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arXiv 2004.03243physics.plasm-phmath-phmath.MP
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平衡电子温度各向异性下等离子体中磁涡旋链的线性稳定性

Linear stability of magnetic vortex chains in a plasma in the presence of equilibrium electron temperature anisotropy

C. Granier, E. Tassi

摘要:

本文采用简化的流体模型,在强导场和平衡电子温度各向异性的条件下,在二维空间中解析地研究了等离子体中磁涡旋链的线性稳定性。磁涡旋链的建模通过经典的“猫眼”的解决方案和线性稳定性进行了研究,通过分析的第二个变化的保守功能,根据能量Casimir方法。稳定性分析是在以涡的分离面为界的区域上进行的。两种情况下被认为是,对应于垂直平衡离子和电子温度之间的比率远大于或远小于统一,分别。在前一种情况下,平衡流取决于任意函数。如果平衡电子温度各向异性是有界的,从上面和下面,与下限对应的条件,防止消防水龙带不稳定性,达到稳定性。对于给定的平衡流的选择,另一个条件为旋涡的振幅设定了上限。对于冷离子,必须考虑两种子情况。在第一种情况下,平衡对应于速度场与局部阿尔文速度成比例的平衡。稳定性条件意味着:流动幅度的上限,这自动意味着消防水龙带的稳定性,电子温度各向异性的上限和再次的涡旋的大小的上限。第二子情况指的是平衡静电势,其在磁通量表面上不是恒定的,并且所得到的稳定性条件对应于在没有流动的情况下的第一子情况。

英文摘要:

The linear stability of chains of magnetic vortices in a plasma is investigated analytically in two dimensions by means of a reduced fluid model assuming a strong guide field and accounting for equilibrium electron temperature anisotropy. The chain of magnetic vortices is modelled by means of the classical "cat's eyes" solutions and the linear stability is studied by analysing the second variation of a conserved functional, according to the Energy-Casimir method. The stability analysis is carried out on the domain bounded by the separatrices of the vortices. Two cases are considered, corresponding to a ratio between perpendicular equilibrium ion and electron temperature much greater or much less than unity, respectively. In the former case, equilibrium flows depend on an arbitrary function. Stability is attained if the equilibrium electron temperature anisotropy is bounded from above and from below, with the lower bound corresponding to the condition preventing the firehose instability. A further condition sets an upper limit to the amplitude of the vortices, for a given choice of the equilibrium flow. For cold ions, two sub-cases have to be considered. In the first one, equilibria correspond to those for which the velocity field is proportional to the local Alfvén velocity. Stability conditions imply: an upper limit on the amplitude of the flow, which automatically implies firehose stability, an upper bound on the electron temperature anisotropy and again an upper bound on the size of the vortices. The second sub-case refers to equilibrium electrostatic potentials which are not constant on magnetic flux surfaces and the resulting stability conditions correspond to those of the first sub-case in the absence of flow.

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