Flux-driven ion temperature gradient (ITG) turbulence and associated transport regulated by non-local and non-diffusive processes are investigated based on GKNET simulations in a global toroidal geometry. Among these processes, the instantaneous formation of radially extended quasi-coherent structure, which leads to the transport burst, is found to play an important role in causing global profile formation and relaxation. To elucidate the characteristics of such a transport process, we introduce the size probability distribution function (size-PDF) to analyze heat flux eddies in the real space, with the eddy size, incorporated with Fourier-based approaches in spectral space. In the size-PDF to the quiescent phase, is found to be fitted by three piecewise power laws which transitions at two typical sizes, and , as , , and , where and in squared gyro-radius unit for the system with (a: the minor radius). On the other hand, the size-PDF in the bursting phase exhibits non-power-law irregular humps which corresponds to the quasi-coherent structures for reaching to . Such a coherent structure is ascribed to the spontaneous alignment of smaller scale eddies through phase matching in radial direction, which is classified as a quasi-deterministic process. Resultantly, a large amount of free energy is extracted from the system due to subsequent growth of the event, by which a self-organized profile is established. The coherent structure is then readily disintegrated by self-generated zonal flows, followed by the energy transferred to smaller eddies. Finally, turbulent transport in the steady state of a flux-driven system is found to be regulated by the mixture of such quasi-deterministic process and probabilistic processes, which leads to stiffness and resilience in the profile formation and self-similarity in the relaxation.
Plasma size and collisionality scaling of ion-temperature-gradient-driven turbulence