Acceleration optimization of real-time equilibrium reconstruction for HL-2A tokamak discharge control

Real-time equilibrium reconstruction is crucially important for plasma shape control in the process of tokamak plasma discharge.However,as the reconstruction algorithm is computationally intensive,it is very difficult to improve its accuracy and reduce the computation time,and some optimizations need to be done.This article describes the three most important aspects of this optimization：（1） compiler optimization;（2） some optimization for middle-scale matrix multiplication on the graphic processing unit and an algorithm which can solve the block tri-diagonal linear system efficiently in parallel;（3） a new algorithm to locate the X＆O point on the central processing unit.A static test proves the correctness and a dynamic test proves the feasibility of using the new code for real-time reconstruction with 129？×？129 grids;it can complete one iteration around 575 μs for each equilibrium reconstruction.The plasma displacements from real-time equilibrium reconstruction are compared with the experimental measurements,and the calculated results are consistent with the measured ones,which can be used as a reference for the real-time control of HL-2 A discharge.

Coupling Effect between Equilibrium Field and Heating Field and Modification of the Power Supply System on SUNIST Spherical Tokamak

Strong inductive coupling between the heating field and equilibrium field is confirmed to be responsible for the poor plasma equilibrium in initial discharges on the SUNIST spherical tokamak. A modification project for the power supply system of equilibrium field coils is successfully performed to increase the duration time of plasma current flattop from much less than 1ms to about 2 ms.

Review of the Equilibrium Fitting for Non-Circular Tokamak

As the equilibrium fitting code (EFIT) is developing to perform the magnetic andthe kinetic-magnetic analysis for tokamak device operation, it can be not only run in either thefitting mode or the equilibrium mode but also control operation of modern experimental fusiondevice. In this paper the history of EFIT code and its capabilities are described in section 2. Abrief description of the off-line EFIT code and the development of the real-time EFIT (RTEFlT)code is shown in section 3 and 4 respectively. In the last section the summary of this paper isgiven.

Study of Plasma MHD Equilibrium in HL-2A Tokamak

EFIT（Equilibrium Fitting） code is successfully transplanted for HL-2A tokamak parameters. The evolution of the equilibrium configurations for shot 2898 is simulated. It is shown that the discharge starts with a limiter configuration and develops into a divertor configuration gradually after t = 200 ms. The latter lasts until the end of the discharge at t = 900 ms. The evolution of the major plasma shape parameters such as the boundary magnetic fluxes, the positions of the x-point and magnetic axis, and the minor radii obtained are calculated and compared with the experimental results. The agreement between the simulation and experiments are shown to be reasonable. The possibility for discharge quality improvement is discussed.

Fast parallel Grad–Shafranov solver for real-time equilibrium reconstruction in EAST tokamak using graphic processing unit

To achieve real-time control of tokamak plasmas, the equilibrium reconstruction has to be completed sufficiently quickly. For the case of an EAST tokamak experiment, real-time equilibrium reconstruction is generally required to provide results within 1ms. A graphic processing unit（GPU） parallel Grad–Shafranov（G-S） solver is developed in P-EFIT code,which is built with the CUDA？ architecture to take advantage of massively parallel GPU cores and significantly accelerate the computation. Optimization and implementation of numerical algorithms for a block tri-diagonal linear system are presented. The solver can complete a calculation within 16 μs with 65×65 grid size and 27 μs with 129×129 grid size, and this solver supports that P-EFIT can fulfill the time feasibility for real-time plasma control with both grid sizes.

Effect of Equilibrium Current Profiles on External Kink Modes in Tokamaks

Based on a linearized MHD model, the effect of equilibrium current profiles on external kink modes in tokamaks is studied by MARS code. Three types of equilibrium current profiles are adopted in this work. Firstly, a set of parabolic equilibrium current profiles are chosen. In these profiles the maximum current values in the center of the plasma are fixed, and the currents have different gradient and jump at the plasma boundary. The effects of the current gradient and jump on the growth rate of external kink mode are investigated. It is found that the current jump which causes the q profiles to change plays an important role in the externM kink modes in tokamaks. Secondly, a set of step equilibrium current profiles with different jump positions are chosen. The effect of jump position on external kink modes is discussed. Thirdly, a set of parabolic equilibrium current profiles with current bumps are chosen for the case of off-axis heating. The effects of height~ width and position of the current bumps on external kink modes are analyzed. The fiat equilibrium current profiles are disadvantageous for the MHD stabilities of tokamaks, because of the large current jump at the plasma edge. The peaked equilibrium current profiles and a large and localized current bump near the plasma edge benefit the MHD stabilities of tokamaks.

Plasma equilibrium calculation in J-TEXT tokamak

Plasma equilibrium has been calculated using an analytical method. The plasma profiles of the current density, safety factor, pressure and magnetic surface function are obtained. The analytical solution of the Grad–Shafranov（GS） equation is obtained by the variable separation method and compared with the computed results of the equilibrium fitting code EFIT.

Effect of shear equilibrium flow in Tokamak plasma on resistive wall modes

A code named LARWM with non-ideal magnetohydrodynamic equations in cylindrical model is used to describe the instability in Tokamak plasma surrounded by a conducting wall with finite resistivity. We mainly take three factors related to the shear equilibrium plasma flow into consideration to study the stabilizing effect of the shear flow on the resistive wall modes （RWMs）. The three factors are the velocity amplitude of flow, the shear rate of flow on plasma surface, and the inertial energy of equilibrium plasma flow. In addition, a local shear plasma flow is also calculated by the LARWM code. Consequently, it is found that the inertial energy of the shear equilibrium plasma flow has an important role in the stabilization of the RWMs.

MHD Equilibrium Configuration Reconstructions for HL-2A Tokamak

The EFIT （Equilibrium Fitting） code is modified for the equilibrium configuration reconstruction in HL-2A. Signals from Langmuir probe （LP） at the divertor target plates are employed in the reconstruction of divertor configurations. The results show that discharge #2895 starts with a limiter configuration and develops gradually into a divertor configuration after t = 230 ms. This transition process is clearly demonstrated by the LP signals for the reconstruction. The profiles of plasma parameters such as safety factor q, pressure and current density as well as the evolution of major shape parameters of plasma, such as the boundary magnetic fluxes, the positions of both x-point and magnetic axis, are calculated from the reconstructed configurations. The possibility to apply the method to the swing of strike point on the target plate is discussed.

The Effect of Equilibrium Current Profiles on MHD Instabilities in Tokamaks

A cylindrical model of linear MHD instabilities in tokamaks is presented. In the model, the cylindrical plasma is surrounded by a vacuum which is divided into inner and outer vacuum areas by a conducting wall. Linearized resistivity MHD equations with plasma viscosity are adopted to describe our model, and the equations are solved numerically as an initial value problem. Some of the results are used as benchmark tests for the code, and then a series of equilibrium current profiles are used to simulate the bootstrap current profiles in actual experiments with a bump on tail. Thus the effects of these kinds of profiles on MHD instabilities in tokamaks are revealed. From the analysis of the numerical results, it is found that more plasma can be confined when the center of the current bump is closer to the plasma surface, and a higher and narrower current bump has a better stabilizing effect on the MHD instabilities.

基于Python的托卡马克等离子体位形编辑器设计与实现

等离子体位形控制是等离子体实验控制的重要组成部分,设计满足放电要求的等离子体平衡位形是等离子体控制系统的重要功能之一。根据位形计算原理、中国聚变工程实验堆等离子体控制系统用户界面集成原理及用户界面需求,采用开源的Python语言及PyQt库,设计开发位形编辑器,用于等离子体期望位形设计和优化;并提供期望位形输入数据,供其集成使用。对主要模块进行复用,开发可独立运行的位形编辑器,能够灵活适用于不同的托卡马克装置。测试结果显示,该编辑器能满足单机运行的需求,同时消除了必须登录等离子体控制系统才可进行位形设计工作的弊端。

基于Python 的等离子体平衡重建程序设计及实现

基于Python环境,设计和编写了等离子体平衡重建算法(Py-EFIT)。利用NumPy和SciPy库求解平衡重建算法中矩阵的运算问题,运用Matplotlib库实现重建算法计算结果的可视化,基于交互式可视化设计包QT Designer,使用PyQt库设计并实现该程序的用户界面。Py-EFIT的测试结果显示等离子体平衡重建过程操作更加简单、直观,为托卡马克实验数据分析提供了一种有效的工具。

Online Plasma Shape Reconstruction for EAST Tokamak

An online plasma shape reconstruction, based on the offiine version of the EFIT code and MPI library, can be carried out between two adjacent shots in EAST. It combines online data acquisition, parallel calculation, and data storage together. The program on the master node of the cluster detects the termination of the discharge promptly, reads diagnostic data from the EAST mdsplus server on the completion of data storing, and writes the results onto the EFIT mdsplus server after the calculation is finished. These processes run automatically on a nine-nodes IBM blade center. The total time elapsed is about 1 second to several minutes, depending on the duration of the shot. With the results stored in the mdsplus server, it is convenient for operators and physicists to analyze the behavior of plasma using visualization tools.

Design, simulation and construction of the Taban tokamak

This paper describes the design and construction of the Taban tokamak, which is located in Amirkabir University of Technology, Tehran, Iran. The Taban tokamak was designed for plasma investigation. The design, simulation and construction of essential parts of the Taban tokamak such as the toroidal field(TF) system, ohmic heating(OH) system and equilibrium field system and their power supplies are presented. For the Taban tokamak, the toroidal magnetic coil was designed to produce a maximum field of 0.7 T at R?=?0.45 m. The power supply of the TF was a130 kJ, 0–10 kV capacitor bank. Ripples of toroidal magnetic field at the plasma edge and plasma center are 0.2% and 0.014%, respectively. For the OH system with 3 kA current, the stray field in the plasma region is less than 40 G over 80% of the plasma volume. The power supply of the OH system consists of two stages, as follows. The fast bank stage is a 120 μF, 0–5 k V capacitor that produces 2.5 kA in 400 μs and the slow bank stage is 93 mF, 600 V that can produce a maximum of 3 kA. The equilibrium system can produce uniform magnetic field at plasma volume. This system’s power supply, like the OH system, consists of two stages, so that the fast bank stage is 500 μF, 800 V and the slow bank stage is 110 mF, 200 V.

HL-2M装置实时等离子体平衡重建算法

利用模拟得到的平衡数据进行了等离子体平衡重建,将结果与准确的平衡结果进行细致对比,验证实时等离子体平衡重建程序的准确性;同时在模拟产生平衡数据的过程中引入随机误差,验证反演程序的强壮性。此外,实时等离子体平衡重建程序还使用EAST装置的实验数据进行反演,将反演结果与EAST的RTEFIT反演结果对比,验证了单一时间平衡重建结果和连续时间反演结果的正确性。结果表明,选择合适的电流分布模型和磁诊断数据,通过等离子体平衡重建算法可以正确识别等离子体位形。

欧姆驱动托卡马克平衡位形的确定

欧姆驱动条件下,托卡马克等离子体中的电流由欧姆驱动电流和等离子体内部的自恰电流构成。在简单的Spitzer电阻率模型下,欧姆驱动的环向电流密度剖面,主要由每一时刻的电子温度剖面和有效电荷数Zeff的剖面决定。讨论并给出了确定了平衡位形的基本方程,在大环径比近似下,给出了存在锯齿振荡条件下的环向电流剖面和小的非圆变形的平衡解。

HL-2A等离子体实时平衡重建的GPU并行化

描述了HL-2A等离子体实时平衡重建的GPU并行化算法,主要包括G-S方程的并行化处理、三对角方程求解、网格边界磁通计算以及一系列矩阵相乘的并行加速。并行后,在129×129的网格下完成一次迭代计算需要约575μs。

HL-1M装置欧姆等离子体实验的初步分析

从１９９４年１０月２４日开始，对ＨＬ－１Ｍ装置进行欧姆加热等离子体的调试实验，获得了Ｉｐ＝３１０ｋＡ，ｑａ＜２．５，ｎｅ＝３×１０１３ｃｍ－３，Ｔｅ（０）＞１ｋｅＶ，Ｔｉ（０）＞０．５ｋｅＶ和τＥ≈１０ｍｓ的平衡稳定等离子体。本文简述了ＨＬ－１Ｍ装置及其诊断、数据采集与处理系统，并对有关气体再循环。

EAST超导托卡马克等离子体位形平衡和反演算法

等离子体位形平衡和反演算法是EAST超导托卡马克控制系统的基础和重要组成部分。文中介绍了应用于托卡马克装置上的EFIT算法的物理含义;提出了EAST版EFIT算法开发移植的总体计划和主要流程结构,简要介绍了格林函数、平衡和反演核心子函数的构成;介绍了移植开发遇到的3类主要问题和解决方案。分析比较了算法产生的格林函数和等离子体特征参数的数据。

HT-6M托卡马克等离子体平衡的1MW反馈控制系统

针对ＨＴ－６Ｍ托卡马克（它具有无解耦的极向场线圈系统和薄壁真空室），成功地研制出１ＭＷ快响应等离子体平衡反馈控制系统。主电源采用ＧＴＯ直流斩波器。主控采用带微分反馈环节的开关斩控模式。导出了由载流等离子体、薄壁真空室和反馈场磁体所构成的反馈控制系统在Ｂａｎｇ－Ｂａｎｇ控制模式下的系统传递函数及控制模型。系统技术指标达到：电压１ｋＶ，电流１ｋＡ，功率１ＭＷ，频率（１—２）ｋＨｚ，系统电压响应时延＜１２０μｓ。在各种实验条件下，等离子体实际水平位置控制在±３ｍｍ以内，相应的控制精度优于１．５％。