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.     

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.     

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从Braginskii冷离子流体模型出发,利用准环坐标系,导出了轴对称(环向模数为零的)扰动密度和扰动电位所服从的两个二维线性偏微分本征波方程。采用WKB法及Langer变换,解出了测地声模过转向点一致有效的整体模结构和分立本征频率谱;论述了不存在连续谱解的原因;指出Schrödinger意义下的径向高激发态对应了近零频模;论证了与测地声模定级分析的自洽性将导致“蝌蚪”定域化;并讨论了“蝌蚪”定域化理论与实验上所观察到的“多个测地声模共存”现象之间的关係。     

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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。     

Intermittent transport associated with the geodesic acoustic mode near the critical gradient regime

Turbulent transport near the critical gradient in toroidal plasmas is studied based on global Landau-fluid simulations and an extended predator-prey theoretical model of ion temperature gradient turbulence. A new type of intermittent transport associated with the emission and propagation of a geodesic acoustic mode (GAM) is found near the critical gradient regime, which is referred to as GAM intermittency. The intermittency is characterized by new time scales of trigger, damping, and recursion due to GAM damping. During the recursion of intermittent bursts, stationary zonal flow increases with a slow time scale due to the accumulation of undamped residues and eventually quenches the turbulence, suggesting that a nonlinear upshift of the critical gradient, i.e., Dimits shift, is established through such a dynamical process.     

Effect of subsonic toroidal flows on plasma poloidal rotation and ion heat conductivity. In collisional plasmas of elongated tokamaks

The ion poloidal rotation and heat conductivity in collisional plasmas of axially-symmetric tokamaks with elongated cross-sections and with subsonic toroidal plasma flows are considered. It is shown that subsonic toroidal plasma flows, induced by neutral beam injection or radio frequency waves, can strongly affect the poloidal plasma velocity and ion heat conductivity in collisional plasmas of tokamaks. The transport coefficients also depend on the tokamak ellipticity parameter which, in combination with the Mach number, allows to operate transport processes at smaller values of the toroidal Mach number. The importance of taking into account the ion-electron heat exchange and electron temperature toroidal perturbations to find ion temperature toroidal perturbations is demonstrated. This work was partially supported by the State University of Rio de Janeiro (UERJ) and the Rio de Janeiro Research Foundation (FAPERJ).     

Collisionless Damping of Geodesic Acoustic Mode in a Multi‐Ion Plasma with Superthermal Ions

The dispersion relation of geodesic acoustic mode is investigated in a multi‐ion toroidal plasma on the basis of linear gyrokinetic equations where ions are assumed to take a nonextensive distribution. It is found that the frequency of GAM becomes larger with the decrease of q. Consequently, GAM will damp more rapidly. The effective charge corresponding to the maximum damping rate is found to move towards unity as q decreases. As indicates that in a plasma with superthermal bulk ions, the influence of the impurity ion on the damping rate is weakened. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

气体体积粘性对二维环形激波聚焦的影响

基于体积粘性系数ζ的分子运动论和连续介质理论,对二维环形激波聚焦（马赫数Ma=2.0）的体积粘性效应进行数值研究,结果表明：对于热完全气体,体积粘性使得激波汇聚中心点处的压力减小、温度增加、密度减小,聚焦点物理参数的改变量分别可达20%、10%、30%,体积粘性效应对环形激波聚焦的影响是不可忽略的;与转动模态相比,在振动模态下环形激波聚焦的体积粘性效应更为明显,因为激波聚焦点附近的体积粘性应力ζ▽·V与热力学压力p达到同一数量级,从而显著改变了流动参数.     

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.     

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在文献[1]中,通过分析实验上观察到的测地声模的小密度-电位比与测地声模谐波定级的自洽性,论证了测地声模是在转向点附近一种“蝌蚪状”的定域结构,但没有给出导致这种结构的物理机制.从随机媒质对波传播产生定域化的角度进行了探讨,采用测地声模由漂移波湍流参量激发的产生模型,计算了随机定域化导致的也是文献[1]所关注的相干长度.讨论了与实验观测比较的有关问题.     

Tokamak equilibria with reversed current density

Observations of nearly zero toroidal current in the central region of tokamaks (the "current hole") raises the question of the existence of toroidal equilibria with very low or reversed current in the core. The solutions of the Grad-Shafranov equilibrium equation with hollow toroidal current density profile including negative current density in the plasma center are investigated. Solutions of the corresponding eigenvalue problem provide simple examples of such equilibrium configurations. More realistic equilibria with toroidal current density reversal are computed using a new equilibrium problem formulation and computational algorithm which do not assume nested magnetic surfaces.     

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.     

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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在HL-2A装置孔栏位形放电的等离子体实验中,电子回旋辅助加热期间观察到了等离子体约束改善的现象,并对等离子体从低约束模式(L模)向约束改善模式转换时的等离子体线平均电子密度、等离子体储能、分界面内辐射功率、能量约束时间、Hα辐射等进行了研究。同时,分析了电子密度和等离子体辐射功率的空间分布随时间的演化。对改善约束的相关功率(辅助加热、欧姆加热功率和损失功率)进行了分析,并研究了等离子体约束改善转换时的边界净输入功率(阈值)与电子线平均密度和环向磁场的关系。     

Experimental evidence of a zonal magnetic field in a toroidal plasma

A zonal magnetic field is found in a toroidal plasma. The magnetic field has a symmetric bandlike structure, which is uniform in the toroidal and poloidal directions and varies radially with a finite wavelength of mesoscale, which is analogous to zonal flows. A time-dependent bicoherence analysis reveals that the magnetic field should be generated by the background plasma turbulence. The discovery is classified as a new kind of phenomenon of structured magnetic field generation, giving insight into phenomena such as dipole field generation in rotational planets.     

HL-2A装置的约束改善和边界净输入功率分析

在HL-2A装置孔栏位形放电的等离子体实验中,电子回旋辅助加热期间观察到了等离子体约束改善的现象,并对等离子体从低约束模式(L模)向约束改善模式转换时的等离子体线平均电子密度、等离子体储能、分界面内辐射功率、能量约束时间、H_α辐射等进行了研究。同时,分析了电子密度和等离子体辐射功率的空间分布随时间的演化。对改善约束的相关功率(辅助加热、欧姆加热功率和损失功率)进行了分析,并研究了等离子体约束改善转换时的边界净输入功率(阈值)与电子线平均密度和环向磁场的关系。     

Modelling of particle flows in a scrape-off layer with limiter biasing

The superconducting tokamak Tore Supra will be equipped with an actively cooled toroidal pump limiter (TPL), in the framework of the CIEL (Composants Internes Et Limiteurs) project, dedicated to plasma facing component design for steady state operation. The TPL is equipped with throats, located only on the high field side, for particle collection allowing the control of plasma density which is essential for long plasma discharges. The present design work of the CIEL includes a biasing system in order to enhance the particle pumping. A fluid model, based on the classical fluid equation, is used to estimate the effects of the electric field on the particle flows in the Scrape-Off Layer (SOL). The modifications of the density, the particle flow (toroidal and poloidal) and the position of the stagnation point are discussed as a function of the bias voltage. The model clearly illustrates the different resulting effects on particle pumping for a divertor and a limiter configuration which are designed respectively for poloidal or parallel particle collection. The model is used to interpret the ALT-biasing experiments recently carried out on TEXTOR-94. The pumping capability is shown to be improved by about (15–20)% for positive biasing while the experimental measurements of parallel Mach number are reproduced as a function of the applied voltage. The e-folding length of the edge density in the SOL is also shown to increase from 1.5 to about 2.0 cm for a biased voltage of −400 to 400 V, respectively, in accordance with the model. Finally, the model is used to extrapolate the TEXTOR-94 results to CIEL suggesting that pumping speed enhancement of 25 to 30% may be obtained. Partner in Trilateral Euregio Cluster Partner in Trilateral Euregio Cluster Presented at the Workshop on Role of Electric Fields in Plasma Confinement and Exhaust, Budapest, 18–19 June 2000.     

Toroidal momentum pinch velocity due to the coriolis drift effect on small scale instabilities in a toroidal plasma

In this Letter, the influence of the "Coriolis drift" on small scale instabilities in toroidal plasmas is shown to generate a toroidal momentum pinch velocity. Such a pinch results because the Coriolis drift generates a coupling between the density and temperature perturbations on the one hand and the perturbed parallel flow velocity on the other. A simple fluid model is used to highlight the physics mechanism and gyro-kinetic calculations are performed to accurately assess the magnitude of the pinch. The derived pinch velocity leads to a radial gradient of the toroidal velocity profile even in the absence of a torque on the plasma and is predicted to generate a peaking of the toroidal velocity profile similar to the peaking of the density profile. Finally, the pinch also affects the interpretation of current experiments.     

Identification of zonal flows in a toroidal plasma

This Letter presents experimental confirmation of the presence of zonal flows in magnetically confined toroidal plasma using an advanced diagnostic system--dual heavy ion beam probes. The simultaneous observation of an electric field at two distant toroidal locations (approximately 1.5 m apart) in the high temperature (approximately 1 keV) plasma provides a fluctuation spectrum of electric field (or flow), a spatiotemporal structure of the zonal flows (characteristic radial length of approximately 1.5 cm and lifetime of approximately 1.5 ms), their long-range correlation with toroidal symmetry (n=0), and the difference in the zonal flow amplitude with and without a transport barrier. These constitute essential elements of turbulence-zonal flow systems, and illustrate one of the fundamental processes of structure formation in nature.