Study of nonlinear dynamics among zonal flow, GAM, and turbulence on the HL-2A strongly heated L-mode plasmas

Experiments to directly measure the nonlinear energy exchange among turbulence, zonal flows, and GAMs were carried out on the HL-2A tokamak at the Southwestern Institute of Physics (SWIP) in China. At various discharge conditions, the turbulent kinetic energy was clearly shown to transfer from turbulence with intermediate frequencies (20-60 kHz) to zonal flows (0-5 kHz) and GAMs ($\sim$10 kHz) and to turbulent fluctuations with high frequencies (\textgreater 60 kHz). The turbulent Reynolds stress $\left\langle {\tilde{{v}}_{r} \tilde{{v}}_{pol} } \right\rangle $ profiles were shown consistent with the time-averaged ExB and TDE (time-delay estimation) poloidal velocity profiles. Other micro statistics, such as particle flux $\left\langle {\tilde{{n}}\tilde{{v}}_{r} } \right\rangle $ and vorticity flux $\left\langle {\tilde{{v}}_{r} \tilde{{\omega }}} \right\rangle $, together with the macro equilibrium profiles at various discharge conditions will also be presented, which form a consistent picture that turbulent vortices mediate turbulent energy and momentum and integrate them into sheared flows across the edge plasmas.