内电磁箍缩型不稳定性的基本模型
Elementary model of internal electromagnetic pinch-type instability
摘要：
本文用数值方法分析了由固体壁围成的、带有均匀电流的无粘导电液体的半无限平板层中的夹持型不稳定性。我们的模型尽可能简单，但仍然捕捉到了不稳定性的显著特征，否则可能会被更全面的数值模型和实验室实验的技术细节所掩盖。首先，我们表明，在液体金属，这是相对较差的导体的不稳定性，显着不同的天体物理学相关的泰勒不稳定性。在液态金属中，不稳定性在磁响应时间尺度上发展，这取决于电导率，并且比Alfvén时间尺度长得多，在Alfvén时间尺度上，泰勒不稳定性在良好导电的流体中发展。其次，我们证明了这种不稳定性是由磁场曲率引起的边缘效应，其增长率由线电流密度决定，与系统尺寸无关。我们的研究结果表明，这种不稳定性可能会影响未来的液态金属电池，当它们的尺寸达到几米时。
英文摘要：
We analyse numerically a pinch-type instability in a semi-infinite planar layer of inviscid conducting liquid bounded by solid walls and carrying a uniform electric current. Our model is as simple as possible but still captures the salient features of the instability which otherwise may be obscured by the technical details of more comprehensive numerical models and laboratory experiments. Firstly, we show the instability in liquid metals, which are relatively poor conductors, differs significantly from the astrophysically-relevant Tayler instability. In liquid metals, the instability develops on the magnetic response time scale, which depends on the conductivity and is much longer than the Alfvén time scale, on which the Tayler instability develops in well conducting fluids. Secondly, we show that this instability is an edge effect caused by the curvature of the magnetic field, and its growth rate is determined by the linear current density and independent of the system size. Our results suggest that this instability may affect future liquid metal batteries when their size reaches a few meters.
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