Direct causality analysis of the multi-scale interactions among macro-scale tearing mode (TM), meso-scale geodesic acoustic mode (GAM) and small-scale turbulence in the edge plasma of the HL-2A tokamak utilizing transfer entropy method is reported. Experimental results have demonstrated that the (m/n)=(2/1) (with m and n being the poloidal and toroidal mode numbers, respectively) TM modulates the turbulence with the frequency range of f=50-150 kHz and the GAM mainly modulates that with higher frequencies. The TM has both amplitude and phase modulation on turbulence energy while the GAM has only amplitude regulation effect. Transfer entropy analyses have shown that both TM and GAM will modulate the turbulence energy during which the impact of the former is of about an order magnitude larger than the latter, whereas the causal effect of TM on particle transport is about twice as that of the GAM, which owes to the different causal effects on density and electric field fluctuations caused by TM and GAM, respectively. It is suggested that the magnetic fluctuation strongly modulates the Reynolds stress which serves as a mediator, leading to a cooperative interaction between TM and GAM in the edge of tokamak plasmas.

The effect of island width on the multi-scale interactions between magnetic island (MI) and ion temperature gradient (ITG) turbulence has been investigated based on the global gyrokinetic approach. It is found that the coupling between the island and turbulence is enhanced when the MI width (w) becomes larger. A vortex flow that is highly sensitive to the width of the magnetic island can be triggered, ultimately resulting in a potent shear flow and a consequent reduction in turbulent transport. The shearing rate induced by the vortex flow is minimum at the O-point while it is maximum at both of the two reconnection points of the island, i.e., the X-points, regardless of the island width. There exists a nonmonotonic relationship between zonal flow (ZF) amplitude and island width, showing that the ZF is partially suppressed by medium-sized MIs whereas enhanced in the case of large island. A larger MI can tremendously damage the ITG mode structure, resulting in higher turbulent transport at the X-point whereas a lower one at the O-point, respectively. Such phenomenon will be less distinct at very small island widths below w/a ~ 8%≈ 12ρi (a is the minor radius and ρi the ion gyroradius), where it shows that turbulence near the X-point is hardly affected although it is still suppressed inside the island. Furthermore, the influence of different island sizes on turbulence transport level is also discussed.

Statistical spectral features of the dependence of geodesic acoustic modes (GAMs) and their nonlinear couplings with ambient turbulence on the magnetic island (MI) width (W) in the edge region of HL-2A tokamak plasmas are analyzed. Experimental observations have indicated that the modulation influence as well as the strength of nonlinear interactions between GAMs and turbulence generally shows a gradual decay while the couplings between MIs and the latter are increased simultaneously as the MI becomes larger. The magnetic islands mainly reduce the couplings between GAMs and potential fluctuations, whereas the changes in the nonlinear interactions between density fluctuations and MIs are more evident. Moreover, it is found that there exists a nonmonotonic relationship between the turbulence correlation length and island width, in which it exhibits a minimum around W~3.7 cm, suggesting that the MI around such scale would have significant suppression effect on turbulent transport. These findings would promote the understanding of the nonlinear interactions between magnetic islands and turbulence in the edge of fusion plasmas.