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arXiv 1208.0966physics.plasm-phastro-ph.SR
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Sweet-Parker电流片中的等离子体团和Kelvin-Helmholtz不稳定性

Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets

N. F. Loureiro, A. A. Schekochihin, D. A. Uzdensky

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21 pages, 9 figures, submitted to Phys. Rev. E
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摘要：

本文在约化磁流体动力学的框架下发展了Sweet-Parker（SP）电流片不稳定性的二维线性理论。考虑到一般的平衡配置文件上的流出坐标的依赖性进行本地分析。恢复了等离子体团不稳定性[Loureiro等人，Phys. Plasmas { \bf 14}，100703（2007）]，即，电流片对于形成大波数的等离子体团链（$k_{\rm max}\Lsheet \sim S^{3/8}$，其中$k_{\rm max}$是最快增长模式的波数，$S=\Lsheet V_A/η$是伦德奎斯特数，$\Lsheet$是片的长度，$V_A$是阿尔文速度，$η$是等离子体电阻率）是不稳定的，其生长超阿尔文快（$\gmaxτ_A\sim S^{1/4}$，其中$\gmax$是最大生长速率，以及$τ_A=\Lsheet/V_A$）。对于典型的背景轮廓，增长率和波数被发现{ \it增加}在流出方向。这是由于存在另一种模式，即开尔文-亥姆霍兹（KH）不稳定性，它在层的外围触发，其中流出速度超过与上游磁场相关的阿尔文速度。KH不稳定性的增长甚至比等离子体团不稳定性$\gmax τ_A \sim k_{\rm max} \Lsheet\sim S^{1/2}$更快。粘度（$ν$）对等离子体团不稳定性的影响也得到了解决。在大磁普朗特数$Pm=ν/η$的极限下，发现了$\gmax\sim S^{1/4}Pm^{-5/8}$和$k_{\rm max} \Lsheet\sim S^{3/8}Pm^{-3/16}$，从而预言了在$Pm\gg1$区等离子体团不稳定性的临界Lundquist数为$\Scrit\sim 10^4Pm^{1/2}$ .这些结果通过直接数值模拟的线性化方程，使用一个新的，分析二维SP平衡解决方案进行了验证。

英文摘要：

A 2D linear theory of the instability of Sweet-Parker (SP) current sheets is developed in the framework of Reduced MHD. A local analysis is performed taking into account the dependence of a generic equilibrium profile on the outflow coordinate. The plasmoid instability [Loureiro et al, Phys. Plasmas {\bf 14}, 100703 (2007)] is recovered, i.e., current sheets are unstable to the formation of a large-wave-number chain of plasmoids ($k_{\rm max}\Lsheet \sim S^{3/8}$, where $k_{\rm max}$ is the wave-number of fastest growing mode, $S=\Lsheet V_A/η$ is the Lundquist number, $\Lsheet$ is the length of the sheet, $V_A$ is the Alfvén speed and $η$ is the plasma resistivity), which grows super-Alfvénically fast ($\gmaxτ_A\sim S^{1/4}$, where $\gmax$ is the maximum growth rate, and $τ_A=\Lsheet/V_A$). For typical background profiles, the growth rate and the wave-number are found to {\it increase} in the outflow direction. This is due to the presence of another mode, the Kelvin-Helmholtz (KH) instability, which is triggered at the periphery of the layer, where the outflow velocity exceeds the Alfvén speed associated with the upstream magnetic field. The KH instability grows even faster than the plasmoid instability, $\gmax τ_A \sim k_{\rm max} \Lsheet\sim S^{1/2}$. The effect of viscosity ($ν$) on the plasmoid instability is also addressed. In the limit of large magnetic Prandtl numbers, $Pm=ν/η$, it is found that $\gmax\sim S^{1/4}Pm^{-5/8}$ and $k_{\rm max} \Lsheet\sim S^{3/8}Pm^{-3/16}$, leading to the prediction that the critical Lundquist number for plasmoid instability in the $Pm\gg1$ regime is $\Scrit\sim 10^4Pm^{1/2}$. These results are verified via direct numerical simulation of the linearized equations, using a new, analytical 2D SP equilibrium solution.

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