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采用流体模型理论推导了等熵平衡条件下环向转动托卡马克等离子体中带状流的色散关系。从理论上分析了环向转动对测地声模、低频带状流和声波的频率、压力和密度扰动量的影响。结果表明,环向转动对低频带状流的频率没有影响,但会使测地声模的频率逐渐增大。此外,存在环向转动时,低频带状流会具有驻波形式的压力和密度扰动量,且测地声模和声波可以沿着极向传播。而且还发现,等熵平衡可以看成是等温平衡的一种特殊情况。     

托卡马克等熵平衡条件下等离子体环向转动对带状流的影响

采用流体模型理论推导了等熵平衡条件下环向转动托卡马克等离子体中带状流的色散关系。从理论上分析了环向转动对测地声模、低频带状流和声波的频率、压力和密度扰动量的影响。结果表明,环向转动对低频带状流的频率没有影响,但会使测地声模的频率逐渐增大。此外,存在环向转动时,低频带状流会具有驻波形式的压力和密度扰动量,且测地声模和声波可以沿着极向传播。而且还发现,等熵平衡可以看成是等温平衡的一种特殊情况。     

轴对称环状静电模的漂移波湍流参量激发理论研究

本文所论述的轴对称环状静电模是指环形磁约束等离子体(如托卡马克)中环向模数为零的近理想静电流体模,它包含有测地声模和基频率与之较低的声模;也含有所谓的‘近零频带状流’.本文根据冷离子流体模型在圆形磁面构成的准环坐标系中的表示,对涉及以上三种模式的漂移波湍流参量激发理论,在一级环形效应近似下,进行了系统讨论,并证明了带状流的四个新命题.利用对漂移波能谱的参数化描写,注意到由漂移波能谱径向有限宽度所引发的特性,如波能传播量的双Landau奇点,揭示了有限宽度对径向δ谱所得结果的重要修正:如,对近零频带状流和测地声模的参量激发条件带来的严格限制.此外,还讨论了密度带状流在高q条件下被激发的可能性.本文选用合理的物理参数.采用图示方法详细地讨论了有关的数值结果.分析表明,测地声模和近零频带状流的参量激发不可能发生在同一小半径处;如果测地声模被参量激发,也应能观察到密度带状流.     

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.     

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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。     

Properties of geodesic acoustic modes and the relation to density fluctuations

The geodesic acoustic mode (GAM) is a high frequency branch of zonal flows, which is observed in toroidal plasmas. Because of toroidal curvature effects, density fluctuations are excited, which are investigated with the O-mode correlation reflectometer at TEXTOR. This Letter reports on the poloidal distribution of GAM induced density fluctuation and compares them with theoretical predictions. The influence of the GAM flows on the ambient turbulence is studied, too.     

Toroidal symmetry of the geodesic acoustic mode zonal flow in a tokamak plasma

The toroidal symmetry of the geodesic acoustic mode (GAM) zonal flows is identified with toroidally distributed three step Langmuir probes at the edge of the HuanLiuqi-2A (commonly referred to as HL-2A) tokamak plasmas for the first time. High coherence of both the GAM and the ambient turbulence for the toroidally displaced measurements along a magnetic field line is observed, in contrast with the high coherence of the GAM but low coherence of the ambient turbulence when the toroidally displaced measurements are not along the same field line. The radial and poloidal features of the flows are also simultaneously determined. The nonlinear three wave coupling between the high frequency turbulent fluctuations and the flows is demonstrated to be a plausible formation mechanism of the flows.     

Mean and oscillating plasma flows and turbulence interactions across the L-H confinement transition

A complex interaction between turbulence driven E × B zonal flow oscillations, i.e., geodesic acoustic modes (GAMs), the turbulence, and mean equilibrium flows is observed during the low to high (L-H) plasma confinement mode transition in the ASDEX Upgrade tokamak. Below the L-H threshold at low densities a limit-cycle oscillation forms with competition between the turbulence level and the GAM flow shearing. At higher densities the cycle is diminished, while in the H mode the cycle duration becomes too short to sustain the GAM, which is replaced by large amplitude broadband flow perturbations. Initially GAM amplitude increases as the H-mode transition is approached, but is then suppressed in the H mode by enhanced mean flow shear.     

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     

Intense geodesic acousticlike modes driven by suprathermal ions in a tokamak plasma

Intense axisymmetric oscillations driven by suprathermal ions injected in the direction counter to the toroidal plasma current are observed in the DIII-D tokamak. The modes appear at nearly half the ideal geodesic acoustic mode frequency, in plasmas with comparable electron and ion temperatures and elevated magnetic safety factor (q_{min}>or=2). Strong bursting and frequency chirping are observed, concomitant with large (10%-15%) drops in the neutron emission. Large electron density fluctuations (n[over ]_{e}/n_{e} approximately 1.5%) are observed with no detectable electron temperature fluctuations, confirming a dominant compressional contribution to the pressure perturbation as predicted by kinetic theory. The observed mode frequency is consistent with a recent theoretical prediction for the energetic-particle-driven geodesic acoustic mode.     

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.     

Thermal dynamics in the flux-coordinate independent turbulence code GRILLIX

GRILLIX employs the flux-coordinate independent approach (FCI), which allows us to study boundary plasma turbulence in realistic diverted configurations. Recently, the physical model in GRILLIX has been extended to a global drift-reduced Braginskii model, without any separation between background and fluctuations. It includes electromagnetic and thermal dynamics with hot ions, relaxation of the Boussinesq approximation and non-linear parametric dependencies. This contribution presents solutions to associated issues, that is, the ion diamagnetic polarization and the stiff parallel heat conduction. Simulations based on parameters characteristic for the Alcator C-Mod tokamak were carried out. In circular geometry, the self-consistent electric field contains zonal flows and geodesic acoustic modes in the confined region. In the scrape-off layer, the electron parallel heat conduction and its boundary condition determine the temperature and electric field, leading to sheared flows at the last closed flux surface.     

Drift effects on geodesic acoustic modes

We present a fluid model for geodesic acoustic modes including diamagnetic effects due to inhomogeneous plasma density and temperature. Effects of ion parallel viscosity (pressure anisotropy), which allows to recover exactly the adiabatic index obtained in kinetic theory are considered. We show that diamagnetic effects lead to the positive up-shift of the GAM frequency and appearance of the second (lower frequency) branch related to the drift frequency. The latter is a result of modification of the degenerate (zero frequency) zonal flow branch which acquires a finite frequency or becomes unstable in regions of high temperature gradients.     

Geodesic acoustic mode induced by toroidal rotation in tokamaks

The effect of toroidal rotation on the geodesic acoustic mode (GAM) in a tokamak is studied. It is shown that, in addition to a small frequency upshift of the ordinary GAM, another GAM, with much lower frequency, is induced by the rotation. The new GAM appears as a consequence of the nonuniform plasma density and pressure created by the centrifugal force on the magnetic surfaces. Both GAMs in a rotating plasma are shown to exist both as continuum modes with finite mode numbers m and n at the rational surfaces q=m/n as well as in the form of axisymmetric modes with m=n=0.     

Geodesic acoustic eigenmode for tokamak equilibrium with maximum of local GAM frequency

The geodesic acoustic eigenmode for tokamak equilibrium with the maximum of local GAM frequency is found analytically in the frame of MHD model. The analysis is based on the asymptotic matching technique.     

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采用回旋动理学方程推导得到了环向转动托卡马克等离子体中测地声模的色散关系,分析了环向转动对测地声模、低频模和声波分支的频率以及无碰撞阻尼率的影响.结果表明,测地声模的频率会随着环向转动马赫数而逐渐增大,而其无碰撞阻尼率则会随着环向转动马赫数而迅速减小.此外,低频模和声波分支的频率以及无碰撞阻尼率都会随着环向转动马赫数而逐渐减小,其中环向转动对声波分支的频率以及无碰撞阻尼率的影响非常小,基本上可以忽略.     

托卡马克等离子体环向转动对测地声模的影响

采用回旋动理学方程推导得到了环向转动托卡马克等离子体中测地声模的色散关系,分析了环向转动对测地声模、低频模和声波分支的频率以及无碰撞阻尼率的影响。结果表明,测地声模的频率会随着环向转动马赫数而逐渐增大,而其无碰撞阻尼率则会随着环向转动马赫数而迅速减小。此外,低频模和声波分支的频率以及无碰撞阻尼率都会随着环向转动马赫数而逐渐减小,其中环向转动对声波分支的频率以及无碰撞阻尼率的影响非常小,基本上可以忽略。     

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.     

Verification of Energetic-Particle-Induced Geodesic Acoustic Mode in Gyrokinetic Particle Simulations

The energetic-particle-induced geodesic acoustic mode(EGAM) is studied using gyrokinetic particle simulations in tokamak plasmas.In our simulations,exponentially growing EGAMs are excited by energetic particles with a slowing-down distribution.The frequencies of EGAMs are always below the frequencies of GAMs,which is due to the non-perturbative contribution of energetic particles(EPs).The mode structures of EGAMs are similar to the corresponding mode structures of GAMs.Our gyrokinetic simulations show that a high EP density can enhance the EGAM growth rate,due to high EP free energy,and that EPs' temperature and the pitch angle of the distribution modify the EGAM frequency/growth rate by means of the resonance condition.Kinetic effects of the thermal electrons barely change the EGAM frequency,and have a weak damping effect on the EGAM.Benchmarks between the gyrokinetic particle simulations and a local EGAM dispersion relation exhibit good agreement in terms of EGAM frequency and growth rate.     

Zonal flows, GAM, and radial electric field in the H-1 heliac

Experimental results on the role of zonal flows and geodesic acoustic modes in formation of transport barriers in the H-1 heliac are reviewed. Presented at the Workshop “Electric Fields, Structures and Relaxation in Edge Plasmas”, Roma, Italy, June 26–27, 2006.