Understanding L-H transition in tokamak fusion plasmas

This paper reviews the current state of understanding of the L-H transition phenomenon in tokamak plasmas with a focus on two central issues:(a) the mechanism for turbulence quick suppression at the L-H transition;(b) the mechanism for subsequent generation of sheared flow.We briefly review recent advances in the understanding of the fast suppression of edge turbulence across the L-H transition.We uncover a comprehensive physical picture of the L-H transition by piecing together a number of recent experimental observations and insights obtained from 1D and 2D simulation models.Different roles played by diamagnetic mean flow,neoclassical-driven mean flow,turbulence-driven mean flow,and turbulence-driven zonal flows are discussed and clarified.It is found that the L-H transition occurs spontaneously mediated by a shift in the radial wavenumber spectrum of edge turbulence,which provides a critical evidence for the theory of turbulence quench by the flow shear.Remaining questions and some key directions for future investigations are proposed.     

Effects of sawtooth heat pulses on edge flows and turbulence in a tokamak plasma

Enhancements of edge zonal flows,radial electric fields,and turbulence are observed in electron cyclotron resonance heating-heated plasmas(Zhao et al 2013 Nucl.Fusion 53 083011).In this paper,the effects of sawtooth heat pulses on flows and turbulence are presented.These experiments are performed using multiple Langmuir probe arrays in the edge plasmas of the HL-2A tokamak.The edge zonal flows,radial electric fields,and turbulence are all enhanced by sawteeth.Propagation of the zonal flow and tu...     

Dynamics of oscillatory plasma flows prior to the H-mode in the HL-2A tokamak

This paper discusses edge oscillatory plasma flows, geodesic acoustic mode(GAM) and limit cycle oscillations(LCOs), which have been measured by Doppler reflectometry prior to the high confinement mode(H-mode) in the HL-2A tokamak. The complex relations between the flows and background turbulence have been analyzed. It was observed that the GAM and LCO coexist,and these two flows and turbulence have strong nonlinear interactions during the intermediate confinement phase(I-phase). Dynamics of the shear flows and turbulence prior to the H-mode shows that the oscillatory flows quench the turbulence along with the increase of the mean E × B flow at the early stage of the I-phase, then the oscillatory flows are damped and the further increased mean flow takes over the role in turbulence suppression. The reduced turbulent transport results in the formation of a steep edge transport barrier. It suggests that the oscillatory flows can initiate the L–H transition through providing a positive feedback for the increase of the mean E × B flow strength.     

A brief review: experimental investigation of zonal flows and geodesic acoustic modes in fusion plasmas

Zonal flows self-generated by turbulence play an important role in regulating turbulence, reducing transport level, and thus improve plasma confinement in fusion plasmas. The zonal flows and geodesic acoustic modes have been identified in various devices. The related issues, such as the poloidal and toroidal symmetries, coupling to turbulence, effects on turbulence and transport, nonlinear energy transfer between turbulence and zonal flows, dependence of the plasma parameters, roles in the confinement regime transitions etc are overviewed briefly in this paper. The interaction between zonal flows and magnetic islands is emphasized.     

Impact of the mass isotope on plasma confinement and transport properties in the HL-2A tokamak

The impact of the mass isotope on plasma confinement and transport properties has been investigated in Ohmically-heated hydrogen and deuterium plasmas in the HL-2A tokamak. Experimental results show that under similar discharge parameters the deuterium plasma has better confinement and lower turbulent transport than the hydrogen one, and concomitantly, it is found that the magnitude of geodesic acoustic mode zonal flows, the tilting angle of the Reynolds stress tensor and the turbulence correlation lengths are all larger in the edge region of the deuterium plasma. The results provide direct experimental evidence on the importance of the nonlinear energy coupling between ambient turbulence and zonal flows for governing the isotope effects in fusion plasmas.     

Wave-Number Spectral Characteristics of Drift Wave Micro-Turbulence with Large-Scale Structures

Wave-number spectral characteristics of drift wave micro-turbulence with large-scale structures (LSSs) including zonal flows (ZFs) and Kelvin-Holmheltz (KH) mode are investigated based on three dimensional gyrofluid simulations in a slab geometry. The focus is on the property of the wave-number spectral scaling law of the ambient turbulence under the back reaction of the self-generated LSSs. A comparison of the spectral scaling laws between ion/electron temperature gradient (ITG/ETG) driven turbulences is presented. It is shown that the spectral scaling of the ITG turbulence with robust ZFs are fitted well by an exponential-law function in and a power-law one in . However, the ETG turbulence is characterized by a mixing Kolmogorov-like power-law and exponential-law scaling for both and spectra due to the ZFs and KH mode dynamics, with and the slope index factors. The underlying physical mechanism is understood as the spectral scattering caused by the back-reaction of the LSSs on the ambient turbulence. These findings may provide helpful guideline to diagnose the plasma fluctuations and flow structures in experiments.     

The residual zonal flow in tokamak plasmas with a poloidal electric field

In a tokamak plasma with auxiliary heating by cyclotron waves, a poloidal electric field will be produced, and as a consequence influence the residual zonal flow(RZF) level. The poloidal electric field can also be induced through biasing electrodes at the edge region of tokamaks.Numerical evaluation for a large aspect ratio circular cross section tokamak for the electron cyclotron wave heating indicates that the RZF level decreases significantly when the poloidal electric field increases. Qualitatively, the ion cyclotron wave heating is able to increase the RZF level. It is difficult to apply the calculation to the real cyclotron wave heating experiments since we need to know factors such as the plasma profiles, the exact power deposition and the cross section geometry, etc. It is possible to use the cyclotron wave heating to control the zonal flow and then to control the turbulence level in tokamak experiments.     

The theoretical study on intermittency and propagation of geodesic acoustic mode in L-mode discharge near tokamak edge

Through a systematically developed theory, we demonstrate that the motion of Instanton identified in Zhang et al(2017 Phys. Plasmas 24 122304) is highly correlated to the intermittent excitation and propagation of geodesic acoustic mode(GAM) that is observed in tokamaks.While many numerical simulations have observed the phenomena, it is the first theory that reveals the physical mechanism behind GAM intermittent excitation and propagation. The preceding work is based on the micro-turbulence associated with toroidal ion temperature gradient mode, and slab-based phenomenological model of zonal flow. When full toroidal effect is introduced into the system, two branches of zonal flow emerge: the torus-modified low frequency zonal flow(TLFZF), and GAM, necessitating a unified exploration of GAM and TLFZF. Indeed, we observe that the transition from the Caviton to Instanton is triggered by a rapid zero-crossing of radial group velocity of drift wave and is found to be strongly correlated with the GAM onset. Many features peculiar to intermittent GAMs, observed in real machines,are thus identified in the numerical experiment. The results will be displayed in figures and in a movie; first for single central rational surface, and then with coupled multiple central rational surfaces. The periodic bursting first shown disappears as being replaced by irregular one, more similar to the intermittent characteristics observed in GAM experiments.     

A new model of the L–H transition and H-mode power threshold

In order to understand the mechanism of the confinement bifurcation and H-mode power threshold in magnetically confined plasma,a new dynamical model of the L–H transition based on edge instability phase transition(EIPT) has been developed.With the typical plasma parameters of the EAST tokamak,the self-consistent turbulence growth rate is analyzed using the simplest case of pressure-driven ballooning-type instability,which indicates that the L–H transition can be caused by the stabilization of the edge instability through EIPT.The weak E?×?B flow shear in L-mode is able to increase the ion inertia of the electrostatic motion by increasing the radial wave number of the tilted turbulence structures,which play an important role for accelerating the trigger process of EIPT rather than directly to suppress the turbulent transport.With the acceleration mechanism of E?×?B flow shear,fast L–H and H–L transitions are demonstrated under the control of the input heating power.Due to the simplified scrape-offlayer boundary condition applied,the ratio between the heating powers at the H–L and L–H transition respectively differs from the ratio by Nusselt number.The results of the modeling reveal a scaling of the power threshold of the L–H transition,P_(L-H)?∝?n~(0.76) B~(0.8) for deuterium plasma.It is found finite Larmor radius induces an isotope effect of the H-mode power threshold.     

Analysis of dynamical flow structure in a square arrayed rod bundle

Large eddy simulation (LES) of turbulent flow in a bare rod bundle was performed, and a new concept about the flow structure that enhances heat transport between subchannels was proposed. To investigate the geometrical effect, the LES was performed for three different values of rod diameter over pitch ratio (D/P = 0.7, 0.8, 0.9). The computational domain containing 4 subchannels was large enough to capture large-scale structures wide across subchannels. Lateral flow obtained was unconfined in a subchannel, and some flows indicated a pulsation through the rod gap between subchannels. The gap flow became strong as D/P increased, as existing experimental studies had reported. Turbulence intensity profile in the rod gap suggested that the pulsation was caused by the turbulence energy transferred from the main flow to the wall-tangential direction. This implied that the flow pulsation was an unsteady mode of the secondary flow and arose from the same geometrical effect of turbulence. This implication was supported by the analysis results: two-points correlation functions of fluctuating velocities indicated two length-scales, P-D and D, respectively of cross-sectional and longitudinal motions; turbulence stress in the cross-sectional mean flow contained a non-potential component, which represented energy injection through the unsteady longitudinal fluid motion.     

5×5棒束通道内流动转捩特性研究

棒束通道的特殊结构导致其内部流动转捩情况较为复杂,探究其内部流动转捩规律具有重要意义。本文针对棒束通道内的流动转捩特性开展实验与CFD模拟研究,通过实验获得了棒束通道内沿程阻力系数的变化规律;采用不同湍流模型进行了数值模拟。结果表明,SST k-ω模型能较好地反映实验结果。进一步对比了不同雷诺数工况下通道内不同位置的沿程阻力系数与湍流强度,发现对于不同子通道,中心子通道湍流强度与沿程阻力系数高于边角子通道;对于同一子通道,子通道中心处湍流强度与壁面切应力高于子通道边缘处。这一结果说明,受壁面影响,棒束内湍流强度、壁面切应力、阻力特性具有不均匀性,这些空间上的不均匀性相互作用会引起总体上棒束转捩点不明显。     

Flow Transition Characteristics in 5×5 Rod Bundle Channel

The special geometric structure of the rod bundle channel can induce complicated flow transition of the coolant, and investigation on the flow transition rules is sufficiently important. In the current study, experimental and numerical study on the flow transition characteristics in the 5×5 rod bundle channel was carried out. Experiments were performed to obtain the variation characteristics of the resistance coefficient and CFD simulation was performed using different turbulence models in ANSYS Fluent. The results show that the simulation with SST k-ω turbulence model agrees well with the experimental data. The simulated turbulence intensity and resistance coefficient at different measurement locations and in different flow conditions were compared. For different subchannels, the turbulence intensity and the resistance coefficient are higher in the center subchannel than those in the edge subchannel. For the same subchannel, the turbulence intensity and the shear stress in the subchannel center are higher than those in the subchannel edge. This result indicates that the turbulence intensity, shear stress and resistance coefficient in the rod bundle are not uniform due to the influence of the wall surface. This non-uniform spatial interaction makes the transition point obscure.     

Toroidal component of velocity for geodesic acoustic modes in the edge plasmas of the J-TEXT tokamak

The toroidal component of the velocity for geodesic acoustic modes (GAMs) is first demonstrated.Multiple Langmuir probe arrays set up near the top tokamak of the J-TEXT were utilized for this study.A significant peak at the GAM frequency is observed in Mach number fluctuations.The toroidal velocity for the GAMs is estimated as ～10-100 m s-1 and increases with the poloidal velocity.The ratio of toroidal component to the poloidal one of the velocity is mainly located in the interval between 0.3 and 1.0.With higher safety factors q,the ratio almost does not change with decreasing the safety factor,whereas it goes up sharply at low q.The coherencies between poloidal electric fields and Mach number fluctuations in turbulence frequency bands are also evaluated,and are higher than those between radial electric fields and Mach number fluctuations.     

The investigation of quasi coherent mode on EAST using Doppler reflectometry

An electrostatic Quasi coherent mode has been observed in density fluctuations and perpendicular velocity fluctuations with the frequency range of 3–80 k Hz on the Experimental Advanced Superconducting Tokamak using multi-channel Doppler reflectometry. It appears in the edge localized mode(ELM)-free period after L-H transition or in the inter-ELM period. The mode rotates almost together with the plasma with the poloidal wave number around 0.6cm~(-1) and its frequency chirps with plasma poloidal velocity. The mode can exist in a large radial coverage(ρ?=?0.75–0.98), and peaks near the top of pedestal, suggesting that it might be excited in the steep gradient pedestal region, and spread into the core area.     

Effect of resonant magnetic perturbation on boundary plasma turbulence and transport on J-TEXT tokamak

The effect of resonant magnetic perturbation(RMP) on boundary turbulence and transport in J-TEXT plasma is experimentally investigated.Edge plasma fluctuations in discharges with and without the(m/n=3/1) RMP currents are diagnosed by using Langmuir probe arrays.It was found that fluctuations in the edge and scrape-off layer(SOL) regions decrease with the application of a 6 kA RMP.The broadband turbulence at the radial location of ρ～0.9 which has a characteristic frequency of 40-150 kHz was strongly suppressed when applying RMP,as was the radial turbulent particle flux and blob transport in the near-SOL region.These experimental findings make RMP a promising method of suppressing and controlling turbulence and particle transport in a plasma boundary.     

Kinetic Theories of Geodesic Acoustic Modes: Radial Structure,Linear Excitation by Energetic Particles and Nonlinear Saturation

Geodesic Acoustic Modes (GAMs) are oscillating zonal mode structures unique to toroidal plasmas and are capable of regulating microscopic turbulence and associated transports. In this paper, we investigate three important aspects of GAM dynamics: (1) GAM continuous spectrum and its mode conversion to kinetic GAM (KGAM); (2) linear excitation of energetic particle induced GAM (EGAM) and its coupling to the GAM continuum, and (3) nonlinear saturation of EGAM via wave particle trapping. The analogy between the GAM-EGAM dynamics and the well known beam-plasma instability is also discussed.     

Turbulent heat transfer to longitudinal flow through a triangular array of circular rods

Temperature distribution and heat transfer to longitudinal turbulent, fully developed flow through triangular arrays of smooth circular rods are analysed for liquids with Prandtl number 1 and 1. Nusselt number is plotted versus pitch and turbulence for constant heat flow and for constant temperature on the rod surface, and the optimum pitch is determined. The influence of Prandtl number on Nusselt number is analysed.     

双探头光学探针识别受热工况两相流流型的基本方法研究

由于流型识别手段受到限制．目前常用的流型图以及流型转变判据．都是在绝热工况下根据实验得到的；关于受热工况两相流流型还没有足够的实验数据。光学探针的运用为受热工况两相流流型的研究提供了有力的测量手段。本文对双探头光学探针4种流型识别的基本方法进行了研究，包括探针原始电平信号概率密度函数(PDF)分析识别流型、信号时序波形识别流型、空间波形识别流型以及汽泡尺寸PDF分析识别流型。研究结果表明，汽泡贯穿弦长PDF分析可得出满意的流型识别结果。     

Analysis of the Variability of the L-H Transition Power Threshold in a Helium-4 Discharge

In this paper, a mechanism about the variability of the L-H transition power thresh- old PL-H is proposed which is based on the ion orbit losses. Only in the edge where there are enough ion orbit losses and the negative radial electric field Er is high enough can the H-mode be triggered. The ion orbit losses are determined by the ion in the loss region under certain edge conditions. For different mass A and different charge Z, the critical loss energy E Z2/A in the loss region. In H and D charges, because the D＋ loss region is larger than H＋, it can be deduced that the PL-H of H is larger than that of D. In a 4He discharge, experiment finds there exist a considerable number of 4He1＋ in the plasma edge. The actual ion orbit losses are determined by the mixing ratio of a He1＋ and 4He2＋. The 4He1＋ loss region is larger than that of 4He2＋, and the loss region of D＋ interposes between 4He1＋ and 4He2＋. Different 4He1＋ content can cause the edge ion losses in a 4He discharge to be greater than, less than or equal to that in a D discharge. So a 4He discharge can exhibit multiple experimental phenomena in the PL-H.