等离子体轴向运动对撕裂模不稳定性影响研究

从电阻磁流体模型出发,详细推导了柱形位形下低β等离子体中包括等离子体宏观轴向运动效应的电阻性撕裂模线性不稳定性理论。数值研究发现：等离子体轴向运动速度本身对撕裂模具有明显的稳定作用,而轴向运动速度剪切的作用并不明显。分析表明：轴向运动通过改变扰动势函数和磁通函数之间的相位差(偏离π/2)来降低撕裂模增长率,同时产生一个较低的撕裂模频率。     

反磁剪切等离子体中的电阻交换模不稳定性

具有内部输运垒（ITB）的反磁剪切（RS）等离子体位形是在托卡马克中获得高参数的最具前景的途径之一。这种位形不仅改善等离子体约束,而且可以改进象气球模和新经典撕裂模等这类宏观模的稳定性。然而,反磁剪切区域的高压强可以驱动电阻交换模不稳定性,从而破坏中心区的等离子体高参数。为了研究电阻交换模不稳定性的性质,并确定其在RS等离子体中发展的区域,我们利用在HL－2A中使用中性束注入建立的RS位形来分析电阻交换模不稳定性。     

双撕裂模非线性演化过程中有理面上的剪切流

在二维平板几何模型下,利用磁流体力学方程组数值模拟托卡马克装置中双撕裂模非线性演化过程中有理面上剪切流的时间和空间分布.结果表明,双撕裂模非线性演化的早期阶段,有理面上没有形成明显的剪切流.剪切流主要存在于快速磁重联阶段,随着磁重联的结束而逐渐消失,剪切流的强度和空间分布随磁岛的演化而改变.另外,较大的等离子体电阻加速磁重联,但是对剪切流的强度和变化趋势没有直接的影响.     

粘滞效应对非线性电阻撕裂模的影响

本文研究粘滞效应对非线性电阻撕裂模的影响。利用准环坐标将具有标量电阻率和粘滞系数的MHD方程简化为一组无量纲的非线性方程。并对这组方程采用二步交替隐式差分格式进行数值计算。结果给出了2/1模的演变过程对无量纲粘滞系数的依赖关系和电流密度的分布。发现粘滞效应对饱和磁岛宽度的修正大约为5％(此时R=10~(-5)),同时发现由于粘滞效应的引入导致电流分布在奇异面附近的涨落明显减小。     

基于有限体积法数值模拟双撕裂模非线性演化

以磁流体理论为基础,采用基于有限体积法的通量差分分裂格式数值求解具有双曲保守律形式的电阻磁流体方程组。编写C++程序对平板几何位形下的等离子体双撕裂模进行了长时间数值模拟,得到双撕裂模不稳定性的演化图景,捕捉到了双撕裂模非线性发展过程中磁场重联的几个典型阶段,讨论了等离子体电阻和两个有理面之间的距离对双撕裂模不稳定性非线性发展的影响。为研究磁流体动力学提供了一种可行的高精度数值算法。     

输运与撕裂模相互作用下等离子体的时空结构

本文应用等离子体一维输运模型与撕裂模理论,对于不同的输运模型和托卡马克放电参数下撕裂模的演变进行了数值研究。结果表明,能量过程是影响等离子体宏观稳定性行为的一个不可低估的重要因素,它们与磁流体稳定性的相互影响,会使其磁流体形态构成多种时间或空间结构,等离子体温度、密度等宏观参量也将表现出不同的时空特征。 关键词：     

撕裂模方程的数值分析

从数值计算的角度，讨论了撕裂模方程的解。用龙格－库塔方法计算了撕裂模（2／1模）的本征函数及其连接参数。计算结果同Wesson的结果符合得很好。     

负磁剪切位形中等离子体气球模稳定性研究

根据ＭＨＤ气球模稳定性理论，计算了负磁剪切位形中等离子体气球边缘稳定性区域。结果表明，在同样参数下，负磁剪切区域比正磁剪切区域允许更大的β值。     

托卡马克等离子体中撕裂模不稳定性研究

本论文共六章。第一章简要介绍了撕裂模不稳定性研究的发展历史及其重要意义。第二章描述了经典撕裂模的物理基础，包括基本方程组、物理图象、磁岛、旋转频率及m=1的撕裂模的特征。经典撕裂模是考虑等离子体的有限电阻之后，在奇异表面附近的磁力线就要断开和重连，并形成磁岛结构。撕裂模的不稳定性判据Δ′〉0时，模式是不稳定的。第三章概述了经典撕裂模的实验研究。     

反常电子粘滞性引起的线性双撕裂模研究

用圆柱位形的磁流体动力学方程对由反常电子粘滞性引起的双撕裂模的线性行为做了数值研究.分析了两个有理面的间距、粘滞率大小和极向模数对双撕裂模模式结构的影响,给出了各种情况下双撕裂模线性增长率跟表征反常电子粘滞率大小的电子雷诺数的定标关系.     

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.     

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以磁流体理论为基础,采用基于有限体积法的通量差分分裂格式数值求解具有双曲保守律形式的电阻磁流体方程组.编写C++程序对平板几何位形下的等离子体双撕裂模进行了长时间数值模拟,得到双撕裂模不稳定性的演化图景,捕捉到了双撕裂模非线性发展过程中磁场重联的几个典型阶段,讨论了等离子体电阻和两个有理面之间的距离对双撕裂模不稳定性非线性发展的影响.为研究磁流体动力学提供了一种可行的高精度数值算法.     

Compressibility effects on double tearing mode interlocking in differentially rotating plasmas

Effects of compressibility on the double tearing modes (DTMs) in rotating plasmas are numerically investigated by using a compressible magnetohydrodynamics (MHD) model. It is found that due to the compressibility effects, the threshold of the interlocking magnetic island width in the slow and intermediate rotation regimes is larger than the counterpart in the incompressible plasmas. In the fast rotation regime, the compressible effect makes the DTM islands interlock more easily and faster. Moreover, in the very fast rotation regime, the plasma rotation can more effectively suppress the DTM islands. The scalings of the interlocking threshold in the different rotation regimes are obtained. Effects of plasma viscosity and beta on the DTM interlocking in the compressible plasmas are also discussed.     

ITER装置中等离子体旋转和反馈控制对电阻壁模影响的数值研究

在托卡马克等离子体中,电阻壁模是非常重要的磁流体不稳定性,特征时间在毫秒量级.对长时间稳态运行下的先进托卡马克,电阻壁模限制着聚变装置的运行参数空间(放电时间和比压),影响经济效益,所以研究电阻壁模稳定性至关重要.本文使用MARS程序,针对ITER装置上9 MA先进运行平衡位形,研究了等离子体旋转和反馈控制对电阻壁模的...     

Color-electric conductivity in a viscous quark-gluon plasma

Several different transport processes, such as heat, momentum, and charge transports, may occur simultaneously in a thermal plasma system. The corresponding transport coefficients are heat conductivity, shear viscosity, and electric conductivity. In the present study, we investigate the color-electric conductivity of the quark-gluon plasma(QGP) in the presence of shear viscosity, focusing on the connection between the charge transport and momentum transport. To achieve this goal, we solve the viscous chromohydrodynamic equations obtained from the QGP kinetic theory associated with the distribution function modified by shear viscosity. According to the solved color fluctuations of hydrodynamic quantities, we obtain the induced color current through which the color-electric conductivity is derived. Numerical analysis shows that the conductivity properties of the QGP are mainly demonstrated by the longitudinal part of the color-electric conductivity. Shear viscosity has an appreciable impact on real and imaginary parts of the color-electric conductivity in some frequency regions.     

剪切磁场位形下电阻壁模不稳定性的数值模拟

数值研究了平衡磁场位形对电阻壁模稳定性的影响。研究发现,磁场剪切对电阻壁模有解稳作用,对于不同的剪切磁场位形,最不稳定的电阻壁模的环向模数和极向模数不同。等离子流对电阻壁模的增长有抑制作用,稳定住电阻壁模的临界流速度随着磁场剪切率的增大而增大。电阻壁模经线性增长后,进入非线性演化阶段,最后达到饱和状态,剪切磁场位形下的扰动磁能比均匀磁场位形下的扰动磁能饱和度高。     

Linear analysis of plasma pressure-driven mode in reversed shear cylindrical tokamak plasmas

The linear behavior of the dominant unstable mode ($m=2$, $n=1$) and its high order harmonics ($m=2n$, $nge 2$) are numerically investigated in a reversed magnetic shear cylindrical plasma with two $q=2$ rational surfaces on the basis of the non-reduced magnetohydrodynamics (MHD) equations. The results show that with low beta (beta is defined as the ratio of plasma pressure to magnetic field pressure), the dominant mode is a classical double tearing mode (DTM). However, when the beta is sufficiently large, the mode is driven mainly by plasma pressure. In such a case, both the linear growth rate and mode structures are strongly affected by pressure, while almost independent of the resistivity. This means that the dominant mode undergoes a transition from DTM to pressure-driven mode with the increase of pressure, which is consistent with the experimental result in ASDEX Upgrade. The simulations also show that the distance between two rational surfaces has an important influence on the pressure needed in mode transition. The larger the distance between two rational surfaces, the larger the pressure for driving the mode transition is. Motivated by the phenomena that the high-$m$ modes may dominate over low-$m$ modes at small inter-resonance distance, the high-$m$ modes with different pressures and $q$ profiles are studied too.