Quasilinear analysis of the zonal flow back-reaction on ion-temperature-gradient mode turbulence

There is strong evidence in favor of zonal flow suppression in 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 by 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.     

Change of zonal flow spectra in the JIPP T-IIU tokamak plasmas

When Ohmically heated low-density plasmas are additionally heated by higher-harmonics ion-cyclotron-range-of frequency heating, heated by neutral beam injection, or strongly gas puffed, the intensity of zonal flows in the geodesic acoustic mode frequency range in the tokamak core plasma decreases sharply and that of low-frequency zonal flow grows drastically. This is accompanied by a damping of the drift wave propagating in the electron diamagnetic drift direction, turbulence by trapped electron mode (TEM), and the increase of the mode propagating to ion diamagnetic drift direction (ITG). In the half-radius region, TEM and high-frequency zonal flows remain intense in both OH and heated phases. ITG and low-frequency zonal flows grow in heated plasmas, suggesting a strong coupling between ITG and low-frequency zonal flow.     

Role of the zonal flow in multi-scale multi-mode turbulence with small-scale shear flow in tokamak plasmas

The structural characteristics of zonal flows and their roles in the nonlinear interaction of multi-scale multi-mode turbulence are investigated numerically via a self-consistent Landau-fluid model. The multi-mode turbulence here is composed of a shorter wavelength electromagnetic (EM) ion temperature gradient (ITG) mode and a Kelvin-Helmholtz (KH) instability with long wavelengths excited by externally imposed small-scale shear flows. For strong shear flow, a prominent periodic intermittency of fluctuation intensity except for dominant ITG component is revealed in turbulence evolution, which onset time depends on the ion temperature gradient and the shear flow amplitudes corresponding to different KH instabilities. It is identified that the intermittency phenomenon results from the zonal flow dynamics, which is mainly generated by the KH mode and back-reacts on it. It is demonstrated that the odd symmetric components of zonal flow (same symmetry as the external flow) make the radial parity of the KH mode alteration through adjusting the drift velocities at two sides of the resonant surface so that the KH mode becomes bursty first. Afterwards, the ITG intermittency follows due to nonlinear mode coupling. Parametric dependences of the features of the intermittency are elaborated. Finally, associated turbulent heat transport is evaluated.     

Interaction between small-scale zonal flows and large-scale turbulence: a theory for ion transport intermittency in Tokamak plasmas

Interaction between small-scale zonal flows and large-scale turbulence is investigated. The key mechanism is identified as radially nonlocal mode coupling. Fluctuating energy can be nonlocally transferred from the unstable longer to the stable or damped shorter wavelength region, so that the turbulence spectrum is seriously deformed and deviates from the nonlinear power law structure. Three-dimensional gyrofluid ion-temperature gradient (ITG) turbulence simulations show that an ion transport bursting behavior is consistently linked to the spectral deformity with the causal role of ITG-generated zonal flows in tokamak plasmas.     

离子温度梯度模湍流的带状流最小自由度模型

在离子温度梯度模(ITG)湍流背景中,通过最小自由度模型中模耦合方式产生带状流,对此模型做了动力学稳定性分析及数值求解.并在此基础上初步探讨了湍流中漂移波与带状流的能量转移,以及雷诺协强与带状流的关系. 关键词： 等离子体 离子温度梯度模 湍流 带状流     

磁场剪切对离子温度梯度模带状流产生的影响

对离子温度梯度模湍流非线性流体方程进行了解耦处理,得到包含磁场剪切效应的带状流与漂移波相互作用的非线性动力学方程.采用调制不稳定性的四波相互作用模型,研究了磁场剪切对带状流产生的影响.研究表明,在k_//值较小的范围内,当|k_//|增加时,带状流的增长率也呈增加的趋势. 关键词： 托卡马克等离子体 离子温度梯度模湍流 带状流 磁场剪切     

Zonal flow dynamics and control of turbulent transport in stellarators

The relation between magnetic geometry and the level of ion-temperature-gradient (ITG) driven turbulence in stellarators is explored through gyrokinetic theory and direct linear and nonlinear simulations. It is found that the ITG radial heat flux is sensitive to details of the magnetic configuration that can be understood in terms of the linear behavior of zonal flows. The results throw light on the question of how the optimization of neoclassical confinement is related to the reduction of turbulence.     

Nonlinear saturation of trapped electron modes via perpendicular particle diffusion

In magnetized fusion plasmas, trapped electron mode (TEM) turbulence constitutes, together with ion temperature gradient (ITG) turbulence, the dominant source of anomalous transport on ion scales. While ITG modes are known to saturate via nonlinear zonal flow generation, this mechanism is shown to be of little importance for TEM turbulence in the parameter regime explored here. Instead, a careful analysis of the statistical properties of the ExB nonlinearity in the context of gyrokinetic turbulence simulations reveals that perpendicular particle diffusion is the dominant saturation mechanism. These findings allow for the construction of a rather realistic quasilinear model of TEM induced transport.     

基于电阻性交换模湍流的环带流动力学

基于电阻性交换模湍流研究了托卡马克等离子体中的环带流激发动力学.利用低自由度近似 对电阻性交换模湍流 环带流系统做了解析和数值求解.结果表明，在足够强的压力梯度（ 驱动力）情况下，电阻性交换模湍流将激励出大尺度环带流或振荡型环带流. 关键词： 等离子体 电阻性交换模湍流 环带流     

Effect of collisional zonal-flow damping on flux-driven turbulent transport

The effect of collisional damping of zonal flows (ZFs) on ion-temperature gradient (ITG) driven turbulence in a toroidal plasma is investigated by means of a 3D global fluid model with flux boundary conditions. Results from simulations show an increase of the energy confinement time and a stabilization of turbulence with the inverse of the collisionality nu(*). The stabilization mechanism is identified as an effect of the increased shearing rate of ZFs, which shift upwards the ITG turbulence effective threshold. The shearing rate of ZFs is also seen to depend on the injected power. As a consequence, the effective heat conductivity depends parametrically on the input power.     

Zonal flows in tokamak plasmas with toroidal rotation

Zonal flows in tokamak plasmas with toroidal rotation are theoretically investigated. It is found that the low-frequency branch of zonal flows, which is linearly stable in a nonrotating system, becomes linearly unstable in a rotating tokamak, and that the high-frequency branch of zonal flows, the geodesic acoustic mode, can propagate in the poloidal direction with the frequency significantly lower than the frequency of the standing wave geodesic acoustic mode in the nonrotating system.     

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利用往返式朗缪尔探针组在HL-2A装置等离子体边缘首次同时观测到明显的低频(ƒ=0~5kHz)和测地声模(ƒ=16kHz)带状流的极向和环向对称性(m~0,n~0),径向结构及其传播特征。并同时推算出流的径向波矢(Kr-LF=0.6 cm-1,Kr-GAM=2cm-1)。双谱分析的结果表明低频和测地声模带状流的形成可能都是由于高频湍流和这种流之间的非线性三波耦合引起的。初步研究了电子回旋加热功率和边界安全因子引起带状流幅度的变化。此外,也观测了带状流幅度在径向方向的改变。     

等离子体湍流理论研究的最新进展

评述和分析了磁约束核聚变理论研究、数值模拟和实验研究等方面最近几年共同关心的一个重要问题——寻找托卡马克等离子体湍流中的带状剪切流（zonal flows）。简要介绍了作者最近对电阻性-重力模湍流中的带状剪切流的研究结果。 Progress of the research on the zonal flows in tokamak plasma turbulence is surveyed, especially it is reviewed that the zonal flows observed in the experiments and numerical simulations on atmosphere turbulence and ocean turbulence and the discovery of H-mode in tokamak experiments how lead the researchers in magnetic confinement fusion community to find out the existence of the zonal flow in tokamak plasma turbulence and subsequently give the experimental verification of its existence. Finally, the results of our research on zonal flow generation and evolution in resistive-g mode turbulence are presented in brief.     

Small-scale turbulence in a closed-field-line geometry

Plasma turbulence due to small-scale entropy modes is studied with gyrokinetic simulations in a simple closed-field-line geometry, the Z pinch, in low-beta parameter regimes that are stable to ideal interchange modes. We find an enormous variation in the nonlinear dynamics and particle transport as a function of two main parameters, the density gradient and the plasma collisionality. This variation is explained in part by the damping and stability properties of spontaneously formed zonal flows in the system. As in toroidal systems, the zonal flows can lead to a strong nonlinear suppression of transport below a critical gradient that is determined by the stability of the zonal flows.     

HL-2A装置中的带状流三维特性研究和探针设计

HL-2A装置边缘等离子体测地声模带状流的三维特征采用外中平面上三组三台阶探针阵列组成具有环向、极向和径向分辨的独特结构的探针系统进行了研究.其中两组具有极向距离为65mm的三台阶5探针阵列组成极向带状流10探针组,另一组电动式带状流6探针阵列与带状流10探针组之间的环向距离为800mm. 此外,采用快速往复气动6探针组研究了磁分界面附近的温度、密度、雷诺协强及其径向分布.在HL-2A装置上同时观测到测地声模带状流(频率f=7kHz)的极向和环向对称性(m≈0,n 关键词： 三台阶式ZF探针 带状流 三维空间结构     

On the baroclinic instability of nonplanar flows

Summary Different ocean models with one or two layers having constant static stability and supporting constant-shear flows, whose directions are allowed to change with depth, are examined in the frame-work of the linear nonzonal baroclinic stability theory and in the absence of the β-effect. The analysis is reduced to solving a simple Sturm-Liouville boundary value problem in one dimension. A fairly general dispersion relation is found which correctly reproduces several special cases analysed by other authors. This relation shows a fair variety of possible behaviours for stability curves of two-layer models. The results show that the presence of a nonplanar shear-flow may have profound consequences on the stability character of the stationary geostrophic flow. In fact, it appears that the stability properties are strongly dependent on the propagation angle of the disturbance so that wave numbers which appear stable in the usual zonal theory may result unstable on such a nonzonal flow andvice versa. Paper presented at the 1^o Congresso del Gruppo Nazionale per la Fisica dell'Atmosfera e dell'Oceano, June 19–22, 1984, Rome.     

Some Stability and Instability Criteria for Ideal Plane Flows

We investigate stability and instability of steady ideal plane flows for an arbitrary bounded domain. First, we obtain some general criteria for linear and nonlinear stability. Second, we find a sufficient condition for the existence of a growing mode to the linearized equation. Third, we construct a steady flow which is nonlinearly and linearly stable in the L² norm of vorticity but linearly unstable in the L² norm of velocity.     

Low-frequency potential structures in a nonuniform dusty magnetoplasma

The linear and nonlinear properties of a modified convective cell (MCC) in a nonuniform dusty magnetoplasma with a perpendicular plasma flow are investigated. It is shown that the free energy of the equilibrium plasma flow can drive the MCC at nonthermal levels. By choosing some specific profiles for the sheared plasma flow and the dust number density, we analyze the eigenvalue equation for deducing the growth rate and the threshold of a convective mode instability which arises due to its interaction with the shear plasma flows. Our analytical results show that a Rayleigh-type instability sets in provided that the characteristic width of the flow does not exceed a certain value. On the other hand, the nonlinear equation, which governs the dynamics of the nonlinearly interacting convective modes, admits stationary solutions in the form of a vortex chain associated with zonal flows, as well as tripolar and global vortices. The relevance of our investigation to a laboratory experiment is discussed.     

Quasiparticle approach to the modulational instability of drift waves coupling to zonal flows

The interaction between broadband drift mode turbulence and zonal flows has been studied through the wave-kinetic approach. Simulations have been conducted in which a particle-in-cell representation is used for the quasiparticles, while a fluid model is employed for the plasma. The interactions have been studied in a plasma edge configuration which has applications in both tokamak physics and magnetopause boundary layer studies. Simulation results show the development of a zonal flow through the modulational instability of the drift wave distribution, as well as the existence of solitary zonal flow structures about an ion gyroradius wide, drifting towards steeper relative density gradients.     

Nonlinear damping of plasma zonal flows excited by inverse spectral transfer

Plasma zonal-flow excitation and saturation in fluid electron-drift-wave turbulence are studied spectrally. The zonal flow is a spectral condensation onto the zero-frequency linear-wave structure. In the representation diagonalizing the wave coupling that dominates interactions at long wavelengths, nonlinear triad interactions involving zero-frequency waves are greatly enhanced. Zonal modes are excited on both unstable and purely stable eigenmode branches. Coupling to the latter introduces robust, finite amplitude-induced damping of zonal flows, providing saturation.