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。     

Comparative measurements of plasma position using coils,hall probes,and bolometers on CASTOR tokamak

Plasma position on CASTOR tokamak is measured by several systems based on different experimental methods. Vertical and horizontal plasma displacements are deduced from data of 4 Mirnov coils spaced poloidaly by 45°. Output of the Mirnov coils is routinely used as an input for automatic feed-back control of plasma position on CASTOR. Independently, we used an array of 16 Hall sensors, which measure the required magnetic field directly. Additional information on plasma position is obtained from two arrays of bolometers that measure horizontal and vertical profile of plasma radiation. Principle design of the all used diagnostics is given. Comparison of horizontal and vertical displacements deduced using various experimental methods is presented.     

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利用SOLPS和DINA程序,对偏滤器的数值模拟进行综合研究。结合HL-2M装置,针对偏滤器的结构优化、脱靶物理过程、偏滤器送气与抽气、垂直位移事件(VDE)等问题进行了模拟研究。分析了偏滤器靶板位形以及脱靶对偏滤器靶板热载荷的影响,研究了偏滤器的送气位置、送气速率、抽气速率等因素对于偏滤器性能的影响;同时,利用DINA程序对HL-2M装置的VDE过程进行了预测分析,并给出了HL-2M装置发生VDE过程的等离子体电流剖面变化,从而为HL-2M装置的偏滤器结构设计和分析提供输入数据。     

HL-2M偏滤器的综合模拟技术初步研究

利用SOLPS和DINA程序,对偏滤器的数值模拟进行综合研究。结合HL-2M装置,针对偏滤器的结构优化、脱靶物理过程、偏滤器送气与抽气、垂直位移事件(VDE)等问题进行了模拟研究。分析了偏滤器靶板位形以及脱靶对偏滤器靶板热载荷的影响,研究了偏滤器的送气位置、送气速率、抽气速率等因素对于偏滤器性能的影响;同时,利用DINA程序对HL-2M装置的VDE过程进行了预测分析,并给出了HL-2M装置发生VDE过程的等离子体电流剖面变化,从而为HL-2M装置的偏滤器结构设计和分析提供输入数据。     

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.     

Plasma Modelling for the PSI Linear Plasma Device

Deuterium discharges in the PSI device have been modelled using the coupled package of the B2 hydrodynamic plasma code and the Eirene Monte‐Carlo neutral code. Radial and axial plasma profiles have been calculated for different magnetic field configurations, various radial diffusion laws and for different values of the flux limiter in the parallel electron heat conduction law used in the B2 code. The results are compared with experimental findings. The axial variation of the magnetic field strength is found to have an important influence on the plasma state via the axial plasma flow which closely resembles the neutral gas streaming through a series of laval nozzles. For particular magnetic field configurations, an appropriate ansatz for the parallel electron heat conduction turns out to be a crucial point for the applicability of hydrodynamic models to linear devices like the plasma generator PSI. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

ITER装置中等离子体旋转和反馈控制对电阻壁模影响的数值研究

在托卡马克等离子体中,电阻壁模是非常重要的磁流体不稳定性,特征时间在毫秒量级.对长时间稳态运行下的先进托卡马克,电阻壁模限制着聚变装置的运行参数空间(放电时间和比压),影响经济效益,所以研究电阻壁模稳定性至关重要.本文使用MARS程序,针对ITER装置上9 MA先进运行平衡位形,研究了等离子体旋转和反馈控制对电阻壁模的影响.结果表明,在没有反馈控制时,当比压参数Cβ取0.7,等离子体环向旋转频率达到1.1%的阿尔芬频率时,可以完全稳定电阻壁模;在等离子体环向旋转和反馈控制共同作用时,比压参数Cβ取0.7,反馈增益|G|取0.6时,稳定电阻壁模所需要的等离子体旋转频率为0.2%的阿尔芬频率.可见,单独靠等离子体环向旋转稳定电阻壁模所需的旋转频率较大;而等离子体环向旋转和反馈控制共同作用可以降低稳定电阻壁模的旋转频率临界值,符合先进托卡马克的运行.本文的研究结果对中国聚变工程试验堆CFETR的工程设计和运行具有一定指导意义.     

A method for calculating active feedback system to provide vertical position control of plasma in a tokamak

In designing tokamaks, the maintenance of vertical stability of plasma is one of the most important problems. Systems of the passive and active feedbacks are applied for this purpose. Role of the passive system consisting of a vacuum vessel and passive coils is to suppress fast MHD (magnetohydrodynamic) instabilities. The active feedback system is applied to control slow motions of plasma. The objective of the paper is to investigate two successive problems, solution of which allows to determine the possibility of controlling plasm a motions. One of these is the problem of vertical stability under the assumption of ideal conductivity of plasma and passive stabilizing elements. The problem is solved analytically and on the basis of the obtained solution a criterion of MHD-stability is formulated. The other problem is connected with the control of plasma vertical position with active feedback system. Calculation of feedback control parameters is formulated as an optimization problem and an approximate method to solve the problem is suggested. Numerical simulations are performed with parameters of the T-15M tokamak in order to justify the suggested method.      

The Electrotechnical Complex of the KTM Tokamak Pulsed Power Supply System

The pulsed power supply equipment belongs to the basic technological systems intended for implementing the required scenarios of changing currents in magnetic coils. The accuracy of implementing these scenarios directly determines the possibility of attaining the plasma breakdown and the required ultimate plasma parameters. Given the uniqueness of each facility under construction in the world and the installed capacity of the electrotechnical equipment applied in the power supply configuration, one can state with confidence that the construction of similar power supply complexes and their control systems, the optimization of their electrotechnical parameters, and the subsequent accident-free operation are vital tasks in mastering controlled thermonuclear fusion technologies. This paper describes the pulsed power supply system of the KTM tokamak (Kazakhstan) designed for material testing, the digital control system for its power conversion equipment, electrotechnical solutions adopted in the design of the KTM tokamak pulsed power supply system, and findings of tests of some items of equipment and their components. The tests have demonstrated sufficient efficiency of the adopted electrotechnical solutions and the possibility of applying them to implement the pulsed power supply systems for small and medium sized tokamaks.     

Tokamak position control

A set of sensing coils to measure plasma position is described. The possibility of placing these coils outside a vacuum vessel (as a resistive shell) is considered by analyzing a feedback system for controlling otherwise unstable axisymmetric motion. A simple model was used to study the axisymmetric stability of a noncircular plasma surrounded by a conducting vacuum vessel and a feedback control system. Suitable choice of the various constants allowed a study of either horizontally or vertically unstable motion, either with or without an iron core and with various configurations for the vacuum vessel. Analytic expressions for the stability limits are derived, together with the specific response to a requested step displacement, giving the overshoot, steady-state error, decay times, and maximum power supply voltage. By suitably choosing an effective decay index both vertical and horizontal motion were studied. The results are applied to TEXT Upgrade (horizontal elongated, with iron core, horizontal unstable) using an effective decay index of -1     

HL-2A等离子体约束参数的实时确定

在HL-2A等离子体放电过程中，利用CF编码计算出的等离子体边界磁场，计算出Shafranov 积分S₁，S₂和S₃,再利用反磁磁通导出极向比压β_p，等离子体内自感l_i，等离子体磁轴的大半径R_m，等离子体的能量W_dia，能量约束时间τ_E；再用电流矩导出等离子体的电流中心(R_c,Z_c).实时确定这些量对于及时了解和改进装置的放电和改善等离子体性能很有意义. 关键词： 等离子体约束 Shafranov 积分     

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介绍了HL-2M装置控制系统的静态架构、动态行为、控制理论以及模拟仿真。设计采用通讯网络将各控制子系统有机地连接起来,以实现各子系统的实时通讯和控制。等离子体放电控制系统将保证实验的各种参数达到预定要求,监控系统的故障处理机制可以减少各种实验异常对装置造成破坏,磁场控制系统的各种控制器则用来控制等离子体电流和位形,模拟仿真系统可以实现方便地验证控制器的目的。     

Tokamak equilibria with reversed current density

Observations of nearly zero toroidal current in the central region of tokamaks (the "current hole") raises the question of the existence of toroidal equilibria with very low or reversed current in the core. The solutions of the Grad-Shafranov equilibrium equation with hollow toroidal current density profile including negative current density in the plasma center are investigated. Solutions of the corresponding eigenvalue problem provide simple examples of such equilibrium configurations. More realistic equilibria with toroidal current density reversal are computed using a new equilibrium problem formulation and computational algorithm which do not assume nested magnetic surfaces.     

HL-2A 等离子体垂直不稳定性控制研究

采用了PID 控制、输入误差直接自适应控制和输出误差直接自适应控制三种控制方式对HL- 2A 装置的等离子体垂直不稳定性进行了研究。模拟结果显示, 在现有条件下三种控制方式都能满足控制要求, 而两种自适应控制系统具有更好的系统性能、更强的鲁棒性、对电源要求更低的特点, 尤其是输出误差直接自适应控制系统结构非常简单, 具有可实施性。     

Hot Vertical-Displacement-Event Process due to Internal Energy Perturbations for HL-2M Tokamak Plasma

During the tokamak operation,variation of the stored energy can cause internal perturbations of the plasma.These perturbations may develop into large-scale vertical movement of the whole column for the vertically elongated tokamak,eventually generating the hot vertical displacement event(VDE).It will cause considerable damage to the machine.In this work,the hot VDE process due to stored energy perturbations is investigated by a mature non-linear time-evolution code DINA.The influence on the vertical instability,the displacement direction and the electromagnetic loads on in-vessel components during the hot VDE are analyzed.It is shown that a larger perturbation leads to faster development of the vertical instability.Meanwhile the variation of the Shafranov shift,due to the energy change,is related to the VDE direction.The vertical electromagnetic force on the vacuum vessel and the halo current flowing in the divertor baffle become larger in the case of VDE moving towards the X point.     

There are no Magnetically Charged Particle-like Solutions of the Einstein Yang-Mills Equations for Models with an Abelian Residual Group

We prove that there are no magnetically charged particle-like solutions for any model with an Abelian residual group in Einstein Yang-Mills, but for the non-Abelian models the possibility remains open. An analysis of the Lie algebraic structure of the Yang-Mills fields is essential to our results. In one key step of our analysis we use invariant polynomials to determine which orbits of the gauge group contain the possible asymptotic Yang-Mills field configurations. Together with a new horizontal/vertical space decomposition of the Yang-Mills fields this enables us to overcome some obstacles and complete a dynamical system existence theorem for asymptotic solutions with nonzero total magnetic charge. We then prove that these solutions cannot be extended globally for Abelian models and begin an investigation of the details for non-Abelian models.     

CONTROL DESIGN OF ACTIVE VIBRATION ISOLATION USING μ -SYNTHESIS

Numerical and experimental investigations on active vibration isolation system are presented in this paper. Two configurations are implemented for a statically balanced three-mount system. To reduce the influence of payload dynamics and coupling among the control actuators, intermediate masses are added to the system. Linear quadratic Gaussian control andμ -synthesis are employed in the controller synthesis. The controllers are implemented on the platform of a floating-point digital signal processor. The results obtained from simulations and experiments indicated that the optimal controllers achieved the desired performance under the constraint of robust stability.     

高比压环流器等离子体位形的稳定性

本文用解析方法表示了高比压环流器的平衡位形,进而计算了局部理想磁流体判据,并着重讨论了低q运行的可能性。结果发现存在一大类具有这些特性的环流器平衡位形,有的位形其中心约束区域有很高的稳定性余度。对p′(ψ)剖面不同的位形以及不同位移函数的位形的稳定性做比较,发现大的位移及平坦的p′(ψ)剖面有更好的稳定性。 关键词：     

HT—6M闭环反馈平衡控制系统

本文描述HT-6M托卡马克装置闭环反馈平衡控制系统的结构组成,通过对各个环节的简化,得到了有效实用的数学模型,进而分析了系统稳态和动态性能。实验结果表明,该系统运行可靠;并且,将等离子体环水平位移控制在2mm以内。