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arXiv 1807.01458physics.plasm-ph
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双组分量子和经典等离子体中线性静电波的解析性质

Analytical Properties of Linear Electrostatic Waves in Two-Component Quantum and Classical Plasmas

Shane Rightley, Dmitri Uzdensky

摘要:

我们研究了线性静电波的性质,在非磁化量子和经典等离子体组成的一个或两个人口的电子与解析易处理的分布函数中存在一个固定的中和离子背景。从动力学量子等离子体的纵向磁化率,我们评估的影响,由于背景分布函数的复杂性增加。首先,我们分析了单组分等离子体中的色散和朗道阻尼,并考虑了具有各种解析性质的分布函数:Dirac δ函数,具有两个复一阶极点的Cauchy分布,具有两个二阶极点的平方Cauchy分布,以及具有四个一阶极点的逆四次分布;我们还简要讨论了非亚纯的完全退化和任意退化的Fermi-Dirac分布。为了研究静电不稳定性,然后我们转向等离子体与两个群体的电子流相对于彼此在两种情况下:一个对称的情况下,两个逆流相同的人口和一个凸点的情况下,一个主要的人口和一个三角函数束。我们得到相应的线性动力学色散关系和评估的不稳定性时,电子分布函数的δ函数,柯西,平方柯西,或逆四次类型的属性。与其他研究一致,我们发现,一般来说,量子效应减少波长范围的不稳定模式在长波长。我们还发现了第二个窗口的不稳定性在较短的波长,并阐明其性质是由于量子反冲。我们注意到实验室和天体物理量子等离子体研究的可能影响。

英文摘要:

We examine the properties of linear electrostatic waves in unmagnetized quantum and classical plasmas consisting of one or two populations of electrons with analytically tractable distribution functions in the presence of a stationary neutralising ion background. Beginning with the kinetic quantum plasma longitudinal susceptibility, we assess the effects due to increasing complexity of the background distribution function. Firstly, we analyse dispersion and Landau damping in one-component plasmas and consider distribution functions with a variety of analytical properties: the Dirac delta function, the Cauchy profile with two complex first-order poles, the squared Cauchy profile with two second order poles, and the inverse-quartic profile with four first-order poles; we also briefly discuss the non-meromorphic totally- and arbitrarily-degenerate Fermi-Dirac distribution. In order to study electrostatic instabilities, we then turn to plasmas with two populations of electrons streaming relative to each other in two cases: a symmetric case of two counter-streaming identical populations and a bump-on-tail case with a primary population and a delta-function beam. We obtain the corresponding linear kinetic dispersion relations and evaluate the properties of instabilities when the electron distribution functions are of the delta function, Cauchy, squared-Cauchy, or inverse-quartic types. In agreement with other studies, we find that in general quantum effects reduce the range of wavelengths for unstable modes at long wavelengths. We also find a second window of instability at shorter wavelengths and elucidate its nature as being due to quantum recoil. We note the possible implications for studies of laboratory and astrophysical quantum plasmas.

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