Hybrid Method for Tokamak MHD Equilibrium Configuration Reconstruction

A hybrid method for tokamak MHD equilibrium configuration reconstruction is proposed and employed in the modified EFIT code. This method uses the free boundary tokamak equilibrium configuration reconstruction algorithm with one boundary point fixed. The results show that the position of the fixed point has explicit effects on the reconstructed divertor configurations. In particular, the separatrix of the reconstructed divertor configuration precisely passes the required position when the hybrid method is used in the reconstruction. The profiles of plasma parameters such as pressure and safety factor for reconstructed HL-2A tokamak configurations with the hybrid and the free boundary methods are compared. The possibility for applications of the method to swing the separatrix strike point on the divertor target plate is discussed.     

Optimization and performance of a high-speed plasma position digital control system

This paper addresses optimization of a high-speed digital feedback controller for a plasma position in Damavand tokamak. Damavand tokamak discharges have plasma currents up to 40 kA with discharge duration greater than 15 ms and toroidal magnetic fields up to 1.2 T. The plasma position is measured using saddle-loops and Rogowski coil and is controlled by electromagnetic forces generated by passing currents through control coils placed around the plasma. A desired control objective is maintaining the plasma in the center of vacuum vessel and to stabilize the plasma in the presence of disturbances in a time domain of the order of few milliseconds. In order to achieve maximum performance it is essential to optimize the control system. In this paper plasma position measurement and the details of implementing high-speed PID controllers based on a TMS320c25 digital signal processor along with the system optimization are presented.     

Identification of the magnetic island structure in the HL-2A tokamak

The identification of the magnetic island structure in the HL-2A tokamak is presented. First, the perturbation current as a source for the perturbation flux can be determined by using Mirnov probe measurements. By superposing the perturbation flux and the equilibrium flux reconnected by equilibrium fitting, the structure and the width of the magnetic islands can be estimated. The method has been used in the HL-2A experiments.     

Suppression of the magnetic surface shift by plasma rotation in a tokamak

The equilibrium of a toroidally rotating plasma in an axisymmetric tokamak-like system is considered. The equilibrium equation is represented in the form of the Grad-Shafranov equation in which, in contrast to the static case (with no plasma rotation), the plasma pressure depends on both the flux surface label and major radius. It is shown that the dependence of the pressure on the major radius makes it possible to choose the profile of the plasma rotation velocity so as to minimize the effect of the plasma pressure on the shift of the flux surfaces, in which case it might be anticipated that the maximum pressure of the confined plasma will be higher. This result was derived analytically and tested numerically for a number of typical tokamak configurations with a fixed plasma boundary.     

Comparative analysis of the possibility of applying low-melting metals with the capillary-porous system in tokamak conditions

The use of capillary-porous systems (CPSs) with liquid Li, Ga, and Sn is considered as an alternative for solving the problem of creating plasma-facing elements (PFEs) of the fusion neutron source (FNS) and the DEMO-type reactor. The main advantages of CPSs with liquid metal compared with hard materials are their stability with respect to the degradation of properties in tokamak conditions and capability of surface self-restoration. The evaluation of applicability of liquid metals is performed on the basis of the analysis of their physical and chemical properties, the interaction with the tokamak plasma, and constructive and process features of in-vessel elements with CPSs implementing the application of these metals in a tokamak. It is shown that the upper limit of the PFE working temperature for all low-melting metals under consideration lies in the range of 550–600°С. The decisive factor for PFEs with Li is the limitation on the admissible atomic flux into plasma, while for those with Ga and Sn it is the corrosion resistance of construction materials. The upper limit of thermal loads in the steady-state operating mode for the considered promising PFE design with the use of Li, Ga, and Sn is close to 18–20 MW/m². It is seen from the analysis that the use of metals with a low equilibrium vapor pressure of (Ga, Sn) gives no gain in extension of the region of admissible working temperatures of PFEs. However, with respect to the totality of properties, the possibility of implementing the self-restoration and stabilization effect of the liquid surface, the influence on the plasma discharge parameters, and the ability to protect the PFE surface in conditions of plasma perturbations and disruption, lithium is the most attractive liquid metal to create CPS-based PFEs for the tokamak.     

Methods for reconstructing equilibrium plasma configurations in the Globus-M spherical tokamak

A magnetic diagnostics allowing one to reliably reconstruct equilibrium plasma configurations in a tokamak over a wide range of operating parameters is developed. The accuracy of determining the geometrical parameters and thermal energy of the tokamak plasma is analyzed in detail. The experimental data obtained in the Globus-M tokamak are processed the with help of the EFIT code. The influence of the plasma configuration on the intensity of the main impurity lines is investigated.     

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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。     

Design and construction of hot limiter biasing system for the tokamak

A hot limiter biasing system with a simplified fast switch circuit was designed, constructed, and installed on the IR-T1 tokamak, and then the negative voltage applied to a hot limiter inserted inside the tokamak fixed limiter and the plasma current, poloidal, and radial components of the magnetic fields, loop voltage, diamagnetic flux, and the ion saturation currents in the absence and presence of the biased limiter were measured. Results of measurements of biasing effects on the plasma equilibrium behavior and edge plasma rotation are compared and discussed.     

HT-7U超导托卡马克等离子体位形平衡和反演编码

介绍了应用于托克马克装置上等离子体位形平衡和反演编码(EFTT)的物理含义。提出了HT-7U装置EFTT代码开发移植的总体计划和主要流程结构,介绍了格林函数、平衡和反演核心子函数的构成。提出了在EFIT编码的移植开发中遇到的三类主要问题的解决方案。对编码产生的格林函数和等离子体特征参数的数据进行了分析比较。     

Magnetohydrodynamic equilibrium interpretation of low-aspect-ratio tokamak plasma

It is very important to calculate the equilibrium magnetic field configuration exactly and to estimate the parameters of the device needed for the equilibrium and stability in the design and operate the low-aspect-ratio tokamak, one of the axis-symmetrical torus devices which is widely used in the research of nuclear fusion using plasma. In the previous researches, there were the theoretical and numerical interpretation methods for the high-aspect-ratio tokamak plasma. But for the low-aspect-ratio tokamak plasma, numerical methods such as the finite element method and iteration method are usually used. In this research, we interpreted and examined the features of magnetohydrodynamic equilibrium of the low-aspect-ratio tokamak plasma in combination with the Green function method and finite element method which has high numerical value accuracy.     

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用TSC程序模拟了EAST装置等离子体放电的全过程。模拟中考虑了自举电流，并加入了离子回旋共振加热ICRH和快波电流驱动FWCD，得到了中心电子温度4.5keV、中心离子温度3.8keV、中心电子密度1.2×1020m–3的D形截面的等离子体。根据模拟结果对EAST装置进行了伏秒数分析，并研究了不同等离子体电流上升时间、有效电荷数Zeff对放电的影响。     

HL-2M 装置磁测量系统设计及初始放电实验结果

介绍了 HL-2M 装置上满足等离子体放电的磁测量系统的物理设计,主要包括磁探针、磁通环以及 电流测量系统的设计。通过 HL-2M 装置典型的放电位形参数对磁探针的极向布局、有效面积,磁通环的极向布 局以及测量等离子体电流的罗氏圈互感值进行了初步设计。目前,HL-2M 装置已经完成初始等离子体放电。各个 子系统均能达到其测量目标。      

用磁探针反演磁岛二维结构的方法及其在HL-2A装置上的应用

介绍了HL-2A装置中利用磁探针数据反演磁岛极向二维结构的新方法,以及在反演基础上建立的撕裂模动态分析方法。在实验中通过磁探针测量确定作为扰动磁场来源的扰动电流。将扰动磁通与由EFIT重建的平衡磁通叠加反演出磁岛的结构,并给出磁岛的宽度。然后,按时间顺序建构二维结构图并依次记录,之后依次展现图像就可以对磁岛进行动态分析。应用此方法进行撕裂模分析,得出了磁岛旋转与电子抗磁漂移方向相同,验证了磁岛宽度与扰动场的关系及ECRH对磁岛的抑制作用。这显示了磁探针反演磁岛结构方法的直观性,对观察并控制MHD不稳定性非常有利。     

多道干涉仪测量托卡马克等离子体电子密度

一、引 言 在目前托卡马克等离子体诊断中,采用垂直多道干涉仪测量等离子体电子密度时,由于等离子体水平位移的影响,使得测量信号在沿大环半径方向的分布是非对称的。这就要求采用非对称的Abel变换来给出等离子体电子密度的空间分布。一种常用的非对称Abel变换是分离变量法,它的基本思想是把测量信号分成对称元和非对称的权函数,对称部分采用标准的Abel变换,变换的结果乘上非对称的权函数。这种方法实际上是假定了等离子体电子密度弦积分值的不对称性与局部的不对称性是相同的;而且对称部分采用标准的Abel变换,如Barr的方法,Bockasten方法等。这些方法是把等离子体看成一个个同心圆,没有考虑到等离子体水平位移引起的弦长变化。本文采用一种新的变换方法,这种方法的特点是考虑到等离子体位移的实际情况。     

The possibility of anomalous heat transfer in flows with nonequilibrium boundary conditions

The kinetic Boltzmann equation has been solved for the boundary-value problem of heat transfer with boundary conditions in the form of nonequilibrium distributions. Modes with anomalous heat transfer have been revealed in the spatial zones where the signs of the heat flux and temperature gradient coincide (in the classical statement of the problem with equilibrium conditions, heat transfer conventionally occurs in the entire range of physical parameters). Possible experiments aimed at verifying these effects are discussed.     

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现有的HL-2A实时平衡重建系统采用的是网格尺寸为33×33,将无法满足HL-2M装置对控制精度和速度要求.为此开发了网格尺寸为129×129的重建系统,并通过GPU并行、算法重构等优化方法,使得新的重建系统在保证计算精度的情况下能够使得每一次平均重建计算维持在600μs内,可满足HL-2A和HL-2M中周期为1ms等离子体控制系统对重建系统精度和速度要求.     

HL-2A装置实时等离子体位形重建系统的加速优化

现有的HL-2A实时平衡重建系统采用的是网格尺寸为33×33,将无法满足HL-2M装置对控制精度和速度要求。为此开发了网格尺寸为129×129的重建系统,并通过GPU并行、算法重构等优化方法,使得新的重建系统在保证计算精度的情况下能够使得每一次平均重建计算维持在600μs内,可满足HL-2A和HL-2M中周期为1ms等离子体控制系统对重建系统精度和速度要求。     

Thermal dynamics in the flux-coordinate independent turbulence code GRILLIX

GRILLIX employs the flux-coordinate independent approach (FCI), which allows us to study boundary plasma turbulence in realistic diverted configurations. Recently, the physical model in GRILLIX has been extended to a global drift-reduced Braginskii model, without any separation between background and fluctuations. It includes electromagnetic and thermal dynamics with hot ions, relaxation of the Boussinesq approximation and non-linear parametric dependencies. This contribution presents solutions to associated issues, that is, the ion diamagnetic polarization and the stiff parallel heat conduction. Simulations based on parameters characteristic for the Alcator C-Mod tokamak were carried out. In circular geometry, the self-consistent electric field contains zonal flows and geodesic acoustic modes in the confined region. In the scrape-off layer, the electron parallel heat conduction and its boundary condition determine the temperature and electric field, leading to sheared flows at the last closed flux surface.     

自由边界等离子体平衡问题的数值解法

一、基本方程和边界条件 在轴对称情况下,采用柱坐标系(R,z,),可将磁流体平衡方程用流函数ψ表示为     

On the scarcity of solutions of the equations of magnetohydrodynamic equilibria with flow

While particular analytic solutions to the equations of axisymmetric MHD equilibria with flow are known, it is not clear what possible choosing of the free parameters of the equation of the magnetic flux will yield a solution. The most important of these is the poloidal stream function. We show that for a given flow to be able to yield an equilibrium, the flow itself must satisfy an analogous equation to the generalized Grad-Shafranov one. The problem therefore turns out to be how common are solutions to this type of equations. It is shown that in a natural space of functions, the set of these solutions is contained within a manifold of infinite codimension: extremely small by any criteria. Hence the class of flows for which an equilibrium, even defined only locally and irrespective of boundary conditions, may be found, is highly constrained.