(0≤α≤π) to the magnetic field has been considered. The effects of the parameters of both the dusty plasma and the perturbations have been numerically discussed.
引文
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