Multi-scale interactions between turbulence and magnetic islands and parity mixture—a review

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.