Signature of turbulent zonal flows observed in the DIII-D tokamak

The spectrum of turbulent density fluctuations at long poloidal wavelengths in the edge plasma of the DIII-D tokamak peaks at nonzero radial wave number. The associated electric-potential fluctuations cause sheared E x B flows primarily in the poloidal direction. These zonal flows have been predicted by theory and are believed to regulate the overall level of turbulence and anomalous transport. This study provides the first indirect experimental identification of zonal flows.     

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.     

托卡马克边缘湍流中带状流的负粘滞阻尼

基于Hasegawa-Wakatani湍流模型,数值模拟了托卡马克边缘等离子体中漂移波湍流和相关的反常粒子输运。从等离子体动量守恒方程出发导出了不采用常规的布辛涅斯克近似的带状流方程,论证了大振幅密度扰动和湍性粒子流对激发带状流的贡献可等效地对应于低阶负粘滞阻尼效果。数值模拟表明,大振幅密度扰动的非线性大大增强了带状流饱和振幅,从而有效抑制了湍性粒子输运。研究结果阐明了托卡马克边缘等离子体大振幅密度扰动的非线性对驱动等离子体旋转、动量输运和带状流的重要性。     

�п���˱�Ե�����д�״���ĸ�ճ������

基于Hasegawa-Wakatani湍流模型,数值模拟了托卡马克边缘等离子体中漂移波湍流和相关的反常粒子输运.从等离子体动量守恒方程出发导出了不采用常规的布辛涅斯克近似的带状流方程,论证了大振幅密度扰动和湍性粒子流对激发带状流的贡献可等效地对应于低阶负粘滞阻尼效果.数值模拟表明,大振幅密度扰动的非线性大大增强了带状流饱和振幅,从而有效抑制了湍性粒子输运.研究结果阐明了托卡马克边缘等离子体大振幅密度扰动的非线性对驱动等离子体旋转、动量输运和带状流的重要性.     

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 modes and zonal flows in toroidally rotating tokamak plasmas

The effect of equilibrium toroidal rotation on the rotational eigen-modes in large aspect ratio tokamak is studied. The case of equilibrium with uniform plasma density on magnetic surfaces is considered. It is shown that the toroidal rotation results in a frequency up-shift of ordinary Geodesic Acoustic Modes. A new unstable low frequency branch of the continuum modes is found. This mode appears as a consequence of the non-uniform plasma pressure created by the centrifugal force on the magnetic surfaces. This mode represents a linear eigen-mode counterpart of Zonal Flow modes. It is shown that the growth rate of such a mode increases with the increase of the angular velocity of toroidal rotation.     

Generation of zonal flows by interchange modes in a plasma

The generation of zonal flows by flute-like interchange modes in a nonuniform magnetoplasma is considered. The guiding center particle drifts are then used to derive a system of coupled mode equations. The latter are Fourier analyzed to obtain a nonlinear dispersion relation, which exhibits the excitation of zonal flows by the ponderomotive force of the interchange modes. The growth rate of the parametrically driven zonal flows is obtained. Received 26 July 2002 Published online 24 September 2002 RID="a" ID="a"e-mail: ps@tp4.ruhr-uni-bochum.de     

�п���˵���ƽ�������µ������廷��ת���Դ�״����Ӱ��

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。     

Diagnostics of the magnetic field in a high-temperature tokamak plasma by polarization spectroscopy methods

A spectropolarimetric method for the diagnostics of the magnetic field in a high-temperature tokamak plasma is proposed.     

Effective model of turbulent plasma convection in the tokamak core

It has been shown that low-frequency turbulent convection self-consistently developed in the tokamak core can be effectively described in the framework of a relatively simple model based on a closed system of weakly dissipative reduced magnetohydrodynamic-type equations. The results of the numerical simulation of transient regimes, including regimes with sawtooth oscillations and with a fast spatial redistribution of the auxiliary heating power, are reported. The results indicate that the response of the resulting transport processes to fast changes in the external conditions is nondiffusive and nonlocal and are in reasonable agreement with experiments at various tokamaks.     

Transport control by coherent zonal flows in the core/edge transitional regime

3D Braginskii turbulence simulations show that the energy flux in the core/edge transition region of a tokamak is strongly modulated-locally and on average-by radially propagating, nearly coherent sinusoidal or solitary zonal flows. Their primary drive is the anomalous transport together with the Stringer-Winsor term. The transport modulation and the flow excitation are due to wave-kinetic effects studied for the first time in turbulence simulations. The flow amplitudes and the transport sensitively depend on the magnetic curvature acting on the flows, which can be influenced, e.g., by shaping the plasma cross section.     

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。     

First evidence of the role of zonal flows for the L-H transition at marginal input power in the EAST tokamak

A quasiperiodic Er oscillation at a frequency of <4 kHz, much lower than the geodesic-acoustic-mode frequency, with a modulation in edge turbulence preceding and following the low-to-high (L-H) confinement mode transition, has been observed for the first time in the EAST tokamak, using two toroidally separated reciprocating probes. Just prior to the L-H transition, the Er oscillation often evolves into intermittent negative Er spikes. The low-frequency Er oscillation, as well as the Er spikes, is strongly correlated with the turbulence-driven Reynolds stress, thus providing first evidence of the role of the zonal flows in the L-H transition at marginal input power. These new findings not only shed light on the underlying physics mechanism for the L-H transition, but also have significant implications for ITER operations close to the L-H transition threshold power.     

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.     

Self-organization in a tokamak plasma

Conclusions The observed tendency for certain optimal current-density and pressure profiles to be maintained can be interpreted if one assumes a relaxed state in the plasma, which corresponds to minimal total energy for a given current. With optimal power deposition, when the current-density and pressure profiles also remain optimal, ohmic scaling may be maintained up to fairly high densities, i.e., fairly high _p. If the power deposition profile deviates from optimal, the plasma resists deviation from the optimal profiles, and the more so the higher _p. The thermal-conductivity profile is modified to maintain the relaxed state. Nonoptimal profiles may lead to degradation in the global energy lifetime _E, which can be related phenomenologically to pumping of magnetic noise by the excess free energy F. Our argument provides a qualitative explanation of the self-organization physics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 29, No. 9, pp. 1032–1040, September, 1986.     

Shear flows at the tokamak edge and their role in core rotation and the L-H transition

Pfirsch-Schlüter fluxes in tokamaks are shown to drive strong poloidal and toroidal shear flows that are localized to the edge and scrape-off layer in the presence of temperature gradients and finite bootstrap current in the pedestal. Within a magnetohydrodynamic model, the effect of these flows on core rotation and their role in the magnetic configuration dependence of the power threshold for the low- (L-) to high- (H-)mode transition are discussed. Theoretical predictions based on symmetries of the underlying equations, coupled with computational results, are found to be in general agreement with observations in the Alcator C-Mod tokamak [Phys. Plasmas 12, 056111 (2005)10.1063/1.1876294].     

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.     

Turbulent transport reduction and randomization of coherent fluctuations by zonal flows in toroidal plasma

Fluctuation-driven particle flux is greatly reduced in the plasma radial region where zonal flows are present in the H-1 toroidal heliac. This occurs without reduction in the fluctuation level. Statistical properties of fluctuations are significantly modified in this region. It is shown that the randomization of phases of coherent structures by zonal flows is responsible for the observed effect. This mechanism of transport reduction complements theoretically predicted random shearing of turbulence by zonal flows and does not require the fluctuations suppression.