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 (TE) 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. TE 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 that of the GAM, which is due 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.
Amplitude behaviour of geodesic acoustic modes in the ASDEX Upgrade tokamak
Zonal flows induced by symmetry breaking with existence of geodesic acoustic modes