Zonal-flow dynamics and size scaling of anomalous transport

Nonlinear equations for the slow space-time evolution of the radial drift-wave envelope and zonal flow amplitude have been self-consistently derived for a model nonuniform tokamak equilibrium within the coherent four-wave drift wave-zonal flow modulation interaction model of Chen, Lin, and White [Phys. Plasmas 7, 3129 (2000)]]. Solutions clearly demonstrate turbulence spreading due to nonlinearly enhanced dispersiveness and, consequently, the device-size dependence of the saturated wave intensities and transport coefficients.     

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.     

Turbulence regeneration in pipe flow at moderate Reynolds numbers

We present the results of an experimental investigation into the nature and structure of turbulent pipe flow at moderate Reynolds numbers. A turbulence regeneration mechanism is identified which sustains a symmetric traveling wave within the flow. The periodicity of the mechanism allows comparison to the wavelength of numerically observed exact traveling wave solutions and close agreement is found. The advection speed of the upstream turbulence laminar interface in the experimental flow is observed to form a lower bound on the phase velocities of the exact traveling wave solutions. Overall our observations suggest that the dynamics of the turbulent flow at moderate Reynolds numbers are governed by unstable nonlinear traveling waves.     

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     

Dynamics of fully nonlinear drift wave-zonal flow turbulence system in plasmas

We present numerical simulations of fully nonlinear drift wave-zonal flow (DW-ZF) turbulence systems in a nonuniform magnetoplasma. In our model, the drift wave (DW) dynamics is pseudo-three-dimensional (pseudo-3D) and accounts for self-interactions among finite amplitude DWs and their coupling to the two-dimensional (2D) large amplitude zonal flows (ZFs). The dynamics of the 2D ZFs in the presence of the Reynolds stress of the pseudo-3D DWs is governed by the driven Euler equation. Numerical simulations of the fully nonlinear coupled DW-ZF equations reveal that short scale DW turbulence leads to nonlinear saturated dipolar vortices, whereas the ZF sets in spontaneously and is dominated by a monopolar vortex structure. The ZFs are found to suppress the cross-field turbulent particle transport. The present results provide a better model for understanding the coexistence of short and large scale coherent structures, as well as associated subdued cross-field particle transport in magnetically confined fusion plasmas.     

对称性自发破缺所诱发的种子平行雷诺胁强

根据第二类气球模理论,在托卡马克中诸如不稳定漂移波类的环形局部模将在径向呈现源于环形性的对称性自发破缺。以流体离子温度梯度模模型方程为例,解出在准环坐标系中由对称性自发破缺产生的二维局部模本征模式。在略去边带效应后,它成为具有径向位移修正的平板模式。由位移修正离子温度梯度模式导出了种子平行雷诺胁强,而它在传统的(无位移修正的)平板模式下被证明为零。     

Cz结构浅池内硅熔体热对流的分岔特性

为了了解水平温度梯度作用时Czochralski结构浅池内硅熔体热对流的分岔特性,利用有限差分法进行了非稳态三维数值模拟,坩埚外壁被加热,液池深度为3 mm.模拟结果表明,当逐渐增加温差时,会发生两次流型转变,第一次由二维轴对称流动转变为三维稳态流动,第二次由三维稳态流动转变为热流体波,其可能沿顺时针方向旋转、也可能沿逆时针方向旋转,同时,第二次转变存在分岔现象.     

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.     

Nucleation, drift, and decay of phase bubbles in period-2 oscillatory wave trains in a reaction-diffusion system

This is a report on experimental observations of phase bubbles, simply closed boundaries between domains oscillating 2pi out of phase, associated with period-2 oscillatory traveling waves in a Belousov-Zhabotinsky reaction-diffusion system. The bubbles nucleate spontaneously through a fast localized phase slip, drift radially away from a neighboring spiral wave core in an oscillatory fashion, and gradually shrink to disappear. Their oscillatory drift along the radial direction is a consequence of "period adaptation," while their lateral shrinkage is an attribute of local curvature. Similar dynamic structures can be reproduced in a simple, three-species reaction-diffusion model that supports period-2 oscillatory wave trains.     

Nonlinear dispersion relation of geodesic acoustic modes

The energy input and frequency shift of geodesic acoustic modes (GAMs) due to turbulence in tokamak edge plasmas are investigated in numerical two-fluid turbulence studies. Surprisingly, the turbulent GAM dispersion relation is qualitatively equivalent to the linear GAM dispersion but can have drastically enhanced group velocities. In up-down asymmetric geometry the energy input due to turbulent transport may favor the excitation of GAMs with one particular sign of the radial phase velocity relative to the magnetic drifts and may lead to pulsed GAM activity.     

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。     

Drift mechanism caused by a nonlinear wave and the Cassini Division and Uranian rings formation

The mechanism leading to the observed coexistence of gaps and narrow ringlets in the planetary rings is found. It is based upon the quasi-stationary radial drift of the matter under action of two forces in the disk plane: the Coriolis force and the Reynolds stresses. To an accuracy of the factor of 2 the first force coincides with the Lorentz force, therefore the radial drift in rings is similar to the gradient drift of plasma in the magnetic field. The second force is produced by the wave generated by the nearby satellite in the resonance position. In inertial systems, the second force alone causes a matter flow in its direction, called acoustic streaming. Since the radial drift is caused by nonlinear time-averaged force of high-frequency harmonic interactions in the wave, it exists in the wave propagation zone: from the birth place of the wave-the resonance position, up to the reflection point of the wave, where its group velocity vanishes. Our estimations show that the size of the density wave propagation zone corresponding to the density wave which had been formerly generated the 2:1 orbital resonance with Mimas is consistent with the width of the Cassini Division. In our case the nature of the radial drift is such that first of all it clears out the farthest from the resonance position; later, the closer areas also get affected by the drift. The zone closest to the resonance position itself is the last to be involved in the process. The matter carried away by the drift is partially accumulated near the resonance position forming a narrow dense ringlet. (c) 1996 American Institute of Physics.     

HL-2Aװ�ô�״��������ģ���ֲ�����̽��ϵͳ

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。     

Nonlinear interactions between drift waves and zonal flows

Phase coherent interactions between drift waves and zonal flows are considered. For this purpose, mode coupling equations are derived by using a two-fluid model and the guiding center drifts. The equations are then Fourier analyzed to deduce the nonlinear dispersion relations. The latter depict the excitation of zonal flows due to the ponderomotive forces of drift waves. The flute-like zonal flows with insignificant density fluctuations have faster growth rates than those which have a finite wavelength along the magnetic field direction. The relevance of our investigation to drift wave driven zonal flows in computer simulations and laboratory plasmas is discussed. Received 5 April 2002 Published online 28 June 2002     

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.     

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.     

Rapid beat generation of large-scale zonal flows by drift waves: a nonlinear generic paradigm

The generalized Charney-Hasegawa-Mima equation is unstable to a four wave modulational instability whereby a coherent, monochromatic drift wave can drive a band of modes and associated zonal flows unstable. Although initially the fastest growing modes dominate, a secondary nonlinear instability later drives the longest wavelength zonal flow and its associated sidebands at twice the growth rate of the fastest growing modulationally unstable modes. This results in a direct transfer from strongly unstable short wavelength modes to the weakly unstable long wavelength modes, which drains the short wavelength pump energy. A related but less efficient direct enstrophy cascade generates very short wavelength modes lying outside the band of modulationally unstable modes.     

Spontaneous generation of self-organized solitary wave structures at earth's magnetopause

Spontaneous formation of solitary wave structures has been observed in Earth's magnetopause, and is shown to be caused by the breakup of a zonal flow by the action of drift wave turbulence. Here we show matched observations and modeling of coherent, large-scale solitary electrostatic structures, generated during the interaction of short-scale drift wave turbulence and zonal flows at the Earth's magnetopause. The observations were made by the Cluster spacecraft and the numerical modeling was performed using the wave-kinetic approach to drift wave-zonal flow interactions. Good agreement between observations and simulations has been found, thus explaining the emergence of the observed solitary structures as well as confirming earlier theoretical predictions of their existence.     

Dynamics of zonal flows in helical systems

A theory for describing collisionless long-time behavior of zonal flows in helical systems is presented and its validity is verified by gyrokinetic-Vlasov simulation. It is shown that, under the influence of particles trapped in helical ripples, the response of zonal flows to a given source becomes weaker for lower radial wave numbers and deeper helical ripples while a high-level zonal-flow response, which is not affected by helical-ripple-trapped particles, can be maintained for a longer time by reducing their bounce-averaged radial drift velocity. This implies a possibility that helical configurations optimized for reducing neoclassical ripple transport can simultaneously enhance zonal flows which lower anomalous transport.     

局地强迫激发的非线性长波扰动

利用扰动法导得了非线性强迫Boussinesq方程,利用数值解讨论了地形和外源等局地强迫激发的非线性长波扰动的一般性状和时间演变特征,并对移动性孤波与地形的相互作用进行了分析研究。