摘要
等离子体激波与界面相互作用在惯性约束聚变和天体物理中都是一个重要问题。本文主要研究等离子体中自生电场在激波与界面相互作用过程中对激波面不稳定性和界面不稳定性(如:Rayleigh-Taylor不稳定性)所产生的新的影响。
本文将等离子体激波面视作有厚度的阵面来研究其受扰后的稳定性。因此,我们首先用双流体方程和Maxwell方程组对等离子体激波面结构进行了数值模拟,得到了二维轴向激波面结构和一维强激波结构,并给出了非中性等离子激波的Rankine-Hugoniot关系。在此基础上,将受扰激波面的不稳定性按照扰动波长的大小分为两种情形进行分析。在波长与德拜长度可比的情况下,采用简正模方法,并在全空间取傅氏变换,可得到解析的色散关系。我们发现受扰激波面存在类似Langmiur波和离子声波的不稳定模式,其不稳定性由等离子体激波面上的平衡量梯度和(或)自生电场驱动。在扰动波长与离子间碰撞平均自由程可比的情况下,只在垂直激波运动方向取傅氏变换,可得到关于扰动量的微分方程组,辅以适当的边界条件,构成特征值问题。从所构成的特征值问题和所求色散关系可发现,此时的受扰激波面具有类似Rayleigh-Taylor (R-T)不稳定性的不稳定性模式。
当采用双流体方程和Maxwell方程组来描述等离子体时,在等离子体激波与界面相互作用的另一面——界面不稳定性的演化中也存在类似的自生电场。以R-T不稳定性为例,我们发现考虑流体可压缩性时,该电场均对R-T不稳定性具有致稳作用。在研究上述问题时,我们对流体可压缩性对R-T不稳定性的影响进行了系统地分析,并给出了新的结论。文中分别讨论了表征流体可压缩性的两个参数(绝热指数和分界面上的平衡压力)对R-T不稳定性的增长率的影响。认为仅考虑绝热指数的影响时,其对不稳定性的致稳或退稳效应取决于上下层流体间的相对可压缩性;仅考虑分界面上平衡压力的影响时,压力越小,可压缩性越大,R-T不稳定性增长率越大,具退稳作用。
The interaction of a plasma shock with an interface is an important problem in the iner-tial confinement fusion and in astrophysical phenomenon such as supernovae. In this paper,we investigate new effects of a self-generating electric field in a plasma on the instability ofthe shock front and interface in the evaluation of the shock-interface interactions.
In this paper, the shock front is treated as a finite thickness region to investigate thestability of the perturbed shock. So, the plasma shock structure is investigated at first.The Rankine-Hugoniot relations of the non-neutral plasma shock are derived, and the two-dimensional axial shock and the one-dimensional strong shock structures are numerical sim-ulated with a set of two-?uids equations and Maxwell equations. With these shock struc-tures, the instability of the perturbed shock front is analyzed in two cases according to theperturbed wavelength. When the wavelength is comparable to the Debye length, an ana-lytic dispersion relation can be obtained through the normal mode analysis and the Fouriertransform in all dimensions. There are instability modes that similar to the Langmiur waveand ionic sound wave in the perturbed shock fronts. The instability is driven by the self-generating electric field and (or) the gradients of the equilibrium parameters in the shockfronts. When the wavelength is comparable to the ion-ion collisional mean free path, theFourier transform is performed only in the dimension, which are perpendicular to the shockpropagation direction. Together with appropriate boundary conditions, a set of differentialequations for the perturbed quantities constitute an eigenvalue problem essentially. Aftersolving the eigenvalue problem, the dispersion relations of the instable modes are plotted.The instability of the perturbed shock front with large wavelength is found to be similar tothe Rayleigh-Taylor instability (RTI).
On the other hand of the plasma shock-interface interaction, the evolution of theinterfacial instability, the self-generating field will be emerged also as the plasma describedby the two-?uids equations and Maxwell equations. Taking RTI as an example, the fieldhas stabilized effects on the linear region of the RTI, when the compressibility of the?uid is considered. At the same time, we analyzed the compressibility effects on the RTIsystematically, and concluded new results. The effects of the two parameters representedthe compressibility of the ?uid (the ratio of specific heats and the equilibrium pressure at the interface) on the RTI growth rate are analyzed respectively. When the ratio of specificheats are considered only, the stabilized or destabilized effects on the RTI depend on therelative compressibility of the upper heavy ?uid and lower light ?uid. When the equilibriumpressure at the interface is considered only, the less pressure indicates more compressibilityof the fluid, and larger growth rate. The effects of the equilibrium pressure at the interfaceon the RTI are destabilized.
引文
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