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.     

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.     

A simple model for fast correction of the horizontal position of atokamak plasma

A virtual movement of the plasma in the radial direction was studied in order to obtain the magnitude of the vertical field applied to the Tokamak de Varennes plasma for fast horizontal motion using coils inside the vacuum vessel. The developed model includes the radial dependence of several parameters     

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。     

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。     

EDGE REYNOLDS STRESS STRUCTURE OF LOWER HYBRID WAVE INJECTION IN THE HL—1M PLASMA

The radial profiles of electrostatic Reynolds stress,plasma poloidal rotations,radial and poloidal electric fields have been measured in the plasma boundary region on the HL-1M tokamak using a multi-array of Mach/Langmuir probes.During experiments of lower hybrid wave current drive,the variations in LHW drive power xill cause changes in the edge electric field,poloidal rotation veloity and Reynolds stress.The results indicate that sheared poloidal flow can be generated in the edge plasma due to radially varied Reynolds stress.     

HL-2M等离子体垂直不稳定性的反馈控制研究

使用无源稳定导体和主动控制线圈来控制HL-2M等离子体的垂直不稳定性。计算了等离子体垂直不稳定性增长时间,构建了等离子体垂直不稳定性控制的线性模型,然后用MATLAB对采用PID算法的垂直不稳定性控制系统进行了模拟仿真。结果表明,无源稳定导体和主动控制线圈能够快速稳定等离子体的垂直不稳定性运动,这也表明设计是可行的。     

Synergetic Effects of Runaway Electron and Vertical Instability on the Wall Damage on HL-2A Tokamak

1 Generation of vertical instability Tokamak experiments show that the energy confinement time and performance are better, and the larger plasma current can be achieved for non-circular cross-sectional shape of plasma than circular cross-section. However, the external magnetic fields which are used to produce the non-circular cross sectional shape also cause the confined plasma to become unstable to small vertical displacement. In general, the ratio of elongation k is larger, the possibility of instability is more. In practice, this vertical displacement mode stabilized by feedback control system or other provided external radial magnetic field to balance out the plasma motion. Under some of situations the control system may be fail due to rapid growth rate of instability exceeding the ability of controlling. The plasma will then move vertically upwards or downwards depending upon the characteristics of instability and control failure.     

Study of Globus-M Tokamak Poloidal System and Plasma Position Control

In order to provide efficient performance of tokamaks with vertically elongated plasma position, control systems for limited and diverted plasma configuration are required. The accuracy, stability, speed of response, and reliability of plasma position control as well as plasma shape and current control depend on the performance of the control system. Therefore, the problem of the development of such systems is an important and actual task in modern tokamaks. In this study, the measured signals from the magnetic loops and Rogowski coils are used to reconstruct the plasma equilibrium, for which linear models in small deviations are constructed. We apply methods of the H∞-optimization theory to the synthesize control system for vertical and horizontal position of plasma capable to working with structural uncertainty of the models of the plant. These systems are applied to the plasma-physical DINA code which is configured for the tokamak Globus-M plasma. The testing of the developed systems applied to the DINA code with Heaviside step functions have revealed the complex dynamics of plasma magnetic configurations. Being close to the bifurcation point in the parameter space of unstable plasma has made it possible to detect an abrupt change in the X-point position from the top to the bottom and vice versa. Development of the methods for reconstruction of plasma magnetic configurations and experience in designing plasma control systems with feedback for tokamaks provided an opportunity to synthesize new digital controllers for plasma vertical and horizontal position stabilization. It also allowed us to test the synthesized digital controllers in the closed loop of the control system with the DINA code as a nonlinear model of plasma.     

Plasma confinement in tokamaks with robust torus

We present a non-linear symplectic map that describes the alterations of the magnetic field lines inside the tokamak plasma due to the presence of a robust torus (RT) at the plasma edge. This RT prevents the magnetic field lines from reaching the tokamak wall and reduces, in its vicinity, the islands and invariant curve destruction due to resonant perturbations. The map describes the equilibrium magnetic field lines perturbed by resonances created by ergodic magnetic limiters (EMLs). We present the results obtained for twist and non-twist mappings derived for monotonic and non-monotonic plasma current density radial profiles, respectively. Our results indicate that the RT implementation would decrease the field line transport at the tokamak plasma edge.     

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.      

HL-1M托卡马克边缘参数和雷诺胁强的径向分布

利用多组马赫/郎缪尔探针测量了HL-1M装置刮离层和边缘静电雷诺胁强，等离子体极向旋转，径向和极向电场的径向分布，在低杂波电流驱动，超声分子束注入，多发弹丸注入和中性束注入实验中，给出了雷诺胁强和极向流的关系。结果表明，由于雷诺胁强的径向变化，托卡马克等离子体可以自发地产生剪切极向流。     

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     

The Effective Mode Approximation for Analyzing Position Instability of a Tokamak Plasma

The effect of induced currents in the equilibrium field (EF) coils on ameliorating the instability of a small position perturbation of a rigid tokamak plasma is analyzed. A strong analogy between the position instability of the plasma and supercriticality of a fission reactor core is recognized. The position of the plasma corresponds to the neutron population, and the retardation of the displacement by the induced eddy currents to the suppression of population growth by delayed neutrons. The matrix equation of the dispersion relation for the position instability is diagonalized and factored into a form identical to the in-hour equation of fission reactor kinetics. An Effecitve Mode Approximation (EMA) similar to the one group of delayed neutron approximation has been introduced to greatly simplify the analysis of the position instability and feedback control. With this approximation the dispersion relation is reduced to a linear or cubic algebraic equation depending on the effectiveness of retardation by the eddy currents. The time constant of the unstable mode can be expressed in terms of the plasma parameters and the effective resistance and inductance of the current carriers, which can be conveniently computed. The vertical instability of a typical noncircular tokamak plasma is analyzed numerically as well as analytically by the EMA method. The results agree well within a negligible discrepancy.     

Analyses of edge plasma characteristics in HL-2A

The edge plasma characteristics are studied by both a movable array of Mach/Reynolds stress/Langmuir 10-probes in the boundary region and the fixed flush probe arrays on the 4 divertor neutralization plates at the same toroidal cross-section in the HL-2A tokamak. The dependence of the Reynolds stress on poloidal flow in the edge plasma is analysed. The result indicates that the sheared poloidal flow in tokamak plasma can be induced by the radial gradient of Reynolds stress. In the divertor experiments of HL-2A, the profiles of the electron temperature, density and floating potential on divertor plates are measured by the flush probe arrays. The edge electron temperature in divertor configuration is higher than that in limiter configuration. The temperature asymmetry between outer and inner target plates is observed. The result of magnetic surface reconstructed from 18 Mirnov coils signals is presented. Both the particle recycling and the impurity flux in the bulk plasma during divertor discharges are discussed. Neutral gas pressure in divertor chamber, measured by fast ionization gauge during divertor discharge, is given.     

LBNL14GHz离子源AECR-U的最新进展

A radial sputter probe has been developed for the AECR-U as an additional method of producing metal ion beams.Negative voltage is applied to the probe to incite collisions with target atoms,thereby sputtering material into the plasma.The sputter probe is positioned through one of the 6 radial access slots between the permanent hexapole structure of the AECR-U.The probe position can be varied with respect to the inner edge of the hexapole magnet structure.Charge state distributions and peak beam intensities at bias voltages up to-5kV were obtained for gold samples at varying distances of the probe with respect to the plasma.For high charge states production the radial position with respect to the plasma was more sensitive than for the medium and lower charge states.For high charge state ion production the probe was optimized at a distance of 0.6cm inside the chamber wall(4.1cm from the center of the chamber).Stable beams with peak intensities of up to 28eμA of Au~(24 ) and 1.42eμA of Au~(41 ) have been produced using the sputter probe technique. In addition,a solid state circuit under development by Scientific Solutions,Inc which provides a bandwidth up to 100MHz was used to drive the 14GHz klystron amplifier for the LBNL AECR-U ion source.Various broadband and discrete heating modes were tested and the results for high charge state ion production were compared with single frequency heating.     

Aerodynamic and energy-efficiency-based assessment of plasma actuator's position on a NACA0015 airfoil

In recent years, there has been an increase in the number of research papers on plasma and its use in active flow control applications. The main objective of this study is to assess the plasma actuator's position on a NACA0015 airfoil in terms of aerodynamic forces. In addition, optimization of the plasma actuator's position and its configuration are studied in order to identify the optimum configuration for improvement in lift coefficient. The experiments are conducted in an open-suction-type wind tunnel at Reynolds numbers of 48,000, 75,000, and 100,000. The plasma actuators are mounted on various positions (x/C) starting from the leading edge to trailing edge of the airfoil. The experimental results on aerodynamic force measurement are presented to illustrate the increasing lift effect of the generated plasma. It is also shown that the plasma actuators used as an active flow control device appears to shift the stall angle of the airfoil. The results of the experimental study suggest that the energy efficiency of airborne systems can be improved with the use of plasma actuators due to its increasing lift coefficient effect. This result becomes a vital finding considering that the same flight can be achieved with less fuel and less amount of environmental pollution for the same distance of journey. It is also worth mentioning that increasing lift effect would mean taking off from a shorter runway or allowing the airborne vehicle with the ability to fly with additional payload.     

HL-2A单零偏滤器的位形特征

利用积分方法对多种电流剖面下HL2A装置单零偏滤器位形特征进行了计算研究。积分方法的优点是可以在任意电流剖面下求解具有X-点的自由边界的Grad-Shafranov方程。对HL2A装置而言,大体上可以在合理设定的分界面形状下,经几次叠代计算出各组极向场线圈(垂直场,三对多极场和多极补偿场以及水平场)中的电流。HL-2A的单零偏滤器位形基本上是圆截面加上在X-点附近的局部形变。对刮离区和偏滤器靶板区磁力线特性进行了分析以确定偏滤器的品质。     

Effect of unstable MHD modes on the confinement of a stellarator plasma

The results of an experimental study of the influence of unstable MHD modes on plasma confinement in an L-2M stellarator are presented. The spectral and statistical characteristics of turbulent plasma simultaneously at both the edge and center of the plasma are investigated. It is shown that at constant power of electron-cyclotron heating of the plasma the energy content of the plasma depends strongly on the strength of the externally applied vertical magnetic field used to adjust the position of the plasma column. Appreciable degradation of plasma confinement is observed for values of the vertical field such that ideal MHD modes become unstable in the greater part of the plasma column. This in turn is due to the formation of a magnetic configuration with a magnetic “hump.” At the same time, in the edge plasma the instability of resistive-balloon modes grows, and turbulent particle transport increases. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 6, 407–412 (25 March 1999)     

Tokamak plasma equilibrium analysis based on the relaxation method with a specified magnetic axis

In this contribution, we have presented two techniques for the determination of plasma equilibrium position in IR-T1 tokamak: relaxation and optical methods. An analysis method of tokamak plasma equilibrium by a relaxation method with a specified magnetic axis is presented. The degrees of freedom due to designated positions of the magnetic axis are possible by using poloidal field coil currents. Stable steady-state tokamak plasma equilibria are calculated along with the magnetohydrodynamic potential energy. The plasma generates a plasma current which partially or fully cancels the magnetic field from the poloidal field coils. For low-temperature plasmas, the plasma current distribution is centrally peaked; for high-temperature plasmas, the plasma current has a hole. A centrally peaked current distribution in a low-temperature plasma is evolved into a current distribution with a hole by increasing the plasma pressure by Ohmic heating, radio frequency heating, or by neutral beam injection heating. In the second technique, an image-processing technique was used for the output signal of the charge coupled device camera and plasma emission intensity profile and then the plasma position was obtained. Results are compared and discussed.