The possible role of Reynolds stress in the creation of a transport barrier in tokamak edge plasmas

To obtain a good confinement, mandatory in a fusion reactor, the understanding of the formation of transport barriers in the edge plasma of a tokamak is essential. Turbulence, the major candidate to explain anomalous transport, can be quenched by sheared flows in the edge which rip the convective cells apart, thus forming a barrier. Experimental evidence from the Chinese HT-6M tokamak [Y.H. Xu et al.: Phys. Rev. Lett. 84 (2000) 3867], points to the fact that momentum transfer from the turbulence can create these sheared flows via the Reynolds stresses. A new 1-D fluid model for the generation of the poloidal flow, has been developed taking into account the driving force of the Reynolds stress and the friction forces due to neutrals and parallel viscosity. Special attention has been dedicated to the computation of the flux-surface-averaging for the various terms. This model has been confronted with the experimental results obtained in the HT-6M tokamak, where Reynolds stresses were generated by application of a turbulent heating pulse. If the model is applied in cylindrical geometry, the calculated Reynolds stress-induced flow agrees well with the measured poloidal velocity in the plasma edge. However, when the full toroidal geometry is taken into account, it seems that the Reynolds stresses are too small to explain the observed rotation. This indicates that the role of the Reynolds stresses in inducing macroscopic flow in the torus is weakened. A combined system of probes allowing to measure the Reynolds stress and the rotation velocity simultaneously, has been developed and installed on the CASTOR tokamak (Prague). We report here on the first results obtained.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

HL-1M托卡马克边缘参数和雷诺胁强的径向分布

利用多组马赫/郎缪尔探针测量了HL-1M装置刮离层和边缘静电雷诺胁强，等离子体极向旋转，径向和极向电场的径向分布，在低杂波电流驱动，超声分子束注入，多发弹丸注入和中性束注入实验中，给出了雷诺胁强和极向流的关系。结果表明，由于雷诺胁强的径向变化，托卡马克等离子体可以自发地产生剪切极向流。     

EDGE REYNOLDS STRESS STRUCTURE OF LOWER HYBRID WAVE INJECTION IN THE HL—1M PLASMA

The radial profiles of electrostatic Reynolds stress,plasma poloidal rotations,radial and poloidal electric fields have been measured in the plasma boundary region on the HL-1M tokamak using a multi-array of Mach/Langmuir probes.During experiments of lower hybrid wave current drive,the variations in LHW drive power xill cause changes in the edge electric field,poloidal rotation veloity and Reynolds stress.The results indicate that sheared poloidal flow can be generated in the edge plasma due to radially varied Reynolds stress.     

HL-1M装置边缘等离子体结构研究

描述HL-1M装置上几种典型放电中的边缘等离子体物理实验结果.利用马赫/朗缪尔6探针组、静电4探针组、20组三探针阵列研究了低杂波电流驱动、超声分子束注入、多发弹丸注入和中性束注入放电中的粒子约束性能、等离子体旋转和边缘静电雷诺胁强的变化对改善约束的影响.给出了雷诺胁强和极向相速度的关系.结果表明，雷诺胁强的径向变化可以自发产生托卡马克等离子体的剪切极向流.LHCD能使低密度放电的粒子约束增加1至2倍.弹丸注入后，粒子约束时间和极向旋转至少可增加1倍，而SMBI可使粒子约束时间增加约一个数量级并取得高性能等离子体. 关键词： 粒子约束 雷诺胁强 极向流剪切 马赫/朗缪尔6探针组     

HL-2Aװ�ñ�Ե�Ŷ����Թ۲�

用中平面往复快速扫描6探针组观测HL-2A装置边缘等离子体的扰动特性。在一次放电中能测量到边缘等离子体参数的时空分布及其涨落量，雷诺胁强与极向流和带状流的关系，以及静电涨落驱动的粒子通量和热通量的径向变化。在多发弹丸注入(MPI)和多脉冲超声分子束注入(SMBI)条件下，研究了边缘参数的涨落和相关特性。实验结果表明：SMBI和MPI等注入手段改变了边缘的扰动特性；雷诺胁强的径向梯度可以驱动带状流，抑制湍流输运。     

Direct measurement of poloidal long-wavelength E x B flows in the HT-7 tokamak

The poloidal long-wavelength E x B time-varying flows were directly measured using a forked Langmuir probe in the HT-7 tokamak. Low-frequency (<10 kHz) E x B flows were observed at the plasma edge, which possess many of the characteristics of zonal flows, including a poloidal long-wavelength (k(theta)rho(i) approximately 0) and narrow radial extent (k(r)rho(i) approximately 0.1). The cross bicoherence of turbulent Reynolds stress indicates the existence of nonlinear three-wave coupling processes and the generation of low-frequency E x B flows. The estimated flow-shearing rate is of the same order of magnitude as the turbulence decorrelation rate and may thus regulate the fluctuation level and thereby the turbulence-driven transport.     

HL-2Aƫ����λ�εı�Ե������������

通过中平面活动10探针组、往复快速扫描4探针和低杂波天线口的固定4探针测量了主等离子体边缘的温度、密度、悬浮电位、径向和极向电场、雷诺协强、径向和极向等离子体流速及其径向分布。用偏滤器靶板上的14组嵌入式静电3探针阵列测量了同一环向截面的内外中性化板上的电子温度、密度、悬浮电位及其分布。比较了在孔栏位形和偏滤器位形下边缘等离子体特性的差异,特别是两种位形下边缘温度和密度衰减长度的变化。分析了在多脉冲超声分子束加料和低杂波注入条件下的边界等离子体特性,以及雷诺协强的径向梯度与极向流和径向电场梯度与湍流损失的相互关系。     

Is the critical Reynolds number universal?

This paper is devoted to checking whether the critical Reynolds number is universal in identical conditions for the flow of different fluids. The laminar-turbulent transition in a circular pipe flow has been tested experimentally. The flows of inert gases (He, Ne, Ar, Kr, Xe), molecular gases (N₂, CO, CO₂, SF₆), and two similar liquids (H₂O, D₂O) have been tested. A considerable, up to 40%, difference in critical Reynolds numbers was observed. The possible reasons for nonuniversality of the critical Reynolds number are discussed.     

Measurements of Reynolds stress and turbulence in the boundary plasma of the HT-7 tokamak

Measurements of electric field fluctuations, Reynolds stress and poloidal flow have been performed in the boundary region of the HT-7 tokamak using a Langmuir probe array.Sheared radial electric field and poloidal flow have been found in the vicinity of the limiter and the turbulence has been clearly modified in this region. Furthermore,the electrostatic Reynolds stress component shows a radial gradient close to the velocity shear layer location.All results here indicate that the radial gradient of Reynolds stress may play an important role in the driving of poloidal flows in the plasma boundary region.     

Rheology of blood by NMR

Pipe flow of blood in tubes of 1 and 7 mm inner diameter, respectively, was investigated employing two-dimensional NMR velocity imaging and PFG propagator measurements at different Reynolds numbers between 10 and 3500. The results are compared to flow of a water/glycerol mixture of matching viscosity under identical conditions. The transition from laminar to turbulent flow is observed by both a flattening of the velocity profile and a change of the propagator shape. For blood flow this transition is found to be shifted toward higher Reynolds numbers as compared to the transition of the water/glycerol mixture. This observation is in agreement with predictions from hydraulic measurements and is a consequence of the non-Newtonian flow characteristics of blood as a suspension of erythrocytes and plasma. Likewise, a deviation from the laminar flow condition is observed for blood at low Reynolds numbers between 10 and 100. This phenomenon is unknown for Newtonian liquids and is explained by the onset of a geometrical arrangement of the erythrocytes, the so-called rouleaux effect.     

Analyses of edge plasma characteristics in HL-2A

The edge plasma characteristics are studied by both a movable array of Mach/Reynolds stress/Langmuir 10-probes in the boundary region and the fixed flush probe arrays on the 4 divertor neutralization plates at the same toroidal cross-section in the HL-2A tokamak. The dependence of the Reynolds stress on poloidal flow in the edge plasma is analysed. The result indicates that the sheared poloidal flow in tokamak plasma can be induced by the radial gradient of Reynolds stress. In the divertor experiments of HL-2A, the profiles of the electron temperature, density and floating potential on divertor plates are measured by the flush probe arrays. The edge electron temperature in divertor configuration is higher than that in limiter configuration. The temperature asymmetry between outer and inner target plates is observed. The result of magnetic surface reconstructed from 18 Mirnov coils signals is presented. Both the particle recycling and the impurity flux in the bulk plasma during divertor discharges are discussed. Neutral gas pressure in divertor chamber, measured by fast ionization gauge during divertor discharge, is given.     

Investigation on the drives of the poloidal flow in the ohmic and biased electrode experiments

The experimental investigation on the drives of the poloidal flow in KT-5 D tokamak are presented. It is found that the poloidal flow is the main contributor to the radial electric field, and the Reynolds stress can drive significant poloidal flows in ohmic discharges. The investigation on the relationship between the radial gradient of Reynolds stress and the poloidal flow in biasing discharges indicates that not only Reynolds stress but also the Lorentz's force can drive the poloidal flow.     

HL-2A 装置的边缘参数测量

HL-2A 装置中平面边缘的等离子体特性通过磁力传动的马赫/ 雷诺协强/ 朗缪尔10 探针组进行了研究。10 探针组安装在可径向向里和向外移动, 并可绕轴旋转360^o 的传动杆上, 用于测量主等离子体边缘的温度、密度、悬浮电位、空间电位、径向和极向电场、湍流的雷诺协强、径向和极向等离子体流速及其径向分布。HL- 2A 装置的实验结果表明, 边缘等离子体扰动诱发的雷诺协强产生了边缘极向流; 雷诺协强的径向梯度驱动带状流抑制了湍流输运。     

Laminar-turbulent transition in Hagen–Poiseuille flow of a real gas

The effect of gas non-ideality on the laminar-turbulent transition is studied experimentally as the flow in a long circular tube at room temperature. The gases SF₆ and Ar, differing significantly in the value of the second virial coefficient, were chosen for this study. Experiments were carried out by varying the pressure at the tube inlet (the maximum pressure of 10⁵ Pa) and at the tube outlet up to the chock flow (formation of a supersonic flow at the outlet). The difference between the critical Reynolds numbers in the flow of SF₆ and Ar was found. The largest difference was observed for the maximum pressures; with a decrease in pressure, the critical Reynolds numbers become closer. The conclusion is an effect of the non-ideal character of gas exists on the laminar-turbulent transition in Hagen–Poiseuille flow. Some experiments were suggested to confirm this conclusion.     

Observation of turbulent-driven shear flow in a cylindrical laboratory plasma device

An azimuthally symmetric radially sheared plasma fluid flow is observed to spontaneously form in a cylindrical magnetized helicon plasma device with no external sources of momentum input. A turbulent momentum conservation analysis shows that this shear flow is sustained by the Reynolds stress generated by collisional drift turbulence in the device. The results provide direct experimental support for the basic theoretical picture of drift-wave-shear-flow interactions.     

基于转捩SST模型凸起圆柱绕流数值研究

为了研究局部凸起对边界层转捩的影响,采用转捩SST模型分别对亚临界、临界和超临界状态下带突起的圆柱绕流问题进行了数值模拟,分析了不同Reynolds数下带突起的圆柱绕流问题的近壁面流动特征以及表面时均压力与摩擦力系数的分布和凸起对圆柱表面流动分离以及转捩的影响,对比了有无凸起两侧圆柱表面时均压力、摩擦力系数的不同. 结果表明:当来流Reynolds数处于临界区时,气流在圆柱上表面凸起处形成了3个反向旋转的漩涡,之后随着θ的增大,发生了流动分离和流动转捩现象;对于不同Reynolds数下的来流,圆柱上表面的凸起可以使气流发生转捩的位置提前;圆柱上表面的凸起使流速增大、压强降低,从而导致圆柱产生升力,随着来流Reynolds数的增大,其升力逐渐变大.      

������ŵЭǿ���ܶ��Ŷ��Լ���������Ӱ���ʵ���о�

利用静电探针阵列对HL-2A边缘等离子体径向和极向速度进行了测量,获得了最后闭合磁面附近湍流的雷诺协强〈(v)r(v)θ〉以及(v)r和(v)θ间相位差的剖面.实验表明,虽然(v)r、(v)θ的幅值对雷诺协强的大小会有影响,但雷诺协强的变化趋势主要取决于二者相位差的变化;另一方面,欧姆放电以及不同电子回旋加热功率L模放电条件下的实验结果显示,密度扰动引起的粒子输运所带来的极向动量输运的贡献与雷诺协强项对极向动量输运的贡献是可比的.这表明在分析湍流引起的动量输运时必须考虑粒子输运的贡献.     

使用RSM模型对旋风除尘器内湍流各向异性的数值模拟

旋风除尘器内三维湍流流场具有典型的各项异性,本文采用雷诺应力模型求解该流场得到了三维湍流流场的详细数据,得出了雷诺应力6个分量的分布图,揭示了这类强旋流流场湍流各向异性的特征。典型的几个算例的实践表明:采用雷诺应力模型求解这类流场非常必要,它能较好地反映这类流场的真实物理流动;与相关实验数据的比较表明吻合性较好,显示了本文算法的可行性;计算中发现,发展非结构网格更有利于模拟壁面附近的流动,并节省计算机内存。     

Role of turbulence on edge momentum redistribution in the TJ-II stellarator

Radial profiles of the parallel-radial Reynolds stress component, proportional to the cross correlation between parallel and radial fluctuating velocities, have been measured in the plasma boundary region of the TJ-II stellarator. Experimental results show the existence of significant parallel turbulent forces at plasma densities above the threshold value to trigger perpendicular sheared flows. This finding provides the first experimental evidence of the role of parallel turbulence forces on edge momentum redistribution in fusion devices.     

The intermittent excitation of geodesic acoustic mode by resonant Instanton of electron drift wave envelope in L-mode discharge near tokamak edge

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. Several abrupt phenomena observed in tokamaks, such as intermittent excitation of geodesic acoustic mode (GAM) shown in this paper, could be attributed to the sudden and fast radial motion of Instanton. The composite drift wave—zonal flow system evolves at the two well-separate scales:the micro-scale and the meso-scale. The eigenmode equation of the model defines the zero-order (micro-scale) variation; it is solved by making use of the two-dimensional (2D) weakly asymmetric ballooning theory (WABT), a theory suitable for modes localized to rational surface like drift waves, and then refined by shifted inverse power method, an iterative finite difference method. The next order is the equation of electron drift wave (EDW) envelope (containing group velocity of EDW) which is modulated by the zonal flow generated by Reynolds stress of EDW. This equation is coupled to the zonal flow equation, and numerically solved in spatiotemporal representation; the results are displayed in self-explanatory graphs. One observes a strong correlation between the Caviton-Instanton transition and the zero-crossing of radial group velocity of EDW. The calculation brings out the defining characteristics of the Instanton:it begins as a linear traveling wave right after the transition. Then, it evolves to a nonlinear stage with increasing frequency all the way to 20 kHz. The modulation to Reynolds stress in zonal flow equation brought in by the nonlinear Instanton will cause resonant excitation to GAM. The intermittency is shown due to the random phase mixing between multiple central rational surfaces in the reaction region.