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.     

Kinetic theory of geodesic acoustic modes in toroidal plasmas: a brief review

Geodesic acoustic modes(GAM) are oscillating zonal structures unique to toroidal plasmas,and have been extensively studied in the past decades due to their potential capabilities of regulating microscopic turbulences and associated anomalous transport.This article reviews linear and nonlinear theories of GAM;with emphases on kinetic treatment,system nonuniformity and realistic magnetic geometry,in order to reflect the realistic experimental conditions.Specifically,in the linear physics,the resonant wave–particle interactions are discussed,with the application to resonant excitation by energetic particles(EPs).The theory of EP-induced GAM(EGAM) is applied to realistic devices for the interpretation of experimental observations,and global effects due to coupling to GAM continuum are also discussed.Meanwhile,in the nonlinear physics,the spontaneous GAM excitation by microscale turbulences is reviewed,including the effects of various system nonuniformities.A unified theoretical framework of GAM/EGAM is then constructed based on our present understandings.The first-principle-based GAM/EGAM theories reviewed here,thus,provide the tools needed for the understanding and interpretation of experimental/numerical results.     

Nonlinear Generation of Zonal Fields by the Beta-Induced Alfven Eigenmode in Tokamak

The zonal fields effect on the beta-induced Alfven eigenmode(BAE)destabilized by the energetic particles in toroidal plasmas is studied through the gyrokinetic particle simulations.It is found that the localized zonal fields with a negative value around the mode rational surface are generated by the nonlinear BAE.In the weakly driven case,the zonal fields with a strong geodesic acoustic mode(GAM)component have weak effects on the nonlinear BAE evolution.In the strongly driven case,the zonal fields are dominated by a more significant zero frequency component and have stronger effects on the nonlinear BAE evolution.     

Nonlinear Generation of Zonal Fields by the Beta-Induced Alfvén Eigenmode in Tokamak

The zonal fields effect on the beta-induced Alfvén eigenmode (BAE) destabilized by the energetic particles in toroidal plasmas is studied through the gyrokinetic particle simulations. It is found that the localized zonal fields with a negative value around the mode rational surface are generated by the nonlinear BAE. In the weakly driven case, the zonal fields with a strong geodesic acoustic mode (GAM) component have weak effects on the nonlinear BAE evolution. In the strongly driven case, the zonal fields are dominated by a more significant zero frequency component and have stronger effects on the nonlinear BAE evolution.     

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.     

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.     

Zonal flow energy ratio evolution during L-H and H-L transitions in EAST plasmas

The essential role of zonal flow in the L-H transition and the suppression of turbulence have been studied with a long range correlation technique using Langmuir probe arrays in EAST tokamak.Two toroidally localized probe arrays are used to measure the zonal flow during L-H transition and H-L back transition.The energy ratio of the low frequency zonal flow to the total drift wave turbuletce is calculated.During ELM-free H mode,the energy ratio is higher than that in L mode,which reveals the important role of zonal flows in regulating turbulence amplitude in L-H transition.     

ITER中的电子回旋波电流驱动模拟

通过将相对论Fokker-Planck方程与波迹方程联合求解,对ITER(国际热核实验反应堆)参数下的电子回旋波电流驱动进行了数值模拟。结果表明,当波的环向发射角度不太大时,波功率沉积将发生在ITER的强场侧。当环向发射角度为21°时,电子回旋波的能量在等离子体中心区域被吸收并驱动起等离子体中心区域的电流。当发射角度变大时,电子回旋波将在弱场侧沉积功率。当发射角度为20°～30°时,能够驱动归一化的径向位置(r/a)小于0.35区域内的等离子体电流,并有较高的电流驱动效率。     

Gyrokinetic simulations of nonlinear interactions between magnetic islands and microturbulence

A conservative scheme of kinetic electrons for gyrokinetic simulations in the presence of magnetic islands has been implemented and verified in the gyrokinetic toroidal code, where zonal and nonzonal components of all perturbed quantities are solved together. Using this new conservative scheme, linear simulation of kinetic ballooning mode has been successfully benchmarked with the electromagnetic hybrid model. Simulations of nonlinear interactions between magnetic islands and the ion temperature gradient(ITG) mode in a tokamak show that the islands rotate at the electron diamagnetic drift velocity. The linear ITG structure shifts from the island O-point toward the X-point due to the pressure flattening effect inside the islands, and the nonlinear ITG structure peaks along the magnetic island separatrix because of the increased pressure gradient there.     

Busbar arcs at large fusion magnets: Conductor to feeder tube arcing model experiments with the LONGARC device

Electric arcs moving along the power cables (the so-called busbars) of the toroidal field (TF) coils of ITER may reach and penetrate the cryostat wall. Model experiments with the new LONGARC device continue the VACARC (VACuum ARC) experiments that were initiated to investigate the propagation and destruction mechanisms of busbar arcs in small scale [1]. The experiments are intended to support the development and validation of a numerical model. LONGARC overcomes the space limitations inside VACARC and allows also for advanced 1:3 (vs. ITER full scale) model setups. The LONGARC device and first results are presented below.     

TCB混合堆Li自冷包层MHD流动设计

从磁流体动力学ＭＨＤ压降的物理原理出发，对ＴＣＢ商用混合堆Ｌｉ自冷包层的ＭＨＤ流动方式进行了改进，提出了第一壁环向流动（平行环向磁场流动），核燃料增殖区径向流动的ＭＨＤ流动的设计，以解决混合堆为改善堆的经济性而采取提高包层核燃料富集度的途径所速来的热工，ＭＨＤ压降和安全问题。分析和数值计算结果表明，第一壁环向流动设计可以满足包层核燃料富集度从０．５％增加到１％，相应的热功率从４５００ＭＷ增加到...     

Frequency multiplication with toroidal mode number of kink/fishbone modes on a static HL-2A-like tokamak

In the presence of energetic particles (EPs), the long-lived mode (LLM) frequency multiplication with n = 1, 2, 3, or higher is often observed on HL-2A, where n is the toroidal mode number. Hybrid kinetic-MHD model simulations of the energetic particle (EP) driven kink/fishbone modes on a static HL-2A-like tokamak using NIMROD code find that when the background plasma pressure is relatively high, and the EP pressure and the beam energy are relatively low, the mode frequency increases almost linearly with EP pressure, and the frequency is proportional to n ('frequency multiplication'), even in the absence of any equilibrium plasma rotation. In addition, the frequency multiplication persists as the safety factor at the magnetic axis q0 varies. In the absence of EPs, the growth rate of the 1/1 mode is the largest; however, as the EP pressure increases, the growth rate of 2/2 modes or 3/3 modes becomes dominant, suggesting that higher-n modes are more vulnerable to EPs. These results may shed light on the understanding of the toroidal mode number dependence of kink/fishbone modes in the advanced scenarios of tokamaks with weak or reversed central magnetic shear.     

Zonal Flows and Geodesic Acoustic Mode Oscillations in Tokamaks and Helical Systems

This paper reviews the theoretical foundations of zonal flow, putting emphasis on the linear response function of plasma to the external flow drive. An extension of the theory is made in order to apply it to helical systems and to study the properties of the zonal flow in the low frequency range. Further refinement of the theory is made incorporating the orbital effects of particles more precisely, and the role of neoclassical polarization current is identified.     

Mitigation of edge localised modes with magnetic perturbations in ASDEX Upgrade

The first stage of a significant enhancement of the ASDEX Upgrade experiment with in-vessel coils for non-axisymmetric magnetic perturbations is now operational. First experiments have shown that ELM mitigation can be achieved using various perturbation field configurations with toroidal mode numbers n = 1, 2, 4. The main access criteria is the plasma edge pedestal density to exceed a threshold, which takes the lowest value of about 60% of the Greenwald density for resonant |n| = 1 perturbations. In H-mode plasmas, mode locking or error field-induced magnetic islands are generally not observed. Due to the low local shear of the plasma magnetic field in the vicinity of the perturbation coils around the outboard midplane, the magnetic perturbation is resonant simultaneously on several rational surfaces. It is hypothesised that the existence of image currents on these surfaces ensures good shielding of the error field in the confined plasma.     

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.     

Effects of Gas Flow Rate on the Discharge Characteristics of a DC Excited Plasma Jet

A direct current(DC) source excited plasma jet consisting of a hollow needle anode and a plate cathode has been developed to form a diffuse discharge plume in ambient air with flowing argon as the working gas.Using optical and electrical methods,the discharge characteristics are investigated for the diffuse plasma plume.Results indicate that the discharge has a pulse characteristic,under the excitation of a DC voltage.The discharge pulse corresponds to the propagation process of a plasma bullet travelling from the anode to the cathode.It is found that,with an increment of the gas flow rate,both the discharge plume length and the current peak value of the pulsed discharge decrease in the laminar flow mode,reach their minima at about1.5 L/min,and then slightly increase in the turbulent mode.However,the frequency of the pulsed discharge increases in the laminar mode with increasing the argon flow rate until the argon flow rate equals to about 1.5 L/min,and then slightly decreases in the turbulent mode.     

Imaging of implantation defects by X-ray topography combined with surface acoustic wave excitation

X-ray topographs of the He-implanted LiNbO₃ crystals under 10 μm-surface acoustic wave excitation were taken using monochromatized synchrotron radiation provided by the European Synchrotron Radiation Facility (ESRF, Grenoble). Measurements were made in the stroboscopic mode, i.e. by synchronizing the electron bunch frequency with the resonant frequency of the acoustic wave excitation in the 300 MHz range. These X-ray diffraction images showed plane acoustic wave propagation through the LiNbO₃ crystals as well as wave front distortions due to scattering by extended defects. Secondary spherical waves were observed for the first time as a result of the strong interaction between the acoustic waves and the sub-micron size density perturbations.     

The effect of resonant magnetic perturbation with different poloidal mode numbers on peeling–ballooning modes

The effect of resonant magnetic perturbation (RMP) with different poloidal mode numbers on peeling– ballooning (P–B) modes is simulated with the BOUT++ code. In order to investigate the physical mechanism of edge-localized mode mitigated by RMP, a series of RMPs with different poloidal mode numbers are applied into the four-field P–B mode simulation module separately. The results indicate that RMP has a better reducing effect on the energy loss from the pedestal when the resonant position is near the bottom and top of pedestal rather than near the middle. The RMP could influence P–B modes through the following effects: on the one hand, the E × B shearing rate is significantly stronger when the RMP (resonant surface locates at the top of the pedestal) is added, which can suppress the radial propagation of the negative pressure perturbation and reduce energy loss from the pedestal. On the other hand, the coupling of toroidal modes in the nonlinear phase is enhanced when RMPs are added, which motivated the growth of multiple toroidal modes, and the turbulence fluctuation level is weaker with the RMP when the resonant surface is located at the bottom of the pedestal.     

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...     

Specification of asymmetric VDE loads of the ITER tokamak

During asymmetric vertical displacement events (AVDEs) associated with the kink mode of the plasma two asymmetry phenomena were observed in existing tokamaks, in particular in JET [1]. The related halo currents flowing in the passive structure were identified as the cause of asymmetric EM loads on tokamak components. The first phenomenon is a toroidal peak of the poloidal halo current that flows in the passive structure. The second phenomenon is that the toroidal plasma current is not uniform toroidally, so a toroidally non-uniform current flows in the vessel [2]. The specification of the expected characteristics of both phenomena as well as of the consequent asymmetric loads in ITER are summarized here. The related loads are specified for likely, unlikely and extremely unlikely AVDEs.