The probability distribution functions (PDFs) of momentum flux and zonal flow formation in ion-temperature-gradient (ITG) turbulence are investigated, including the effect of the shear flow on the PDFs. While ITG turbulence maintains high level of transport, this may be suppressed by shear flow. Zonal flows are also shown here to have an enhanced likelihood of generation further from marginal stability which will then regulate the ITG turbulence, which is more prominent with increased shear flow, leading to a self-regulating system.
There is strong evidence in favor for zonal flow suppression of the Ion-Temperature-Gradient (ITG) mode turbulence, specifically close to the linear stability threshold. The present letter attempts to analytically calculate the effects of zonal flow suppression of the ITG turbulence through deriving a modified dispersion relation including the back-reaction of the zonal flows on the ITG turbulence based on the quasilinear theory. The results are manifested in a reduction of the linear growth rate and an increase in the effective linear ITG threshold.
An analytical model for zonal flow generation by toroidal ion-temperature-gradient (ITG) modes, including finite $β$ electromagnetic effects, is derived. The derivation is based on a fluid model for ions and electrons and takes into account both linear and nonlinear $β$ effects. The influence of finite plasma $β$ on the zonal flow growth rate ($γ_{ZF}$) scaling is investigated for typical tokamak plasma parameters. The results show the importance of the zonal flows close to marginal stability where $γ_{ZF}/γ_{ITG}>>1$ is obtained. In this region the parameter $γ_{ZF}/γ_{ITG}$ increases with $β…
The role of parallel ion motion for zonal flow generation in ion-temperature-gradient (ITG) mode turbulence is investigated with focus on the effects of acoustic modes and toroidicity on the zonal flow. One possible reason for the weak suppression of ITG turbulence by zonal flows found in experiments in the Columbia Linear Machine (CLM) [Phys. Plasmas {\bf 13} 055905 (2006)] might be due to the small toroidicity ($ε_n = 2L_n/R$) in the experiment. The zonal flow is often directly dependent on the ITG mode and the coupling of zonal flow to acoustic modes and hence is directly affected by any ch…
The saturated state of turbulence driven by the ion-temperature-gradient instability is investigated using a two-dimensional long-wavelength fluid model that describes the perturbed electrostatic potential and perturbed ion temperature in a magnetic field with constant curvature (a $Z$-pinch) and an equilibrium temperature gradient. Numerical simulations reveal a well-defined transition between a finite-amplitude saturated state dominated by strong zonal-flow and zonal-temperature perturbations, and a blow-up state that fails to saturate on a box-independent scale. We argue that this transitio…
On Phase Transition of ITG Turbulence in the Dimits shift
Laboratoire de Physique des Plasmas, CNRS, Ecole Polytechnique, Sorbonne Université, Université Paris-Saclay , Observatoire de Paris, F-91120 Palaiseau, France
Nonlinear entropy transfer via zonal flows in gyrokinetic plasma turbulence
The Graduate University for Advanced Studies（高级研究大学院大学）；Faculty of Arts and Sciences, Komazawa University（驹泽大学文理学部）；National Institute for Fusion Science（核聚变科学研究所）
The present work investigates the direct interaction of sheared mean flow with zonal flows (ZF) and the effect of parallel ion motion on ZF generation in ion-temperature-gradient (ITG) background turbulence. An analytical model for the direct interaction of sheared mean flows with zonal flows is constructed. The model used for the toroidal ITG driven mode is based on the equations for ion continuity, ion temperature and parallel ion motion whereas the ZF evolution is described by the vorticity equation. The behavior of the ZF growth rate and real frequency is examined for typical tokamak param…
In the present work the zonal flow (ZF) growth rate in toroidal ion-temperature-gradient (ITG) mode turbulence including the effects of elongation is studied analytically. The scaling of the ZF growth with plasma parameters is examined for typical tokamak parameter values. The physical model used for the toroidal ITG driven mode is based on the ion continuity and ion temperature equations whereas the ZF evolution is described by the vorticity equation. The results indicate that a large ZF growth is found close to marginal stability and for peaked density profiles and these effects may be enhan…
The role of magnetic shear for zonal flow generation by ion-temperature-gradient (ITG-) and trapped electron (TE-) mode turbulence is studied analytically using fluid descriptions. The scaling of the zonal flow (ZF) growth rate with magnetic shear is examined and compared with linear growth rates for typical tokamak parameter values. The results indicate that large levels of ZF are obtained in regions of negative magnetic shear, in particular for ZF driven by TE mode turbulence. The strong magnetic shear scaling obtained for TE mode driven zonal flows originates from the bounce average of the …
The probability distribution function (PDF) tails of the zonal flow structure formation and the PDF tails of momentum flux by incorporating effect of a shear flow in ion-temperature-gradient (ITG) turbulence are computed in the present paper. The bipolar vortex soliton (modon) is assumed to be the coherent structure responsible for bursty and intermittent events driving the PDF tails. It is found that stronger zonal flows are generated in ITG turbulence than Hasegawa-Mima (HM) turbulence as well as further from marginal stability. This suggests that although ITG turbulence has a higher level o…
Anisotropy and intermittency in drift-wave turbulence with zonal flows: a two-dimensional continuous wavelet analysis
Institute of Materials and Systems for Sustainability, Nagoya University（名古屋大学材料系统可持续研究所）；Institut de Mathématiques de Marseille (I2M), Aix-Marseille Université, CNRS（马赛数学研究所（I2M），艾克斯-马赛大学，法国国家科学研究中心）；National Institute for Fusion Science（国立核聚变科学研究所）
Turbulence induced by the ion temperature gradient (ITG) is investigated in the helical and axisymmetric plasma states of a reversed field pinch device by means of gyrokinetic calculations. The two magnetic configurations are systematically compared, both linearly and nonlinearly, in order to evaluate the impact of the geometry on the instability and its ensuing transport, as well as on the production of zonal flows. Despite its enhanced confinement, the high-current helical state demonstrates a lower ITG stability threshold compared to the axisymmetric state, and ITG turbulence is expected to…
During the past years the understanding of the multi-scale interaction problems have increased significantly. However, at present there exists a range of different analytical models for investigating multi-scale interactions and hardly any specific comparisons have been performed among these models. In this work, two different models for the generation of zonal flows from ion-temperature-gradient (ITG) background turbulence are discussed and compared. The methods used is the coherent mode coupling model and the wave kinetic equation model (WKE). It is shown that the two models give qualitative…
Abstract Simulation domain in field-aligned coordinates of the electrostatic gyrokinetic nonlinear turbulence global code, NLT, is extended to include the magnetic axis. The artificial boundary near the magnetic axis is replaced by the natural boundary. The singularity at the magnetic axis in Vlasov solver is treated by considering the spatial relation of fixed grid points in field-aligned coordinates. A new Poisson's equation solver is developed, the coefficient matrix of algebraic equations is derived by using Gauss's theorem. Nonlinear relaxation test of the ITG turbulence with adiabatic el…
There are two distinct phases in the evolution of drift wave envelope in the presence of zonal flow. A long-lived standing wave phase, which we call the Caviton, and a short-lived traveling wave phase (in radial direction) we call the Instanton. For drift wave turbulence driven by ion temperature gradient mode (ITG), these two stages of dynamics were displayed in [Zhang Y Z, Liu Z Y, Xie T, Mahajan S M and Liu J 2017 Physics of Plasmas 24 122304]. In this paper we show that the dynamical attributes of ITG turbulence are readily replicated when the turbulence rotates in the electron direction; …
Through a systematically developed theory, we demonstrate that the motion of instanton identified in [Y. Z. Zhang, Z. Y. Liu, T. Xie, S. M. Mahajan, and J. Liu, Physics of Plasmas 24, 122304 (2017)] is highly correlated to the intermittent excitation and propagation of geodesic acoustic mode (GAM) that are observed in tokamaks. While many numerical simulations have observed the phenomena, it is the first theory that reveals the physical mechanism behind GAM intermittent excitation and propagation. The preceding work is based on the micro-turbulence associated with toroidal ion temperature grad…
Cross-scale Interaction between Microturbulence and Fishbone in Fusion Plasmas
CAS Key Laboratory of Frontier Physics in Controlled Nuclear Fusion, School of Nuclear Science and Technology, University of Science and Technology of China（中国科学院受控核聚变前沿物理重点实验室，中国科学技术大学核科学与技术学院）；Institute of Plasma Physics, Chinese Academy of Sciences（中国科学院等离子体物理研究所）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Department of Physics and Astronomy, University of California, Irvine（加州大学尔湾分校物理与天文学系）
Electromagnetic turbulence in EAST plasmas with internal transport barrier
CAS Key Laboratory of Frontier Physics in Controlled Nuclear Fusion, School of Nuclear Sciences and Technology, University of Science and Technology of China（中国科学院前沿物理国家重点实验室，核科学与技术学院，中国科学技术大学）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Department of Physics and Astronomy, University of California, Irvine（加州大学尔湾分校物理与天文学系）
本研究通过全局非线性电磁 gyrokinetic 模拟，揭示弱反剪切 EAST 托卡马克 ITB 区域的电磁湍流特性，发现电磁效应可抑制高频 ITG 模、增强带状流剪切以降低热导率，为准确计算输运系数提供关键依据。
We show that the recently introduced two-field flux-balanced Hasegawa-Wakatani (BHW) model captures the key features of drift-wave turbulent transport mediated by zonal flows observed in more complete and accurate gyrokinetic simulations, such as the existence of a nonlinear upshift of the threshold for drift wave turbulence driven transport, often called the Dimits shift, as well as non-local transport with avalanche bursts and solitary propagating structures. Because of the approximations made in the BHW model, these observations are made for the particle flux instead of the heat flux more c…
We report a first study of time-dependent Probability Density Functions (PDFs) in the Low-to- High confinement mode (L-H) transition by extending the previous prey-predator-type model (Kim & Diamond, Phys. Rev. Lett. 91, 185006, 2003) to a stochastic model. We highlight the limited utility of mean value and variance in understanding the L-H transition by showing strongly non-Gaussian PDFs, with the number of peaks changing in time. We also propose a new information geometric method by using information length, dynamical time scale, and information phase portrait, and show their utility in fore…
A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, "On some statistical properties of hydrodynamical and magnetohydrodynamical fields," Q. Appl. Math. 10, 69 (1952)] is taken to study gyrokinetic plasma turbulence: A finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization …
