Turbulent equipartition and homogenization of plasma angular momentum

A physical model of turbulent equipartition (TEP) of plasma angular momentum is developed. We show that using a simple, model insensitive ansatz of conservation of total angular momentum, a TEP pinch of angular momentum can be obtained. We note that this term corresponds to a part of the pinch velocity previously calculated using quasilinear gyrokinetic theory. We observe that the nondiffusive TEP flux is inward, and therefore may explain the peakedness of the rotation profiles observed in certain experiments. Similar expressions for linear toroidal momentum and flow are computed and it is noted that there is an additional effect due the radial profile of moment of inertia density.     

东方超环上低杂波驱动等离子体环向旋转实验研究

旋转和旋转剪切能抑制磁流体不稳定性和增强等离子体约束.低杂波电流驱动作为未来聚变堆上可能的旋转驱动手段,探索低杂波在现有托卡马克装置上驱动等离子体旋转的驱动机制,可以为未来的聚变堆上旋转预测提供重要参考.在东方超环托卡马克装置上,早期发现了2.45 GHz的低杂波能有效驱动等离子体旋转的现象,认为是边界旋转的改变导致芯部旋转的同电流方向的增加造成的.更高频率下4.6 GHz低杂波电流驱动可以更有效地驱动同电流方向的等离子体旋转.本论文分析在欧姆背景等离子体下,不同功率的低杂波对等离子体环向旋转的影响,研究安全因子剖面变化对环向旋转的关系,利用功率调制获得了低杂波驱动旋转实验中的环向动量输运系数变化情况,发现环向动量扩散系数(χφ)、环向动量箍缩系数(Vpinch)的数值大小趋势是从芯部向靠外的区域逐渐变大.这与低杂波驱动环向旋转时,环向旋转速度由靠外的区域向芯部传递的特性吻合.     

Experimental investigation of the role of fluid turbulent stresses and edge plasma flows for intrinsic rotation generation in DIII-D H-mode plasmas

The first measurements of turbulent stresses and flows inside the separatrix of a tokamak H-mode plasma are reported, using a reciprocating multitip Langmuir probe at the DIII-D tokamak. A strong co-current rotation layer at the separatrix is found to precede intrinsic rotation development in the core. The measured fluid turbulent stresses transport toroidal momentum outward against the velocity gradient and thus try to sustain the edge layer. However, large kinetic stresses must exist to explain the net inward momentum transport leading to co-current core plasma rotation. The importance of such kinetic stresses is corroborated by the success of a simple orbit loss model, representing a purely kinetic mechanism, in the prediction of features of the edge corotation layer.     

Experimental evidence of momentum transport induced by an up-down asymmetric magnetic equilibrium in toroidal plasmas

The first experimental evidence of parallel momentum transport generated by the up-down asymmetry of a toroidal plasma is reported. The experiments, conducted in the Tokamak à Configuration Variable, were motivated by the recent theoretical discovery of ion-scale turbulent momentum transport induced by an up-down asymmetry in the magnetic equilibrium. The toroidal rotation gradient is observed to depend on the asymmetry in the outer part of the plasma leading to a variation of the central rotation by a factor of 1.5-2. The direction of the effect and its magnitude are in agreement with theoretical predictions for the eight possible combinations of plasma asymmetry, current, and magnetic field.     

Dynamic modeling of stepwise internal transport barrier formation in DIII-D negative-central-shear discharges

The GLF23 transport model is used to dynamically follow bifurcations in the energy and toroidal momentum confinement in DIII-D discharges with an internal transport barrier. The temperatures and toroidal velocity profiles are evolved while self-consistently computing the effects of E x B shear stabilization during the formation and expansion of internal transport barriers. The barrier is predicted to form in a stepwise fashion through a series of sudden jumps in the core-electron and ion temperatures and toroidal rotation velocity. These results are consistent with experimental observations. In the simulations, the step transitions are a direct result of local E x B driven transport bifurcations.     

Role of pressure gradient on intrinsic toroidal rotation in tokamak plasmas

The toroidal plasma rotation generated by the external momentum input and by the plasma itself (intrinsic rotation) has been separated through a novel momentum transport analysis in the JT-60U tokamak device. The toroidal rotation, which is not determined by the momentum transport coefficients and the external momentum input, has been observed. It is found that this intrinsic rotation is locally determined by the local pressure gradient and increases with increasing pressure gradient. This trend is almost the same for various plasmas: low and high confinement mode, co and counterrotating plasmas.     

Effects of edge-localized mode-induced neoclassical toroidal viscosity torque on the toroidal intrinsic rotation in the EAST tokamak

Intrinsic rotation has been observed in lower hybrid current-driven (LHCD) H-mode plasmas with type-III edge-localized modes (ELMs) on Experimental Advanced Superconducting Tokamak (EAST), and it is found that the edge toroidal rotation accelerated before the onset of the ELM burst. Magnetic perturbation analysis shows there is a perturbation amplitude growth below 30 kHz corresponding to the edge rotation acceleration. Using the filament model, the neoclassical toroidal viscosity (NTV) code shows there is a co-current NTV torque at the edge, which may be responsible for the edge rotation acceleration. For maximum displacement ～1 cm and toroidal mode number n=15, the calculated torque density is ～0.44 N/m², comparable with the average edge toroidal angular momentum change rate ～1.24 N/m². Here, the 1 cm maximum magnetic surface displacement estimated from the experimental observation corresponds to a maximum magnetic perturbation ～ 10^?3–10^?2 T, in accordance with magnetic perturbation measurements during ELMs. By varying n from 10 to 20, the magnitude of the edge NTV torque density is mainly ～0.1–1 N/m². This significant co-current torque indicates that the NTV theory may be important in rotation problems during ELMs in H-mode plasmas. To better illuminate the problem, magnetic surface deformation obtained from other codes is desired for a more accurate calculation.     

Toroidal momentum pinch velocity due to the coriolis drift effect on small scale instabilities in a toroidal plasma

In this Letter, the influence of the "Coriolis drift" on small scale instabilities in toroidal plasmas is shown to generate a toroidal momentum pinch velocity. Such a pinch results because the Coriolis drift generates a coupling between the density and temperature perturbations on the one hand and the perturbed parallel flow velocity on the other. A simple fluid model is used to highlight the physics mechanism and gyro-kinetic calculations are performed to accurately assess the magnitude of the pinch. The derived pinch velocity leads to a radial gradient of the toroidal velocity profile even in the absence of a torque on the plasma and is predicted to generate a peaking of the toroidal velocity profile similar to the peaking of the density profile. Finally, the pinch also affects the interpretation of current experiments.     

Poloidal spin up and electric-field generation related to displacement current and neoclassical transport

Summary In accordance with the conventional orderings of neoclassical theory, poloidal and toroidal accelerations with constant parallel flow can be driven by heat transport in the absence of external momentum input and with vanishing parallel viscous stress. In a transient phase in which the heat transport is the primary source of the time dependence, the torque generating the rotation is provided at third order in the adiabatic expansion by the surface-averaged (non-ambipolar) displacement current, which is also responsible for charge build-up and for the radial electric field. The heat transport equation has been solved in a narrow layer interfaced with the intensely heated plasma core through heat flux continuity, assuming neoclassical multicollisional coefficients with self-consistent suppression mechanism of anomalous transport. Starting from low temperature in the edge layer, a strong temperature gradient, a mass poloidal rotation in the ion direction and a strongly negative sheared radial electric field can be generated, in agreement with the observations, and reach a stationary state after a displacement current-dominated triggering phase (intrinsically non-ambipolar) lasting few milliseconds. Momentum input becomes important on longer time scale and is responsible for the toroidal rotation, decoupled from temperature gradient and for a further development of the radial electric field. The results show the ability of edge transport processes to adapt flexibly to a high temperature imposed on the inner side of the edge layer and support the view that the edge processes are an integral part of a more fundamental global process involving possibly an internal bifurcation of state.     

Observation of spontaneous toroidal rotation inversion in Ohmically heated Tokamak plasmas

Bulk plasma toroidal rotation is observed to invert spontaneously from counter to cocurrent direction in TCV (Tokamak à Configuration Variable) Ohmically heated discharges, in low confinement mode, without momentum input. The inversion occurs in high current discharges, when the plasma electron density exceeds a well-defined threshold. The transition between the two rotational regimes has been studied by means of density ramps. The results provide evidence of a change of the balance of nondiffusive momentum fluxes in the core of a plasma without an external drive.     

Identification of a low plasma-rotation threshold for stabilization of the resistive-wall mode

The plasma rotation necessary for stabilization of resistive-wall modes (RWMs) is investigated by controlling the toroidal plasma rotation with external momentum input by injection of tangential neutral beams. The observed threshold is 0.3% of the Alfvén velocity and much smaller than the previous experimental results obtained with magnetic braking. This low critical rotation has a very weak beta dependence as the ideal wall limit is approached. These results indicate that for large plasmas such as in future fusion reactors with low rotation, the requirement of the additional feedback control system for stabilizing RWM is much reduced.     

Scaling of spontaneous rotation with temperature and plasma current in tokamaks

Using theoretical arguments, a simple scaling law for the size of the intrinsic rotation observed in tokamaks in the absence of a momentum injection is found: The velocity generated in the core of a tokamak must be proportional to the ion temperature difference in the core divided by the plasma current, independent of the size of the device. The constant of proportionality is of the order of 10 km·s(-1)·MA·keV(-1). When the intrinsic rotation profile is hollow, i.e., it is countercurrent in the core of the tokamak and cocurrent in the edge, the scaling law presented in this Letter fits the data remarkably well for several tokamaks of vastly different size and heated by different mechanisms.     

EAST中n=4共振磁扰动下等离子体的环向旋转制动

在EAST中n=4的共振磁扰动下观察到明显的等离子体旋转制动效应,其分布具有全局性,且峰值靠近等离子体中心。利用模拟得到的新经典环向粘滞(NTV)力矩来反演等离子体环向角速度的变化,结果表明在大部分径向区域与实验测量的速度变化符合得较好,量值上相差约1～2倍。     

Toroidal plasma rotation induced by the dynamic ergodic divertor in the TEXTOR tokamak

The first results of the Dynamic Ergodic Divertor in TEXTOR, when operating in the m/n=3/1 mode configuration, are presented. The deeply penetrating external magnetic field perturbation of this configuration increases the toroidal plasma rotation. Staying below the excitation threshold for the m/n=2/1 tearing mode, this toroidal rotation is always in the direction of the plasma current, even if the toroidal projection of the rotating magnetic field perturbation is in the opposite direction. The observed toroidal rotation direction is consistent with a radial electric field, generated by an enhanced electron transport in the ergodic layers near the resonances of the perturbation. This is an effect different from theoretical predictions, which assume a direct coupling between rotating perturbation and plasma to be the dominant effect of momentum transfer.     

Theory for toroidal momentum pinch and flow reversal in tokamaks

It is demonstrated that besides the well-known toroidal momentum diffusion flux there is a pinchlike flux in the fluctuation-induced toroidal stress. A toroidal flow profile is determined up to a constant, e.g., the value of the flow at the magnetic axis, by balancing these two fluxes. The remaining residual toroidal stress determines the value of the flow at the axis. It is illustrated that the direction of the flow at the axis can change after plasma confinement is improved. The theory is applied to explain the toroidal flow reversal in tokamak experiments.     

声子角动量与手性声子

在经典的物理学理论中,声子广泛地被认为是线极化的、不具有角动量的.最近的理论研究发现,在具有自旋声子相互作用的磁性体系(时间反演对称性破缺)中,声子可以携带非零的角动量,在零温时声子除了具有零点能以外还带有零点角动量;非零的声子角动量将会修正通过爱因斯坦-德哈斯效应测量的回磁比.在非磁性材料中,总的声子角动量为零,但是在空间反演对称性破缺的六角晶格体系中,其倒格子空间的高对称点上声子具有角动量,并具有确定的手性;三重旋转对称操作给予声子量子化的赝角动量,赝角动量的守恒将决定电子谷间散射的选择定则;此外还理论预测了谷声子霍尔效应.     

Multipolar Structure of Equilibrium Shear Flow Field in Toroidal Plasmas

The multipolar velocity field structures are investigated by 2D momentum conservation equation with 3D equilibrium sheared flows in the full toroidal system. Numerical results show that the non-existence of radial velocity field in equilibrium surfaces is suitable only for the zero-order term of our 2D simulation. The non-zero-order radial velocity field is still preserved, even when converted to conventional magnetic surface coordinates. The distribution of velocity field vectors of the order of 1, 2, and 3 are presented respectively in 2, 4, and 6 polar fields with the local vortex structure. The excitation mechanisms of these velocity vortices are the coupling effects of the magneto-fluid structure patterns and the toroidal effects. These results can help us understand the complexity of core physics, the transverse transport across magnetic field by the radial plasma flow and the formation of velocity vortices.     

在动量空间讨论二氯乙烯的同分异构性

通过量化计算得到了二氯乙烯偏式、顺式和反式三种同分异构体的几何结构参数, 并利用电子动量谱学方法计算了二氯乙烯偏式、顺式和反式同分异构体的四个芯轨道的动量密度二维分布图和动量谱线. 对比不同异构体的四个芯轨道在坐标空间和动量空间的电子分布情况发现, 在坐标空间无法体现的原子轨道间的相互干涉作用在动量空间被放大了, 表现为动量曲线具有多峰结构和一定的周期性. 通过计算周期值可以求出不同异构体相邻原子间的间距; 通过判断周期轴的方向能够得到三种异构体的分子轴取向.     

Intrinsic angular momentum in HMO

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Numerical study of physical properties of resistive wall modes in tokamaks

The effect of plasma with toroidal rotation on the resistive wall modes in tokamaks is studied numerically. An eigenvalue method is adopted to calculate the growth rate of the modes for changing plasma resistivity and plasma density distribution, as well as the diffusion time of magnetic field through the resistive wall. It is found that the resistive wall mode can be suppressed by the toroidal rotation of the plasma. Also, the growth rate of the resistive wall mode decreases when the edge plasma density is the same as the core plasma density, but it only changes slightly with the plasma resistivity.