Statistical study for ITG turbulent transport in flux-driven tokamak plasmas based on global gyro-kinetic simulation

Abstract

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) P (S) to analyze heat flux eddies in the real space, with S the eddy size, incorporated with Fourier-based approaches in spectral space. In the size-PDF to the quiescent phase, P (S) is found to be fitted by three piecewise power laws which transitions at two typical sizes, S a and S b , as P ∝ S −2/3 (S ⩽ S a ), P ∝ S −2 (S a ⩽ S ⩽ S b ), and P ∝ S −4 (S ⩾ S b ), where S a ∼ 50 and S b ∼ 200 in squared gyro-radius unit ρ 2 i for the system with a/ρ i ∼ 225 (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 S ⩾ S b reaching to S max ∼ 1500. 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.

Characteristics of constrained turbulent transport in flux-driven toroidal plasmas

“…Figures 3 and 4 exhibit complex transport dynamics with a mixture of multiple elementary processes with different spatio-temporal scales. To characterize such dynamics, as we describe in §2c (also see [29]), we explored a real space (not Fourier space)-based statistical method to directly measure the size distribution of heat flux eddies (figure 13), which is expressed by the PDF P ( S ) with S the eddy size (area). In this method, we define each heat flux eddy designated by ‘ i ’ on the poloidal cross-section (i=1∼N), which contains relevant information such as eddy size S i , heat flux δQi and heat flux density Di/ Si.…”

“…An avalanche is recognized as the propagation of short wavelength pressure perturbation, δTi, which is widely observed in the flux-driven simulations [24–26,29,33]. Two types of avalanches, a hump which propagates downwards, while a hole propagates upward, can be seen depending on the sign of E r shear.…”

“…It can be seen that q+false(Sfalse) and q−false(Sfalse) are cancelled predominantly while the residue provides a net heat flux qfalse(Sfalse) in [0, S ]. Not only the heat flux, but also the heat flux density given by Di±≡qi±/Si± can be estimated, which is a useful method to study the validity of quasi-linear hypothesis [29]. In figure 13 a 1 and b 1, a hump in P±false(Sfalse) and heat flux in δq±false(Sfalse) can be seen in the region 60≤S≤180 with a peak at S ∼ 100, which correspond to linear ITG mode.…”

“…To extract the characteristics of the turbulent transport, we introduced a real space-based statistical method, i.e. size-probability density function (PDF), which directly measures the size distribution of the heat flux eddies [29]. From the size-PDF obtained from the series of simulations, we found that the size-PDF exhibits a piecewise power law P−α depending on the region of eddy size S , where each region corresponds to different transport processes.…”

“…Their fluctuations cause complex structures and dynamics not only in configuration space, e.g. turbulent spreading [20][21][22][23], avalanches and bursts [24][25][26][27][28][29], finescale pressure corrugations, referred to as staircase [30][31][32][33][34][35][36], etc. but also in velocity space, e.g.…”