剪切流Z箍缩的理想稳定性
On the ideal stability of the sheared-flow Z pinch
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中文总结 AI 辅助
该研究在理想MHD框架下分析剪切流Z箍缩的稳定性，发现跨阿尔文剪切流虽无法抑制扭曲不稳定性却会激发剪切驱动模式，指出其稳定性最终依赖于有限轨道宽度与耗散等非理想物理。
中文摘要 AI 辅助
理想磁流体力学（MHD）框架下已对剪切流Z箍缩的稳定性开展了研究，主要通过增长率计算展开，研究发现即使是跨阿尔文（trans-Alfvénic）剪切流也似乎无法抑制扭曲（kink）不稳定性。跨阿尔文剪切流确实能稳定MHD扭曲不稳定性，但同时会激发高雷诺数超声流特有的剪切驱动不稳定性，这一区别可从支撑增长率的色散关系中明确体现，本文在复频率平面上将其计算为解析色散函数。正则化将该函数拆分为绝热部分与共振部分，用于描述离散模式如何从连续谱中产生并与之相互作用。多普勒频移后的流连续谱与交换（interchange）不稳定性、扭曲不稳定性的作用方式存在差异：对于交换不稳定性，连续谱在所有波数下均与不稳定性分支重叠，因此即使是亚阿尔文剪切流也能在适度超出交换阈值的情况下稳定剖面；相比之下，扭曲不稳定性通过频率间隙与连续谱隔离，需跨阿尔文流将连续谱多普勒频移至与扭曲不稳定性共振，由此得到稳定阈值的几何图像。但剪切驱动不稳定性会在该同一阈值处出现，包括反射模式与声学扭曲模式，正是这些剪切驱动模式而非原始MHD不稳定性，在跨阿尔文条件下主导了理想MHD谱。因此，理想分析描述了稳定机制，同时表明剪切流Z箍缩的稳定性最终依赖于非理想物理，包括有限轨道宽度与耗散。
英文摘要
Sheared-flow Z-pinch stability has been studied within ideal MHD primarily through growth rate calculations, which find that even trans-Alfvénic sheared flows apparently fail to suppress the kink instability. Trans-Alfvénic sheared flow does stabilize the MHD kink but also excites shear-driven instabilities characteristic of high-Reynolds-number supersonic flow. This distinction is evident from the dispersion relations underlying the growth rates, computed here as the analytic dispersion function in the complex-frequency plane. Regularization splits this function into adiabatic and resonant parts describing how discrete modes emerge from and interact with the continuous spectrum. The Doppler-shifted flow continuum interacts with the interchange and kink instabilities in distinct ways. For interchange, the continuum overlaps the instability branch at all wavenumbers, so even sub-Alfvénic sheared flow stabilizes profiles modestly beyond the interchange threshold. The kink, by contrast, is shielded from the continuum by a frequency gap, and trans-Alfvénic flow is required to Doppler-shift the continuum into resonance with it, giving a geometric picture of the stabilization threshold. But shear-driven instabilities arise at this same threshold, including reflection modes and an acoustic kink. It is these shear-driven modes, not the original MHD instabilities, that dominate the ideal-MHD spectrum in trans-Alfvénic conditions. The ideal analysis thus describes the stabilization mechanism while showing that the stability of the sheared-flow Z pinch ultimately rests on non-ideal physics, including finite orbit width and dissipation.
