【作者】 杨雪峰；

【导师】 王晓钢；

【作者基本信息】 大连理工大学 ， 等离子体物理， 2009， 博士

【摘要】 本文对等离子体晶格中尘埃晶格波(DLW)的性质(色散关系和声速)进行了系统的研究。在第一章,对复杂等离子体和等离子体晶格的理论与实验做了概述。在第二章,系统地讨论了等离子体晶格中尘埃晶格波的色散关系,给出了三维等离子体晶格中尘埃晶格波色散关系矩阵的概念,推导了三维等离子体晶格(体心立方和面心立方)中尘埃晶格波的色散关系矩阵,并在三个特征方向((1,0,0),(1,1,0)和(1,1,1))上得到了色散关系矩阵的简单形式,带电尘埃和其他所有粒子之间的相互作用都考虑在内。当屏蔽参数κ>>1时,在只考虑带电尘埃和最近八个立方体内的尘埃相互作用的前提下给出了三个特征方向上的色散关系。还讨论了屏蔽参数对尘埃晶格波色散关系的影响。在第三章,讨论了等离子体晶格中尘埃晶格波在长波区域的声速。对于二维尘埃晶格波,当屏蔽参数κ>>1时,给出了纵波和横波在长波区域的声速(依赖于κ),当κ<<1时,给出了纵波在长波区域的声速(依赖于κ),并且沿两个特征方向(x轴和y轴)传播的尘埃晶格波在长波区域的声速是一致的。给出的声速与Peeters和Wu的数值结果非常接近,也与Nunomura等人的实验结果“声速不依赖于传播方向”吻合。对于三维尘埃晶格波,当κ<<1时,分别给出了bcc晶格和fcc晶格中沿三个特征方向传播的纵波在长波区域的声速(依赖于κ),发现沿三个特征方向传播的纵波在长波区域的声速是一致的。然后分别对二维和三维等离子体晶格中尘埃晶格波给出了在长波区域的色散关系。在第四章,分别计算了一维、二维和三维等离子体晶格中带阻尼的尘埃晶格波的“逆”色散关系,带电尘埃和其他所有粒子的相互作用都考虑在内。计算结果和文献中的实验数据非常吻合。还研究了在长波区域内在各个特征方向上传播的尘埃晶格波的“逆”色散关系,发现二维等离子体晶格中沿两个特征方向传播的尘埃晶格波的“逆”色散关系是相同的,三维等离子体晶格中沿三个特征方向传播的尘埃晶格波的“逆”色散关系也是相同的,并得到了相应的显式“逆”色散关系公式。在第五章,分析讨论了一维、二维和三维等离子体晶格中尘埃晶格波的阻尼效应以及对数值研究和实验的影响。发现外部激发模式(实频率和复波数)的“逆”色散关系k_r=k_r(ω)和k_i=k_i(ω)不到达“负色散”区域,这是因为在驻波点附近有强烈阻尼,在那里群速度趋于零。而“自激发”模式(实波数和复频率)的色散关系曲线ω_r=ω_r(k)确实到达了“负色散”区域,但在长波(小波数)一端出现了“截断”现象,并且横波的“截断”波数比纵波的大得多。如果阻尼很弱,外部激发(ω=ω(k_r))和“自激发”(ω_r=ω_r(k))模式的实部在正色散区域与无阻尼模式的色散关系非常接近,而在负色散区域甚至很小的阻尼都可以使色散关系曲线分开。更多还原

【Abstract】 The properties(dispersion relation and acoustic velocity) of dust lattice waves(DLW) in complex plasma crystals have been systematically studied in this thesis.In the first chapter,a brief review of the theories and experiments of complex plasmas and complex plasma crystals has been made.In the second chapter,we discuss the dispersion relations of DLW in complex plasma crystals systematically,propose the concept of dispersion relation matrix of DLW in complex plasma crystals,derive the dispersion relation matrices for DLW in body centred cubic(bcc) and face centred cubic(fcc) in three-dimensional complex plasma crystals,and obtain the simple forms of the dispersion relation matrices of DLW in the three characteristic directions ((1,0,0),(1,1,0) and(1,1,1)).We compute the dispersion relation matrices with the screened Coulomb interaction between a charged dust and all other particles being taken into account or with the screened Coulomb interaction between a charged dust and particles in the nearest eight cubic only being taken into account(screening parameterκ>>1).We then discuss the effects of screening parameters on the dispersion relations of DLW.In the third chapter,we discuss the acoustic velocity of DLW in the long wavelength region in plasma crystals.We obtain theκ-depending acoustic velocity of longitudinal DLW forκ>>1 andκ<<1,and transverse DLW forκ>>1 in two-dimensional plasma crystals, the acoustic velocity in the long wavelength region in the two characteristic directions(x-axis and y-axis) of plasma crystals is the same.The acoustic velocity we obtained is very close to the numerical result of Peeters and Wu,and also agrees with experimental result of Nunomura, "the acoustic velocity is the same for all wave propagation direction".We obtain theκ-depending acoustic velocity of longitudinal DLW forκ<<1 in the long wavelength region in the three characteristic directions in three-dimensional plasma crystals(bcc and fcc),the acoustic velocity in the long wavelength region in the three characteristic directions in three-dimensional plasma crystals is the same.Then we discuss the dispersion relations of DLW in the long wavelength region in two-dimensional and three-dimensional plasma crystalsIn the fourth chapter,we compute the "inversed" dispersion relations for the damped DLW in one-dimensional,two-dimensional and three-dimensional plasma crystals,with the screened Coulomb interaction between a charged dust and all other particles being taken into account.We compare the theoretical "inversed" dispersion relations quantitatively with experimental data from the reference,and they agree very well.We find that the "inversed" dispersion relations of DLW in the long wavelength region in the two characteristic directions of two-dimensional plasma crystals are the same,and the "inversed" dispersion relations of DLW in the long wavelength region in the three characteristic directions of three-dimensional plasma crystals are also the same,and obtain the explicit "inversed" dispersion relation formulae in the long wavelength region.In the fifth chapter,we consider the effects of damping of DLW in one- dimensional, two-dimensional and three-dimensional plasma crystals.For externally excited modes(with a real frequency and a complex wave number),the "inversed" dispersion of k_r=k_r(ω), k_i= k_i(ω) does not reach the "negative dispersion" region,due to the strong damping near the "standing wave" point where the group velocity goes to zero.For "naturally excited" modes(with a real wave number and a complex frequency),the dispersion curveω_r=ω_r(k) does extend all way to the "negative dispersion" region,while however a "cut off" is seen at the long wavelength end of the dispersion.If the damping is weak,the real-part of dispersion for both "externally" and "thermally" excited modes are very close to the no-damping dispersion in the "positive dispersion" region. It is in the "negative dispersion" region however where the small damping makes the dispersion curves depart far away from each other.更多还原