Effects of resonant magnetic perturbation on the instability of single tearing mode with non-shear flow

Non-shear flow can change the O-point position of a magnetic island, and thus it may play an important role in the effects of resonant magnetic perturbation(RMP) on the single tearing mode. We employ the nonlinear magnetohydrodynamics model in a slab geometry to investigate how RMP affects the single tearing mode instability with non-shear flow. It is found that the driving and suppressing effects of RMP on single tearing mode instability will appear alternately. When the flow velocity is small, the suppressing effect plays a major role through the development of the mode, and the tearing mode instability will be suppressed. With the flow velocity increasing, the driving effect will increase, while the suppressing effect will decrease. When the two effects reach equilibrium, the tearing mode will become stable.

Magnetic diagnostics for magnetohydrodynamic instability research and the detection of locked modes in J-TEXT

Magnetohydrodynamic(MHD)instabilities are widely observed during tokamak plasma operation.Magnetic diagnostics provide important information which supports the understanding and control of MHD instabilities.This paper presents the current status of the magnetic diagnostics dedicated to measuring MHD instabilities at the J-TEXT tokamak;the diagnostics consist of five Mirnov probe arrays for measuring high-frequency magnetic perturbations and two saddle-loop arrays for low-frequency magnetic perturbations,such as the locked mode.In recent years,several changes have been made to these arrays.The structure of the probes in the poloidal Mirnov arrays has been optimized to improve their mechanical strength,and the number of in-vessel saddle loops has also been improved to support better spatial resolution.Due to the installation of high-field-side(HFS)divertor targets in early 2019,some of the probes were removed,but an HFS Mirnov array was designed and installed behind the targets.Owing to its excellent toroidal symmetry,the HFS Mirnov array has,for the first time at J-TEXT,provided valuable new information about the locked mode and the quasi-static mode(QSM)in the HFS.Besides,various groups of magnetic diagnostics at different poloidal locations have been systematically used to measure the QSM,which confirmed the poloidal mode number m and the helical structure of the QSM.By including the HFS information,the 2/1 resonant magnetic perturbation(RMP)-induced locked mode was measured to have a poloidal mode number m of~2.

Application of Galerkin spectral method for tearing mode instability

Magnetic reconnection and tearing mode instability play a critical role in many physical processes.The application of Galerkin spectral method for tearing mode instability in two-dimensional geometry is investigated in this paper.A resistive magnetohydrodynamic code is developed,by the Galerkin spectral method both in the periodic and aperiodic directions.Spectral schemes are provided for global modes and local modes.Mode structures,resistivity scaling,convergence and stability of tearing modes are discussed.The effectiveness of the code is demonstrated,and the computational results are compared with the results using Galerkin spectral method only in the periodic direction.The numerical results show that the code using Galerkin spectral method individually allows larger time step in global and local modes simulations,and has better convergence in global modes simulations.

Neoclassical tearing mode stabilization by electron cyclotron current drive for HL-2M tokamak

Investigation of neoclassical tearing mode and its suppression by electron cyclotron current drive(ECCD)has been carried out in HL-2 M tokamak.The current driving capability of the electron cyclotron wave is evaluated.It is found that the deposition location can be effectively controlled by changing the poloidal angle.The validation of electron cyclotron wave heating and current driving has been demonstrated for the upper launcher port.We show that 3.0 MW and2.5 MW modulated ECCD can completely stabilize(2,1)and(3,2)NTMs,respectively.The non-modulated ECCD,radial misalignment as well as current profile broadening have deleterious effect on the NTM stabilization.The time required for suppression of(3,2)mode is shorter than that required for the suppression of(2,1)mode.Moreover,the time needed for complete stabilization at different initial island width has been quantitatively presented and analyzed.

Identification of the magnetic island structure in the HL-2A tokamak

The identification of the magnetic island structure in the HL-2A tokamak is presented. First, the perturbation current as a source for the perturbation flux can be determined by using Mirnov probe measurements. By superposing the perturbation flux and the equilibrium flux reconnected by equilibrium fitting, the structure and the width of the magnetic islands can be estimated. The method has been used in the HL-2A experiments.

Basic features of the multiscale interaction between tearing modes and slab ion-temperature-gradient modes

Nonlinear interaction between tearing modes(TM) and slab ion-temperature-gradient(ITG) modes is numerically investigated by using a Landau fluid model. It is observed that the energy spectra with respect to wavenumbers become broader during the transition phase from the ITG-dominated stage to TM-dominated stage. Accompanied with the fast growth of the magnetic island, the frequency of TM/ITG with long/short wavelength fluctuations in the electron/ion diamagnetic direction decreases/increases respectively. The decrease of TM frequency is identified to result from the effect of the profile flattening in the vicinity of the magnetic island, while the increase of the frequencies of ITG fluctuations is due to the eigenmode transition of ITG induced by the large scale zonal flow and zonal current related to TM. Roles of zonal current induced by the ITG fluctuations in the instability of TM are also analyzed. Finally, the electromagnetic transport features in the vicinity of the magnetic island are discussed.

Stabilization of tearing mode by current drive

The major disruption limits the operation of present tokamaks. Experimental evidences point out that the growth of tearing modes or the magnetic islands is primarily responsible for the occurrence. Taking the non-inductive current drive effects into account, a set of 3D nonlinear equation is derived. It is shown from simulation that the growth of the magnetic island is suppressed effectively by RF current drive. It is consistent with recent experiments on the HL-1 tokamak in which the plasma is stabilized by an RF current drive.

Stability impacts from the current and pressure profile modifications within finite sized island

The stability(or instability)of finite sized magnetic island could play a significant role in disruption avoidance or disruption mitigation dynamics.Especially,various current and pressure profile modifications,such as the current drive and heating caused by electron cyclotron wave,or the radiative cooling and current expulsion caused by the shattered pellet injection could be applied within the island to modify its stability,thus changing the ensuing dynamics.In this study,we calculate the mode structure modification caused by such profile changes within the island using the perturbed equilibrium approach,thus obtain the change of stability criterion Δ′ and assess the corresponding quasi-linear island stability.The positive helical current perturbation is found to always stabilize the island,while the negative one is found to do the opposite,in agreement with previous results.The pressure bump or hole within the island has a more complicated stability impact.In the small island regime,its contribution is monotonic,with pressure bump that tends to stabilize the island while pressure hole destabilizes it.This effect is relatively weak,though,due to the cancellation of the pressure term’s odd parity contribution in the second derivatives of the mode structure.In the large island regime,such cancellation is broken due to the island asymmetry,and the pressure contribution to stability is manifested,which is non-monotonic.The stability analysis in this paper helps to more accurately clarify the expected island response in the presence of profile modifications caused by disruption avoidance or mitigation systems.

Modeling of the influences of multiple modulated electron cyclotron current drive on NTMs in rotating plasma

In this work, physical models of neoclassical tearing modes （NTMs） including bootstrap current and multiple modulated electron cyclotron current drive model are applied. Based on the specific physical problems during the suppression of NTMs by driven current, this work compares the efficiency of continuous and modulated driven currents, and simulates the physical processes of multiple modulated driven currents on suppressing rotating magnetic island. It is found that when island rotates along the poloidal direction, the suppression ability of continuous driven current can be massively reduced due to current deposition outside the island separatrix and reverse deposition direction at the X point, which can be avoided by current drive modulation. Multiple current drive has a better suppressing effect than single current drive. This work gives realistic numerical simulations by optimizing the model and parameters based on the experiments, which could provide references for successful suppression of NTMs in future advanced tokamak such as international thermonuclear experimental reactor.

Identification and Analysis of Magnetic Structures on HL-2A

A method for the identification and analysis of magnetic islands is presented based on the calculation of the perturbative current and magnetic field in plasmas. A cylindrical approximation is adopted and the toroidal effect on plasma equilibrium is also included. This method has been used on the HL-2A tokamak for analysing the magnetic island structures.

涡旋诱发重联模型(Ⅰ)——动力学特性

本文首先从理论上系统地研究了涡旋诱发重联的基本动力学特性.包括:涡旋诱发重联的物理机制;Kelvin—Helmholtz(K-H)不稳定性和撕裂模不稳定性耦合过程;磁流体涡管的基本特性;不同尺度涡旋间的相互作用,动能和磁能间的转化及准稳态时流线、磁力线、等涡度线和等电流密度线的相似性等.用二维MHD数值模拟方法研究了上述一些特性,并与理论分析结论进行了比较.结果表明,模拟结果证实了理论推论.涡旋诱发重联是产生局部磁场重联的重要机制之一,该模型在磁顶区的应用将另文发表.

反常输运与非线性自持磁岛的自洽分析

从沿磁力线的等离子体电流与粒子径向输运相关的新经典ＭＨＤ型的广义欧姆定律出发，提出了分析反常输运与非线性自持磁岛的自洽理论模型，基于该模型导出了反常扩散系数及反常电子热导。结果表明，非线性磁岛链可由磁岛调制的反常输运维持，反过来又通过磁岛短路效应维持反常输运。

单磁岛对热输运影响的数值计算

通过求解二维热输运方程,数值分析了横越单磁岛的热输运现象。仅有背景加热时,当磁岛宽度小于临界磁岛宽度时,磁岛对能量约束影响不明显;当磁岛宽度大于临界磁岛宽度时,磁岛降低的能量损失随着磁岛宽度呈线性增大,有效径向热导系数在磁岛区域呈高斯分布且最大值在有理面处。当等离子体背景加热与ECRH共同加热时,ECRH对磁岛区域的温度分布及能量约束均有别于背景热源,这为进一步研究ECRH抑制撕裂模的问题提供了基础。

电流驱动对磁岛的稳定化

大破裂限定了托卡马克的运行。实验指出，撕裂模或者说磁岛的发展是这种大破裂的主要原因。考虑到无感电流驱动效应，我们重新推导了电阻撕裂模的三维非线性方程组。数值计算表明，跟随磁岛旋转的ＲＦ波电流驱动有效地抑制了磁岛的发展。这与最近在ＨＬ－１托卡马克上电流驱动使等离子体实现稳定化的实验结果是一致的。

多层电流片中撕裂模不稳定性的数值研究

应用二维磁流体动力学模拟方法数值研究了三层电流片中电阻撕裂模不稳定性的特征及磁场重联过程．结果表明，这是一种复杂的非稳态磁场重联．在初期阶段，三个电流片中分别由撕裂模不稳定性引起磁场重联，形成薄而长的磁岛．随着撕裂模不稳定性的非线性发展，每个磁岛的宽度都逐步增大，以至导致新的磁场重联发生．同时，三个电流片的强度都逐渐减弱，且原中心反向电流区最终消失．部分磁能不断地转化为等离子体的热能和动能，引起等离子体的加热和加速．多层电流片中撕裂模不稳定性引起的自发重联，可能对太阳耀斑、日冕加热、太阳风与磁层耦合等有重要影响．

局部驱动螺旋电流对撕裂模不稳定性的影响

采用约化磁流体力学模拟方法,在托卡马克大环径比近似情况下,研究了局部驱动螺旋电流对撕裂模不稳定性的影响,分析了螺旋电流强度、螺旋电流径向沉积宽度以及螺旋电流加入时刻对m=2/n=1经典撕裂模发展过程的影响。研究结果表明:螺旋电流强度的增大和沉积宽度的变窄都会更有效地抑制经典撕裂模的发展,但过强的螺旋电流强度或较小的螺旋电流沉积宽度会引起翻转不稳定性;随着螺旋电流在经典撕裂模发展过程中加入时刻的推迟,其对撕裂模不稳定性的控制效果会越来越差。

射频波电流驱动抑制双撕裂模不稳定性研究

采用不可压缩磁流体模型,在圆柱位形下研究了射频波电流驱动对双撕裂模不稳定性的影响。结果表明,托卡马克装置中沉积在有理面上的同向驱动电流能有效减缓3/1双撕裂模的发展。电流驱动幅值约占等离子体电流初始值的4%、驱动电流沉积宽度约为小环半径的7%时,抑制效果较好。此外,研究表明,在双撕裂模进入快速增长阶段前加入外部驱动电流,才能有效抑制撕裂模的磁爆发。

小磁岛转动引起的沿磁力线电流对撕裂模的影响

利用离子香蕉轨道中心坐标和香蕉轨道平均算符,讨论了磁岛转动引起的沿磁力线电流分布及其对新经典撕裂模演进的影响。结果显示,考虑此电流的影响,当磁岛旋转频率ω=ω_(*i)时,被离子香蕉轨道宽度效应削弱的自举电流驱动项基本恢复;当ω=ω_(*e)时,离子香蕉轨道宽度效应对自举电流驱动项的削弱则加剧。这意味着磁岛转动方向不同时,此沿力线电流能显著增大或减弱离子香蕉轨道宽度效应对自举电流驱动项的削弱作用。

局部电流驱动对稳态撕裂模不稳定性的影响

采用二维可压缩磁流体模型,在平板位型下研究了外部局域电流驱动对稳态撕裂模的影响,详细研究了驱动电流的大小和其开始沉积时间对撕裂模不稳定性的影响。研究结果显示:外部驱动电流越大其对磁岛的抑制作用越大,但最后磁岛的饱和宽度也越宽,主要是因为当外部驱动电流沉积在磁岛X点时会使X点位置偏移,导致稳态撕裂模失稳;而且局部驱动电流对撕裂模的抑制作用跟撕裂模所处的状态也有关,外部驱动电流在磁岛增长率小于零的区间开始沉积对撕裂模抑制效果最佳。

射频波电流驱动对经典单撕裂模影响的数值研究

本文在平板位型下采用二维可压缩磁流体模型,研究了沉积在不同位置的外部局域驱动电流对稳态经典单撕裂模的影响和极向剪切流对驱动电流抑制磁岛作用的影响。研究发现外部驱动电流对撕裂模的抑制作用对其沉积位置很敏感,尤其是对于其沉积位置在径向的偏移。当存在极向剪切流时,外部驱动电流对撕裂模的抑制作用对极向剪切流的幅值有要求,在阈值范围内极向剪切流越大外部驱动电流对磁岛抑制效果越好,超阈值却相反。