Study of the plasma equilibrium in Damavand tokamak via numerical solution of the Grad-Shafranov equation

In this work we study the Damavand tokamak plasma equilibrium with an elongated ross section and fixed boundary conditions. These equilibria are characterized by three parameters such as elongation, triangularity and magnetic axis shift. An iterative scheme f the moment’s method is used to solve the Grad-Shafranov equation in flux coordinate system. Magnetic flux surface contours and main equilibrium parameters have been btained by applying the geometry and boundary conditions of the Damavand tokamak.     

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.     

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.     

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 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.     

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.     

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在HT-7装置上建立了一套高速CCD可见光成像诊断,测量了边界等离子体的可见光辐射成像.在HT-7装置放电中,首次观察到在等离子体边界区域存在一条极向旋转的可见光辐射带,由CCD诊断系统得到其极向旋转的频率为858Hz.根据多道Hα阵列测量得到极向旋转频率为952Hz.多道磁探针信号测量发现,等离子体内部存在m/n=3/1的电磁模,该模的旋转频率为972Hz.从电子回旋辐射诊断系统得到的电子温度剖面发现该模的磁岛宽度约为2.5cm.     

应用高速CCD诊断研究HT-7装置边界等离子体旋转

在HT-7装置上建立了一套高速CCD可见光成像诊断,测量了边界等离子体的可见光辐射成像。在HT-7装置放电中,首次观察到在等离子体边界区域存在一条极向旋转的可见光辐射带,由CCD诊断系统得到其极向旋转的频率为858Hz。根据多道H_α阵列测量得到极向旋转频率为952Hz。多道磁探针信号测量发现,等离子体内部存在m/n=3/1的电磁模,该模的旋转频率为972Hz。从电子回旋辐射诊断系统得到的电子温度剖面发现该模的磁岛宽度约为2.5cm。     

EAST装置放电预测的初步研究

用托卡马克模拟程序对实验前期的放电进行了模拟,获得了期望的等离子体演化过程及主要参数波形,如极向场线圈电流、等离子体电流、等离子体位置等。通过等离子体控制系统将模拟获取的参数波形用于实验,开展了等离子体R位置控制、完全程序场控制及RZIp控制下的放电模拟对实验的预测研究。模拟结果与实验吻合较好,表明放电模拟具有一定的可预测性,为今后EAST装置开展更深入的物理实验提供了一定的参考。     

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用托卡马克模拟程序对实验前期的放电进行了模拟,获得了期望的等离子体演化过程及主要参数波形,如极向场线圈电流、等离子体电流、等离子体位置等。通过等离子体控制系统将模拟获取的参数波形用于实验,开展了等离子体R位置控制、完全程序场控制及RZIp控制下的放电模拟对实验的预测研究。模拟结果与实验吻合较好,表明放电模拟具有一定的可预测性,为今后EAST装置开展更深入的物理实验提供了一定的参考。     

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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。     

托卡马克极向场线圈的优化方法

托卡马克等离子体的三角形变和拉长比对约束和磁流体稳定性有很强的影响，因此在托卡马克装置极向场设计中，在基于物理和工程考虑所预先选定的等离子体平衡位形几何参数下，如何优化确定外部极向场线圈位置和电流，是一个具有重要实际意义的研究课题.为优化确定托卡马克极向场线圈，给出了一个有效的多变量平衡优化方法，能以事先规定的等离子体平衡位形的一些几何参数为目标函数，优化确定极向场线圈位置和电流.并应用它于HT-7U平衡位形计算，得到了所需的结果. 关键词： 等离子体平衡 极向场线圈 优化     

HL-1装置的物理调试(1985)

自1985年4月起正式开展HL-1装置的物理调试,其目的是获得平衡、稳定和比较干净的等离子体,并在此基础上开展初步的物理实验研究。在纵向磁场2.3T下获得等离子体电流135kA,平顶时间150-200ms。等离子体电流的持续时间出乎意料地长达1s,其详细的物理原因尚待深入研究。其它等离子体参数的初步结果为n_e≈ 2.8×10~(13)cm~(-3),T_e≈350-500eV,τ_E≈10ms。     

Pioneering experiments on atomic-beam-assisted generation of drag currents in the Globus-M spherical tokamak

Research data for drag currents in the Globus-M spherical tokamak are presented. The currents are generated by injecting atomic beams of hydrogen and deuterium. Experiments were carried out in the hydrogen and deuterium plasma of the tokamak. It has a divertor configuration with a lower X-point, a displacement along the larger radius from–1.0 to–2.5 cm, and a toroidal field of 0.4 T at a plasma current of 0.17–0.23 MA. The beam is injected into the tokamak in the equatorial plane tangentially to the magnetic axis of the plasma filament with an impact diameter of 32 cm. To provide a 28-keV 0.5-MW atomic beam with geometrical sizes of 4 × 20 cm (at a power level of 1/e), an IPM-2 ion source is used. The generation of noninductive currents is detected from a rise in the loop current and a simultaneous dip of the loop voltage. The injection of the hydrogen and deuterium atomic beams into the deuterium plasma results in a noticeable and reproducible dip of the loop voltage (up to 0.5 V). Using the ASTRA transport code, a model is constructed that allows rapid calculation of noninductive currents. Calculations performed for a specific discharge confirm that the model adequately describes the effect of drag current generation.     

Eddy current effects on plasma equilibrium in a single-turn tokamak

In a fusion experiment based on the single-turn tokamak concept, the plasma is surrounded by a massive conducting structure composed of several layers of material with different resistivities. This conducting shell is located near the plasma edge and is magnetically coupled to the plasma column. The plasma magnetohydrodynamic (MHD) equilibrium is studied by neglecting the effect of structural induced currents. Eddy current effects are then analyzed. Poloidal uniformization of the poloidal field magnet current distribution required for plasma equilibrium is demonstrated. The possibility of continuous-limiter discharges in a single-turn tokamak configuration is pointed out. The significance of these results for the operation of a high-current tokamak experiment is discussed     

Determination of Plasma Position Using Poloidal Flux Loops and Comparison With Magnetic Probe Measurement in IR-T1 Tokamak

In this paper, we present two magnetic techniques for the measurement of plasma position in IR-T1 tokamak: a poloidal flux loop and a magnetic probe method. In the first method, two flux loops were designed and installed toroidally on the outer surface of the IR-T1 tokamak, and then, displacement of the plasma column was measured from them. In addition, to compare the plasma position obtained using the flux loops, an array of four magnetic probes was designed, constructed, and installed on the outer surface of the IR-T1 tokamak, and plasma position was measured from them. Results were compared and found to be in good agreement with each other.      

HT－7托卡马克中等离子体平衡研究

本文解决了二维轴对称近似下带铁芯的托卡马克中等离子体平衡问题，计算了ＨＴ－７托卡马克中的等离子体平衡位形以及极向场系统的非线性电感和垂直场系数。最后应用Ｋｉｒｃｈｈｏｆｆ方程组和平衡垂直场公式得到了一组等离子体、加热场和垂直场线圈的电流波形的自洽曲线。     

Start-up phase plasma discharge design of a tokamak via control parameterization method

The tokamak start-up is a very important phase during the process to obtain a suitable equalizing plasma, and its governing model can be described as a set of nonlinear ordinary differential equations(ODEs). In this paper, we first estimate the parameters in the original model and set up an accurate model to express how the variables change during the start-up phase, especially how the plasma current changes with respect to time and the loop voltage. Then, we apply the control parameterization method to obtain an approximate optimal parameters selection problem for the loop voltage design to achieve a desired plasma current target. Computational optimal control techniques such as the variational method and the costate method are employed to solve the problem, respectively. Finally, numerical simulations are performed and the results obtained via different methods are compared. Our numerical parameterization method and optimization procedure turn out to be effective.     

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。     

J-TEXT装置纵场电源系统及其调试

J-TEXT装置的纵场磁体是由十六个近似圆形的常规铜线圈串联而成。纵场电源系统需要为纵场磁体提供最大电流为160kA、平顶时间为500ms的准梯形电流波形,以在等离子体中心产生最大为3T的磁场。基于原TEXT-U纵场电源的电路结构,重新设计和改造了电源的控制系统和保护系统。目前,纵场电源系统已经通过了测试,在J-TEXT装置首轮放电运行中,该系统可输出92.5kA的平顶电流,在等离子体中心产生了约1.74T的磁场。