三维线束缚等离子体中电流奇异性的构造
Constructing current singularity in a 3D line-tied plasma
摘要：
我们重温帕克的猜想，目前的奇异性形成在三维线束缚等离子体使用最近发展的数值方法，变分积分理想磁流体力学的拉格朗日标记。由于该方法中加入了冻结方程，无需人工重联，因此可以说是研究电流奇异性形成的最佳工具。使用这种方法，形成的电流奇异性先前已被证实在2D的Hamm-Kulsrud-Taylor问题。在本文中，我们将这个问题扩展到三维线束缚几何。线性的解决方案，这是奇异的，在2D中，被发现是光滑的任意系统长度。然而，对于有限振幅，当系统足够长时，线性解可能变得病态。对于短系统，非线性解是光滑的。尽管如此，峰值电流密度与系统长度的比例表明，非线性解决方案可能会成为奇异的有限长度。有了这些结果，我们既不能肯定也不能排除这种可能性，因为我们不能得到系统长度接近外推临界值的解。
英文摘要：
We revisit Parker's conjecture of current singularity formation in 3D line-tied plasmas using a recently developed numerical method, variational integration for ideal magnetohydrodynamics in Lagrangian labeling. With the frozen-in equation built-in, the method is free of artificial reconnection, and hence it is arguably an optimal tool for studying current singularity formation. Using this method, the formation of current singularity has previously been confirmed in the Hahm--Kulsrud--Taylor problem in 2D. In this paper, we extend this problem to 3D line-tied geometry. The linear solution, which is singular in 2D, is found to be smooth for arbitrary system length. However, with finite amplitude, the linear solution can become pathological when the system is sufficiently long. The nonlinear solutions turn out to be smooth for short systems. Nonetheless, the scaling of peak current density versus system length suggests that the nonlinear solution may become singular at finite length. With the results in hand, we can neither confirm nor rule out this possibility conclusively, since we cannot obtain solutions with system length near the extrapolated critical value.
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