Growth rate of peeling mode in the near separatrix region of diverted tokamak plasma

An analytical expression of the peeling mode in the near separatrix region of diverted tokamak plasma is derived. It is shown that in diverted plasmas both with single and double X points, though the perturbed potential energy of the unstable peeling mode tends to be large, its growth rate becomes very small due to the even larger kinetic energy. Compared to some recent studies that give qualitatively correct results about this growth rate, our result is directly related with the diverted equilibrium quantities suitable for application to realistic experiments.

Design of real-time feedback control of vertical growth rate on EAST

Real-time feedback control of vertical growth rate,called gamma control,has been successfully applied to experimental advanced superconducting tokamak(EAST).In this paper,a new gamma control method is proposed to regulate the vertical growth rate,which is an estimator of plasma vertical instability.Thus,the gamma controller can be utilized to keep the tokamak plasma away from its unstable boundary.In this work,the main development process includes three steps:(1)real-time implementation of model-based vertical growth rate calculation,taking advantage of GPU parallel computing capability,(2)design of plasma shape response for dynamic shape control using a slight modification to the plasma boundary,and(3)development of a gamma control algorithm integrated into the EAST plasma control system(PCS).The gamma control was experimentally verified in the EAST 2019 experiment campaign.It is shown that the time evolution of the real-time vertical growth rate agrees with the target value,indicating that the real-time vertical growth rate can be regulated by gamma control.

Tests of the real-time vertical growth rate calculation on EAST

In order to measure controllability of vertical instability in EAST,the calculation of model-based vertical growth rate,called rt-gamma,has been successfully carried out in real time.The numerical computing method is adapted from rigid plasma response model in TokSys,which is a widely-used analysis tool for tokamak devices in Matlab environment,but the code is rewritten by taking advantage of GPU parallel computing capability to accelerate the computation.The calculation of rt-gamma is validated by comparing it with the corresponding result generated by TokSys for totally 3508 cases.It is shown that the average absolute value of relative errors is about 0.85%.In addition,the calculation program of rt-gamma has been successfully applied during 2019 EAST campaign.The comparison with experimental results is discussed in this paper.The real-time calculation tool is well able to calculate model-based vertical growth rate,which is convenient for fast and continuous evaluations of EAST control system stability performances.

Vertical Instability in EAST: Comparison of Model Predictions with Experimental Results

Growth rates of the axisymmetric mode in elongated plasmas in the experimental advanced superconducting tokamak （EAST） are measured with zero feedback gains and then compared with numerically calculated growth rates for the reconstructed shapes. The comparison is made after loss of vertical position control. The open-loop growth rates were scanned with the number of vessel eigenmodes, which up to 20 is enough to make the growth rates settled. The agreement between the growth rates measured experimentally and the growth rates determined numerically is good. The results show that a linear RZIP model is essentially good enough for the vertical position feedback control.

Mode-Coupling Analysis of Parametric Decay Instability in Magnetized Plasmas

In this paper, derived from Maxwell and fluid equations of plasmas, unified nonlinear wave equations are used to describe the parametric decay instability （PDI） in magnetized plasmas, and in view of mode-coupling, we can obtain all the possible PDI channels. By solving the nonlinear equations with a mode-coupling method, we obtain the growth rate of the PDI, of which all of the three waves are ordinary mode （O-mode） or extraordinary mode （X-mode） wave. Under the dipole approximation, an explicit formula of the growth rate of the X-mode and the condition of the equilibrium density scale are obtained. According to the existence conditions of three X-mode waves, this kind of instability might exist in ECRH with the second harmonic X-mode wave.

The stability margin on EAST tokamak

The experimental advanced superconducting tokamak （EAST） is the first full superconducting tokamak with a D-shaped cross-sectional plasma presently in operation. Its poloidal coils are relatively far from the plasma due to the necessary thermal isolation from the superconducting magnets, which leads to relatively weaker coupling between plasma and poloidal field. This may cause more difficulties in controlling the vertical instability by using the poloidal coils. The measured growth rates of vertical stability are compared with theoretical calculations, based on a rigid plasma model. Poloidal beta and internal inductance are varied to investigate their effects on the stability margin by changing the values of parameters αn and γn（Howl et al 1992 Phys. Fluids B 4 1724）, with plasma shape fixed to be a configuration with k = 1.9 and 5 = 0.5. A number of ways of studying the stability margin are investigated. Among them, changing the values of parameters κ and li is shown to be the most effective way to increase the stability margin. Finally, a guideline of stability margin Ms（ki, li, A） to a new discharge scenario showing whether plasmas can be stabilized is also presented in this paper.

EAST装置垂直不稳定性研究

对EAST装置偏滤器位形的放电中发生的垂直位移不稳定性的全过程进行了模拟,计算了磁轴垂直位移及垂直位移不稳定性的增长率。模拟的结果与实验结果符合得较好。

线偏振激光在磁化等离子体中的调制不稳定性

采用洛伦兹变换推导了线性偏振激光在磁化等离子体中的非线性色散关系,根据Karpman方法推导出横波的非线性控制方程,利用线性偏振激光在磁化等离子体中的非线性色散关系和非线性控制性方程,分析了在磁化等离子体中有限振幅的扰动引起的调制不稳定性,得到了线性偏振激光的调制不稳定的时间增长率与扰动波数之间的函数关系。分析结果表明:激光等离子体的临界面附近的磁调制不稳定性的时间增长率显著增大。

HL-2M等离子体垂直不稳定性研究

用DⅢ-D的TokSys研究了HL-2M等离子体垂直不稳定性控制问题。使用真空室和主动线圈控制等离子体垂直不稳定性,分析了真空室的本征模和电流分布,极大简化真空室建模难度,建立了垂直不稳定性数学模型,验证了主动线圈和电源模型参数,计算了不同拉长比位形的等离子体增长率和最大可控垂直位移。利用TokSys建立了雪花、单零、双零偏滤器位形垂直不稳定仿真模型,然后通过simulink对采用PD算法的垂直不稳定系统进行仿真。结果表明,构建的模型能够较好控制不同位形的垂直不稳定性。

非磁化等离子体和磁化等离子体的电磁辐射特性研究

本文研究非磁化和磁化双MAXWELL分布等离子体的电磁不稳定性色散方程和电磁辐射增长率.结果表明,非磁化等离子体不能辐射出电磁波,而磁化等离子体能够辐射出电磁波.并分析讨论了磁化等离子体在不同参数下的电磁辐射增长率随辐射频率、等离子体密度和温度的变化.

用正问题代码求逆问题的尝试

本文介绍了一种用正问题代码通过某种逆过程来求解逆问题的数值方法。我们使用这种方法在平衡代码SWEQU的基础上开发了一个名为SWSTAB的计算非圆截面托卡马克等离子体竖直不稳定性的程序。利用该程序我们计算了成型线圈条件下,上下不对称等离子体的竖直不稳定性,研究了等离子体形状因子(椭圆半轴比,三角形变)及等离子体与成型线圈之间距离对稳定性的影响,方便地得到了用其它方法不易得到的物理结果。