This paper presents a review of multi-scale interactions between small-scale turbulence and large scale magnetic islands. In finite beta plasmas, zonal flows are relatively weak, and thus another electromagnetic coherent structure formation such as magnetic islands becomes important for regulating turbulence. In multi-scale interactions, large-scale modes dominate turbulent fluctuations even when the growth rate of the large-scale mode is much smaller than small-scale modes. On the other hand, small-scale modes influence large-scale modes when the large-scale modes are stable/marginally stable. Thus, the multi-scale interactions are categorized according to the stability of tearing mode (TM), which drives large-scale magnetic islands. When the TM is unstable, wide magnetic islands are produced, and as a result of the multi-scale interactions, the turbulent transport is significantly enhanced inside the separatrix of the island, because large-scale stable modes are excited by mutual interactions between turbulence and the island. On the other hand, a steep temperature gradient is formed around the separatrix of the island, which is consistent with zonal flow shear appearing at the separatrix. When the TM is stable/marginally stable, turbulence drives and sustains magnetic islands of width equal to multiples of the Larmor radius. This excitation of islands by turbulence can be related to the seed island formation of neo-classical TMs. The parity of fluctuations plays crucial role in the multi-scale nonlinear interactions, because pure twisting parity mode does not satisfy the nonlinear fluid/gyrokinetic equations. Magnetic islands belongs to the tearing parity mode and drift-wave instabilities normally belong to the twisting parity mode, and each parity is conserved in the linear growth of the instability. However, when the amplitude of the twisting parity mode becomes finite, the nonlinear energy transfer takes place from the twisting parity to tearing parity modes. Through this nonlinear parity mixture, the magnetic islands are produced by the turbulence. The influence of anomalous current drive and polarization current on the multi-scale interactions is discussed as well.
本论文综述了小尺度湍流与大尺度磁岛之间的多尺度相互作用。在有限β等离子体中，纬向流相对较弱，因此另一种电磁相干结构——磁岛的形成——对湍流调控变得重要。在多尺度相互作用中，大尺度模主导湍流涨落，即使大尺度模的增长率远小于小尺度模。另一方面，当大尺度模稳定或边际稳定时，小尺度模会影响大尺度模。因此，多尺度相互作用可根据撕裂模（TM）的稳定性进行分类，撕裂模驱动大尺度磁岛。当撕裂模不稳定时，会产生宽磁岛，结果在多尺度相互作用下，磁岛分界线内部的湍流输运显著增强，因为大尺度模通过湍流与磁岛之间的相互作用被激发。另一方面，磁岛分界线附近形成陡峭的温度梯度，这与分界线处出现的纬向流剪切一致。当撕裂模稳定或边际稳定时，湍流驱动并维持宽度等于拉莫尔半径整数倍的磁岛。这种由湍流激发的磁岛可能与新经典撕裂模（NTM）的种子岛形成有关。涨落的宇称在多尺度非线性相互作用中起关键作用，因为纯扭曲宇称模不满足非线性流体/回旋动力学方程。磁岛属于撕裂宇称模，而漂移波不稳定性通常属于扭曲宇称模，并且在线性增长阶段各宇称分别守恒。然而，当扭曲宇称模的幅度变为有限时，非线性能量转移从扭曲宇称模向撕裂宇称模发生。通过这种非线性宇称混合，湍流产生了磁岛。此外，还讨论了反常电流驱动和极化电流对多尺度相互作用的影响。