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Eigenmode analysis of the sheared-flow Z-pinch
Physics of Plasmas ( IF 2.2 ) Pub Date : 2020-12-01 , DOI: 10.1063/5.0029716
J. R. Angus 1 , J. J. Van De Wetering 2 , M. Dorf 1 , V. I. Geyko 1
Affiliation  

Experiments have demonstrated that a Z-pinch can persist for thousands of times longer than the growth time of global magnetohydrodynamic (MHD) instabilities such as the m = 0 sausage and m = 1 kink modes. These modes have growth times on the order of t a = a / v i, where vi is the ion thermal speed and a is the pinch radius. Axial flows with d u z / d r ≲ v i / a have been measured during the stable period, and the commonly accepted theory is that this amount of shear is sufficient to stabilize these modes as predicted by numerical studies using the ideal MHD equations. However, these studies only consider specific equilibrium profiles that typically have a modest magnitude for the logarithmic pressure gradient, q P ≡ d ln P / d ln r, and may not represent experimental conditions. Linear stability of the sheared-flow Z-pinch is studied here via a direct eigen-decomposition of the matrix operator obtained from the linear ideal MHD equations. Several equilibrium profiles with a large variation of qP are examined. Considering a practical range of k, 1 / 3 ≲ ka ≲ 10, it is shown that the shear required to stabilize m = 0 modes can be expressed as d u z / d r ≥ C γ 0 / ( k a ) α. Here, γ 0 = γ 0 ( k a ) is the profile-specific growth rate in the absence of shear, which scales approximately with | q P |. Both C and α are profile-specific constants, but C is order unity and α ≈ 1. It is further demonstrated that even a large value of shear, d u z / d r = 3 v i / a, is not sufficient to provide linear stabilization of the m = 1 kink mode for all profiles considered. This result is in contrast to the currently accepted theory predicting stabilization at much lower shear, d u z / d r = 0.1 v i / a, and suggests that the experimentally observed stability cannot be explained within the linear ideal-MHD model.

中文翻译:

剪切流 Z 形夹点的特征模态分析

实验表明,Z 形夹点的持续时间比全球磁流体动力学 (MHD) 不稳定性(例如 m = 0 香肠和 m = 1 扭结模式)的增长时间长数千倍。这些模式的增长时间约为 ta = a / vi,其中 vi 是离子热速度,a 是夹点半径。在稳定期测量了具有duz / dr ≲ vi / a 的轴流,并且普遍接受的理论是,正如使用理想MHD 方程的数值研究所预测的那样,该剪切量足以稳定这些模式。然而,这些研究只考虑了特定的平衡曲线,这些曲线通常对对数压力梯度具有适度的幅度,q P ≡ d ln P / d ln r,并且可能不代表实验条件。这里通过从线性理想 MHD 方程获得的矩阵算子的直接特征分解来研究剪切流 Z 夹点的线性稳定性。检查了 qP 变化很大的几个平衡曲线。考虑到 k, 1 / 3 ≲ ka ≲ 10 的实际范围,表明稳定 m = 0 模式所需的剪切可以表示为 duz / dr ≥ C γ 0 / ( ka ) α。在这里,γ 0 = γ 0 ( ka ) 是没有剪切时的剖面特定增长率,它大约与 | 成比例。qP|。C 和 α 都是剖面特定的常数,但 C 是有序单位,α ≈ 1。进一步证明,即使是大的剪切值,duz / dr = 3 vi / a,也不足以提供线性稳定性对于所有考虑的配置文件,m = 1 扭结模式。
更新日期:2020-12-01
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