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.

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.

Sawtooth Activity in Ohmically Heated Plasma on HT-7 Tokamak

Sawtooth activity on HT-7 tokamak has been investigated experimentally mainly by using soft x-ray diode array and magnetic probes. Their behaviors and occurrences are correlated closely to the discharge conditions: the electron density Ne, the electron temperature Te, the safety factor qa on plasma boundary and wall condition etc. When central line-averaged electron density Ne(0) is over 2.0×1013cm-3 , major sawtooth activity emerges with a period of up to 6.5 ms and a fluctuation amplitude of up to 2-30 % of SXR radiation signal. In some cases such as the safety factor between 4.2-4.7 and Zeff=3.0-6.0, a monster sawtooth activity often emerges without apparent deterioration of plasma confinement and without major disruption. During these events, abundant MHD phenomena are observed including partial sawtooth oscillations. In this paper, the observed sawtooth behaviors and their dependence on the and their dependence density Ne and wall condition in ohmically heated plasma are introduced, the results are discussed and presented.

A general comparison between tokamak and stellarator plasmas

This paper generally compares the essential features between tokamaks and stellarators,based on previous review work individually made by authors on several specific topics,such as theories,bulk plasma transport and edge divertor physics,along with some recent results.It aims at summarizing the main results and conclusions with regard to the advantages and disadvantages in these two types of magnetic fusion devices.The comparison includes basic magnetic configurations,magnetohydrodynamic(MHD)instabilities,operational limits and disruptions,neoclassical and turbulent transport,confinement scaling and isotopic effects,plasma rotation,and edge and divertor physics.Finally,a concept of quasi-symmetric stellarators is briefly referred along with a comparison of future application for fusion reactors.

Effect of the Plasma Pressure on Magnetohydrodynamic Kink Instability in a Cylindrical Geometry

A semi-analytical method is introduced to study kink instability in cylindrical plasma with line-tied boundary conditions. The method is based on an expansion for magnetohydrodynamics （MHD） equations in one-dimensional （1D） radial eigenvalue problems by using Fourier transforms. The MHD equations then become an ordinary differential equation. This method is applicable to both ideal and non-ideal MHD problem. The effect of plasma pressure （P0） on kink instability is studied in a cylindrical geometry. Complex discrete spectra are pre- sented. Two-dimensional （2D） eigenfunctions with the line-tied boundary conditions are obtained. The growth rate and radial eigenfunctions are different in the two cases of P0 = 0 and P0 ≠ 0, which indicate that the effect of plasma pressure can not be ignored if it is large enough. This method allows us to understand the role of individual radial eigenfunctions, and is also computationally efficient compared to direct solutions of the MHD equations by the finite difference method.

Three-Dimensional Simulation of Plasma Deformation During Contact Opening in a Circuit Breaker,Including the Analysis of Kink Instability and Sausage Instability

A three-dimensional （3-D） transient model has been developed to investigate plasma deformation driven by a magnetic field and its influence on arc stability in a circuit breaker. The 3-D distribution of electric current density is obtained from a current continuity equation along with the generalized Ohm＇s law; while the magnetic field induced by the current flowing through the arc column is calculated by the magnetic vector potential equation. When gas interacts with an arc column, fundamental factors, such as Ampere＇s law, Ohm＇s law, the turbulence model, transport equations of mass, momentum and energy of plasma flow, have to be coupled for aria- lyzing the phenomenon. The coupled interactions between arc and plasma flow are described in the fl＇amework of time-dependent magnetohydrodynamic （MHD） equations in conjunction with a K-~ turbulence model. Simulations have been focused on sausage and kink instabilities in plasma （these phenomena are related tO pinch effects and electromagnetic fields）. The 3-D sjm- ulation reveals the relation between plasma deformation and instability phenomena, which affect arc stability during circuit breaker operation. Plasma deformation is the consequence of coupled interactions between the electromagnetic force and plasma flow described in simulations.

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 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.

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.

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。

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.

HL-1M装置上MHD不稳定性磁扰动模的传播

对在HL 1M装置放电实验中发现的宏观MHD不稳定性磁扰动模的传播现象进行了研究。通过对实验中发现的各种极向模数m值的MHD磁扰动模特征的观察,以及在不同放电条件,特别是在偏压H模放电下传播方向不同的分析,深入研究了MHD模传播与等离子体旋转的定性关系。

Analysis of the instability growth rate during the jet-background interaction in a magnetic field

The two-stream instability is common, responsible for many observed phe- nomena in nature, especially the interaction of jets of various origins with the back- ground plasma （e.g. extragalactic jet interacting with the cosmic background）. The dispersion relation that does not consider magnetic fields is described by the well- known Buneman relation. In 2011, Bohata, Bren and Kulhanek derived the relation for the two-stream instability without the cold limit, with the general orientation of a magnetic field, and arbitrary stream directions. The maximum value of the imaginary part of the individual dispersion branches ωn（k） is of interest from a physical point of view. It represents the instability growth rate which is responsible for the onset of turbulence mode and subsequent reconnection on the scale of the ion radius accom- panied by a strong plasma thermalization. The paper presented here is focused on the non-relativistic instability growth rate and its dependence on various input parameters, such as magnitude and direction of magnetic field, sound velocity, plasma frequency of the jet and direction of the wave vector during the jet - intergalactic medium in- teraction. The results are presented in plots and can be used for determination of the plasma parameter values close to which the strong energy transfer and thermalization between the jet and the background plasma occur.

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.

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。

等离子体压强对Line-tied扭曲不稳定性增长率和本征函数的影响

应用半解析方法,研究了直圆柱位形下等离子体压强P0分别为P0=0、P0=常数和P0=f(r)时Line-tied扭曲不稳定性的增长率和二维径向本征函数的演化规律。结果表明,P0=0和P0=常数时的轴向波数k的范围相同,但P0=常数时的增长率比P0=0时的小。P0=f(r)时的轴向波数k的范围和增长率则都比P0=0时的大,同时磁流体的速度变化也较大。因此,P0=f(r)更接近实际的物理模型(例如日冕的喷射问题)。

DⅢ-D高性能运行参数下的离散阿尔芬本征模

采用本征模式的数值打靶方法研究了离散阿尔芬本征模在DⅢ-D高性能运行条件下的物理特性,包括负磁剪切位形、高性能加热、正反中性束注入、内部输运垒以及高自举电流和甚高约束运行状态对这种阿尔芬模式的影响。在DⅢ-D托卡马克装置负磁剪切位形及先进运行状态实验参数下这些离散阿尔芬本征模存在于宽的径向区域,且具有广泛的本征频谱;高性能加热、同向中性束注入以及内部输运垒的存在有利于产生多个较深的气球模驱动势阱,由之得以很好地形成这种阿尔芬束缚态本征模;在高自举电流和甚高约束运行条件下这些离散阿尔芬本征模束缚态能够在更广的径向区域存在,且可具有较高的本征频率。另外,参照DⅢ-D装置放电实验数据的时间演变情况,这些离散阿尔芬本征模能在很宽的运行参数范围内出现,使之成为该类大型托卡马克实验中可能广泛存在的潜在不稳定性。

现行托卡马克参数下的离散阿尔芬本征模

研究了在JT-60U运行参数下的α诱发的环向阿尔芬本征模(αTAE),由其实验数据得到了s和α的径向剖面(s=rdq/qdr,2 q R d/dr)。发现存在α极大值,尤其是在反剪切等离子体和高性能位形下。这证实了托卡马克中存在αTAE的全域捕获条件。在现行托卡马克中发现了多支αTAE。此外,还考察了在中性束注入实验过程中αTAE随时间的变化特性。