Statistical characteristics of turbulent plasmas dominated by zonal flows

Abstract

In order to better understand the feature of turbulent transport in tokamak plasmas dominated by zonal flows and nonlinearly excited tertiary (Kelvin–Helmholtz-like) waves, the radial dependency of the turbulent structure in the back of steady-state zonal flows was analyzed based on gyrofluid simulation of the electron temperature gradient turbulence in a sheared-slab configuration. The zonal flows change the characteristics of plasma turbulence from homogeneous to inhomogeneous. Thus, it is found that turbulent vortices are regulated by a radially alternative potential pattern where the spatiotemporal characteristic scales with respect to local fluctuations change radially. From the cross spectrum analysis between the poloidal electric field and the pressure perturbation, it was found that, in plasmas dominated by zonal flows, the restriction of heat flux is conducted by two mechanisms, i.e. the reduction of coherence and the phase synchronization.

Non-perturbative statistical theory of intermittency in ITG drift wave turbulence with zonal flows

“…[9] and found in the reduced two field model of ITG turbulence in Sec. V whereas it is in agreement with predictions from non-linear simulations of turbulence [19]- [20] and in gyro-kinetic toroidal simulations [21]- [22]. Mathematically it is due to the different highest non-linearity between the two models (i.e.…”

“…This result differs from what has theoretically been found earlier [9] where the zonal flow is treated kinematically. It is however in agreement with predictions from non-linear simulations of turbulence [19]- [20] and gyro-kinetic toroidal simulations [21]- [22]. The reason for this is the cubic non-linearity in Eq.…”

“…Interestingly the predicted PDF tails of momentum flux are Gaussian when the feedback of zonal flow on the turbulence is incorporated. This result differs from what has theoretically been found earlier [9] whereas it is in agreement with predictions from non-linear simulations of turbulence [19]- [20] and gyro-kinetic toroidal simulations [21]- [22]. The reason for this is that previously the zonal flow has been treated as passively evolving by the turbulence without the feedback loop to turbulence.…”

Formation of coherent vortex streets and transport reduction in electron temperature gradient driven turbulence

“…Zonal-flow dynamics and the properties of large-scale coherent vortex structures in the slab ETG turbulence have also been discussed by means of gyrokinetic and gyrofluid simulations. [14][15][16][17][18][19] It has been pointed out that the weak magnetic shear is important for the zonal-flow generation, while the positive magnetic shear leads to the streamer formation. 14,15 The scale length of zonal flow is characterized by the Rhines scaling, which is proportional to the density gradient scale length L n , where the electron heat transport decreases with increasing of L n .…”

“…16 The statistical analyses for the ETG turbulence dominated by zonal flows reveal the phase matching between potential and pressure fluctuations, which is related to the reduction in the radial heat flux and the fractal dimension of the turbulent fluctuations. 17,18 It has also been pointed out that in addition to the zonal flows, the dynamics of nonlinearly excited long wavelength modes is important for the saturation of the ETG instability and for the regulation of the electron heat transport. 19 In the present study, by means of the gyrokinetic Vlasov simulations, we investigate vortex structures of the slab ETG turbulence and velocity-space structures of the distribution function in detail.…”