Unified Description of Tokamak Ideal MHD Instabilities(Ⅰ)

By using a coordinate system associated with magnetic surfaces, a unified eigen-mode equation for describing the tokamak ideal MHD instabilities is derived in the shear-Alfven approximation. Based on this equation having a general operator form, the eigen-mode equation governing the large-scale perturbation (such as the kink mode, the low-n ballooning mode and the Alfven mode) and small-scale perturbation (such as the high-n ballooning mode, the local mode) can be further deduced. In the first part of the present study, the small-scale perturbation is discussed in detail.

The Singular Value Decomposition as a Tool of Investigating Central MHD Instabilities in the HL-1M Tokamak

A variety of strong MHD instabilities are always resulted from MHD activity of Tokamak plasmas. Central MHD instabilities can be observed with pinhole cameras to record soft x-ray (SXR) emission from the plasma along many chords with a high temporal resolution. The investigation of MHD instabilities often necessitates an analysis on spatial-temporal signals. The method of Singular Value Decomposition (SVD) can split such signals into orthogonal spatial and temporal vectors. By this means, the repetition time and the characteristic radius of various MHD phenomena such as sawteeth and snake-like perturbation can be obtained. Moreover, the (1,1) MHD mode is analyzed in great detail by SVD and used to determine the radius of the q = 1 surface.

The Effect of Equilibrium Current Profiles on MHD Instabilities in Tokamaks

A cylindrical model of linear MHD instabilities in tokamaks is presented. In the model, the cylindrical plasma is surrounded by a vacuum which is divided into inner and outer vacuum areas by a conducting wall. Linearized resistivity MHD equations with plasma viscosity are adopted to describe our model, and the equations are solved numerically as an initial value problem. Some of the results are used as benchmark tests for the code, and then a series of equilibrium current profiles are used to simulate the bootstrap current profiles in actual experiments with a bump on tail. Thus the effects of these kinds of profiles on MHD instabilities in tokamaks are revealed. From the analysis of the numerical results, it is found that more plasma can be confined when the center of the current bump is closer to the plasma surface, and a higher and narrower current bump has a better stabilizing effect on the MHD instabilities.

Observation of MHD Instabilities Driven by Energetic Electrons in the Large Helical Device

Coherent magnetic fluctuations in an acoustic range of frequency have been regularly observed in low-density（n_e〈0.2×10^（19）m^（-3））plasmas with strong second harmonic electron cyclotron resonance heating（ECRH）on the Large Helical Device.Hard X-ray measurements indicated that energetic electrons are generated in these ECRH discharges.The magnetic fluctuations are suppressed in higher density discharges where energetic electrons are not present.The ECRH power modulation experiment indicated that the observed magnetohydrodynamic（MHD）mode has an acoustic nature rather than an Alfvenic nature.

Experimental study of core MHD behavior and a novel algorithm for rational surface detection based on profile reflectometry in EAST

Microwave reflectometry is a powerful diagnostic that can measure the density profile and localized turbulence with high spatial and temporal resolution and will be used in ITER,so understanding the influence of plasma perturbations on the reflect signal is important.The characteristics of the reflect signal from profile reflectometry,the time-of-flight(TOF)signal associated with the MHD instabilities,are investigated in EAST.Using a 1D full-wave simulation code by the Finite-DifferenceTime-Domain(FDTD)method,it is well validated that the local density flattening could induce the discontinuity of the simulated TOF signal and an obvious change of reflect amplitude.Experimental TOF signals under different types of MHD instabilities(sawtooth,sawtooth precursors and tearing mode)are studied in detail and show agreement with the simulation.Two new improved algorithms for detecting and localizing the radial positions of the low-order rational surface,the cross-correlation and gradient threshold(CGT)method and the 2D convolutional neural network approach(CNN)are presented for the first time.It is concluded that TOF signal analysis from profile reflectometry can provide a straightforward and localized measurement of the plasma perturbation from the edge to the core simultaneously and may be a complement or correction to the q-profile control,which will be beneficial for the advanced tokamak operation.

衬套内爆ALE方法二维MHD数值模拟

作者在详细介绍了衬套内爆二维磁流体(MHD)力学模拟的ALE方法的基础上,运用算子分裂技术将MHD力学方程组分裂成热扩散、磁扩散、Lagrangian流动、网格生成和对流输运4步求解.作者对Frese等人的Lagrangian流动步方法进行了改进,消除了其拉氏计算的质量损失.编制了二维计算程序并通过验证,获得的二维衬套内爆不稳定性发展与Doughlas和Liberman等人的结果相吻合.

涂层裂纹引起的MHD效应不稳定性实验模拟

介绍了用铜电极和铜导线模拟管道内电绝缘涂层裂纹 ,引起磁流体动力学 (MHD)效应的最新实验结果。结果表明 :绝缘涂层的裂纹不仅使MHD压降大大提高 ,而且产生MHD效应的不稳定性。边界电位差U和MHD压降ΔP产生跃变 ,偏离了经典规律 ,跃变的幅度达 10 0 % ;且在实验参数不变的情况下 ,边界电位差U和MHD压降ΔP随时间在振荡。

HL-1M装置上MHD不稳定性磁扰动的探测和分析

给出了HL 1M装置上的Mirnov磁探针系统的布置及MHD不稳定性磁扰动模式的探测方法,探讨了实验中存在的MHD不稳定性现象。用空间傅立叶变换分析了HL 1M装置上的磁扰动模式,给出了在存在不同极向扰动模式放电条件下的各磁探针信号之间的相位比对关系结果,从而确认实验中所使用的方法的正确性和实用性。

LHCD期间HL-1M装置等离子体中心区域的MHD行为

本文叙述低杂波电流驱动（ＬＨＣＤ）对ＨＬ－１Ｍ等离子体中心ＭＨＤ不稳定性［锯齿振荡（ｍ＝０），ｍ＝１模］的影响。不稳定性的振荡幅度是进入等离子体的低杂波功率的函数。当功率超过某阈值时，不稳定性被抑制，而且存在一个最佳抑制功率范围。在一定条件下，低杂波功率脉冲会激发ＭＨＤ不稳定性。

用GATO代码模拟HL-2A装置实验的MHD稳定性

将理想全二维磁流体(MHD)稳定性数值代码GATO成功移植到HL-2A高性能计算系统,并用其模拟研究了HL-2A装置一次典型弹丸注入实验的等离子体的理想MHD稳定性。利用HL-2A装置第4050次放电的实验数据,应用EFIT代码重建了几个时间片的平衡位形,然后应用GATO代码对每个平衡位形的MHD稳定性进行了计算。通过对结果进行分析比较得出初步结论,由于弹丸注入而造成的反剪切位形的致稳作用,可以提高等离子体的约束性能。

NONLINEAR MHD KELVIN-HELMHOLTZ INSTABILITY IN A PIPE

Nonlinear MHD Kelvin-Helmholtz(K-H)instability in a pipe is treated with the deriva- tive expansion method in the present paper The linear stability problem was discussed in the past by Chandrasekhar(1961)and Xu et al.(1981).Nagano(1979)discussed the nonlinear MHD K-H instability with infinite depth.He used the singular perturbation method and extrapolated the ob- tained second order modifier of amplitude vs.frequency to seek the nonlinear effect on the instability growth rate γ.However,in our view,such an extrapolation is inappropriate.Because when the instabili- ty sets in,the growth rates of higher,order terms on the right hand side of equations will exceed the cor- responding secular producing terms,so the expansion will still become meaningless even if the secular producing terms are eliminated.Mathematically speaking,it's impossible to derive formula(39) when γ_0~2 is negative in Nagano's paper.Moreover,even as early as γ_0~2→O^+,the expansion be- comes invalid because the 2nd order modifier γ_2(in his formula(56))tends to infinity.This weak- ness is removed in this paper,and the result is extended to the case of a pipe with finite depth.

高速CCD诊断MHD不稳定性的初步研究

电荷耦合器件(CCD)作为一种高灵敏度的二维辐射测量传感器,具有使用方便,测量结果可视性好等特点,近年来在托卡马克等离子体研究中得到广泛的应用.在HT-7和EAST托卡马克装置上建立了高速CCD成像诊断系统,并利用其进行磁流体力学(MHD)不稳定性研究.利用高速CCD成功观测到HT-7托卡马克上的锯齿振荡不稳定性和Mirnov振荡行为,以及EAST托卡马克H-mode过程中的边界局域模(ELM)行为,为进一步利用高速CCD诊断技术开展MHD不稳性时空过程的研究奠定了基础.

Kinetic micro-instabilities in the presence of impurities in toroidal magnetized plasmas

The theoretical and numerical studies on kinetic micro-instabilities,including ion temperature gradient（ITG） driven modes,trapped electron modes（TEMs） in the presence of impurity ions as well as impurity modes（IMs）,induced by impurity density gradient alone,in toroidal magnetized plasmas,such as tokamak and reversed-field pinch（RFP） are reviewed briefly.The basic theory for IMs,the electrostatic instabilities in tokamak and RFP plasmas are discussed.The observations of hybrid and coexistence of the instabilities are categorized systematically.The effects of impurity ions on electromagnetic instabilities such as ITG modes,the kinetic ballooning modes（KBMs） and kinetic shear Alfvén modes induced by impurity ions in tokamak plasmas of finite β（=plasma pressure/magnetic pressure） are analyzed.The interesting topics for future investigation are suggested.

Preliminary investigation on electrothermal instabilities in early phases of cylindrical foil implosions on primary test stand facility

Recent experiments on the implosions of 15-mm long and 2-μm thick aluminum liners having a diameter of 12.8 mm have been performed on the primary test stand(PTS) facility. The stratified structures are observed as alternating dark and light transverse stripes in the laser shadowgraph images. These striations perpendicular to the current flow are formed early in the implosion, i.e., at the stage when the bulk of the material mass was almost at rest. A two-dimensional(2 D)magnetohydrodynamics(MHD) code is employed to simulate the behavior of liner dynamics in the early phases. It is found that the striations may be produced by the electrothermal instability(ETI) that results from non-uniform Joule heating due to the characteristic relation between the resistivity and the temperature. In 2 D simulations, the stratified structures can be seen obviously in both density and temperature contours as the liner expands rapidly. By analyzing instability spectrum, the dominant wavelengths of the perturbations are 8.33 μm–20.0 μm, which agree qualitatively with the theoretical predictions.It is also interesting to show that ETI provides a significant seed to the subsequent magneto Rayleigh–Taylor(MRT)instability.

Numerical study on magneto-Rayleigh–Taylor instabilities for thin liner implosions on the primary test stand facility

The thin aluminum liners with an aspect ratio R/?r 1 have been imploded on the primary test stand(PTS) facility,where R is the outer radius of the liner and ?r is the thickness. The x-ray self-emission images present azimuthally correlated perturbations in the liner implosions. The experiments show that at-10 ns before the stagnation, the wavelengths of perturbation are about 0.93 mm and 1.67 mm for the small-radius and large-radius liners, respectively. We have utilized the resistive magnetohydrodynamic code PLUTO to study the development of magneto-Rayleigh–Taylor(MRT) instabilities under experimental conditions. The calculated perturbation amplitudes are consistent with the experimental observations very well. We have found that both mode coupling and long implosion distance are responsible for the more developed instabilities in the large-radius liner implosions.

Preliminary Study of Ideal Operational MHD Beta Limit in HL-2A Tokamak Plasmas

Magnetohydrodynamic （MHD） n=1 kink mode with n the toroidal mode number is studied and the operational beta limit, constrained by the mode, is calculated for the equilibrium of HL-2A by using the GATO code. Approximately the same beta limit is obtained for configurations with a value of the axial safety factor q0 both larger and less than 1. Without the stabilization of the conducting wall, the beta limit is found to be 0.821% corresponding to a normalized beta value of βN^c=2.56 for a typical HL-2A discharge with a plasma current Ip=0.245 MA, and the scaling of βN^c -constant is confirmed.

Alfvén Instabilities Excited by Energetic Particles in a Parameter Regime Similar to EAST Operation

The kinetic excitation of ideal magnetohydrodynamic （MHD） Alfvén instabilities is investigated for operations at the EAST tokamak. The instabilities include α-induced toroidal Alfvén eigenmodes （αTAE; here, α =-q2 Rdβ/dr, with q being the safety factor, β the ratio between the plasma and magnetic pressures, R the major radius, and r the minor radius）, toroidicity-induced Alfvén eigenmodes （TAE）, and the energetic particle continuum mode （EPM）. The αTAE, trapped by α-induced potential wells along the magnetic field line, can be readily destabilized by energetic particles due to negligible continuum damping via wave energy tunneling. It is shown for the geometry and the parameters similar to those of the EAST equilibrium that αTAE is different not only from the EPM by the potential-well determined frequency, but also from the TAE by the broad frequency spectrum outside the toroidal frequency gap.

General Description of Ideal Tokamak MHD Instability Ⅱ

In this subsequent study on general description of ideal tokamak MHD instability, the part II, by using a coordinate with rectified magnetic field lines, the eigenmode equations describing the low-mode-number toroidal Alfven modes (TAE and EAE) are derived through a further expansion of the shear Alfven equation of motion.

SUNIST球形托卡马克MHD不稳定性的探讨

托卡马克已经逐步成为磁约束聚变研究的主流,本文介绍了中国联合球形托卡马克SUNIST上的磁流体力学(MHD)不稳定性的测量和分析,提出了控制不稳定性的设想。

HL-3装置欧姆等离子体中高频磁流体不稳定性的实验观测

在HL-3装置1MA电流等离子体欧姆放电实验期间,米尔诺夫(Mirnov)探针测量到两种高频磁流体(MHD)不稳定性。在等离子体启动阶段,电流爬升受到抑制,碘化钠探测器测量到逃逸电子增加。同时Mirnov探针测量到多分支频率f为20~400k Hz的高频MHD不稳定性。结果表明,这种不稳定性的出现与逃逸电子增加密切相关,并抑制了等离子体电流的爬升,损失了大约7%伏秒数。等离子体电流和密度爬升时,Mirnov探针测量到频率f为110~160k Hz的高频MHD不稳定性。这种不稳定性频率与芯部阿尔芬频率成正比,处于环向阿尔芬本征模频率范围。随着这种不稳定性的演化,等离子体发生了破裂。这些高频MHD不稳定性的研究对于HL-3后续放电及未来ITER的初始放电有重要的参考意义。