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。     

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。     

外部驱动电流抑制双撕裂模的发展

在Hall MHD方程组中引入外部驱动电流项,数值模拟外部驱动电流对双撕裂模不稳定性的影响.结果表明,在x点加入反向外部驱动电流对撕裂模的发展有抑制作用,周期性的外部驱动电流对双撕裂模不稳定性的抑制效果较好,能控制磁岛的尺度在相互驱动的临界尺度以下,避免发生双撕裂模非线性磁场重联的爆发,随着驱动电流周期变大抑制效果变坏,在一定限度内随着驱动电流强度增大抑制效果变好,在一定范围内随着驱动电流宽度变小抑制效果变好.     

等离子体理想及电阻局部模不稳定性

用一个收敛很快的级数构造了非圆截面、线性电流分布环形等离子体的磁流体平衡解。分别用梅瑟判据和格勒塞判据数值研究了几种典型位形在整个等离子体区域的理想和电阻局部模不稳定性。     

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.     

黏滞等离子体中双撕裂模不稳定性的数值模拟研究

本文采用磁流体力学模型,数值研究了平板位形下双撕裂模线性增长率关于等离子体电阻η和黏滞v的定标关系.结果表明,对于有理面间距较大的情况,线性增长率关于电阻和黏滞的指数定标率随着黏滞的增加逐渐由γ∝ η3/5v0的定标变化到γ∝η5/6v-1/6的定标;而对于有理面间距较小的情况,其指数定标率随着黏性的增加从γ∝η 1/3 v0的定标逐渐变化到γ∝η2/3v-1/3的定标.本文还给出了初始阶段对称的双撕裂模的非线性演化,发现在非线性阶段对称的双撕裂模将转化为反对称的双撕裂模,并解释了相应的物理机理.     

高磁雷诺数下剪切流对双撕裂模中二级磁岛的影响

在高磁雷诺数下,当双撕裂模发展进入快速磁场重联阶段时,会发生二级磁岛不稳定性,加剧磁场能量的释放。本文基于扰动形式的守恒磁流体方程组发展高精度的数值模拟程序,在平板位形下研究反对称位形剪切流对双撕裂模中二级磁岛的影响。结果表明：随着剪切流强度和剪切梯度的增加,二级磁岛的数目以及电流片横纵比变小。此外,较强的极向剪切流能够抑制二级磁岛不稳定性的发生。     

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。     

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：     

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。     

The effects of a shear flow on nonlinear evolutions of double tearing mode in Hall magnetohydrodynamics

The effects of a shear flow on nonlinear evolution of double tearing mode in Hall magnetohydrodynamics are investigated. The parallel shear flow displays a suppressing effect on the double tearing mode. Due to the effect of the shear flow, the relative displacements between the magnetic islands are changed, and therefore their mutual interactions become weak. Furthermore, the nonlinear impulsive growth phase of the double tearing mode is delayed with increasing the shear flow velocity. When the magnetic islands are pushing against each other, the width of current sheets decreases drastically, and therefore the Hall effects are dominant and the magnetic reconnection enhances greatly.     

Generation and amplification of magnetic islands by drift interchange turbulence

We investigate the multiscale nonlinear dynamics of a linearly stable or unstable tearing mode with small-scale interchange turbulence using 2D MHD numerical simulations. For a stable tearing mode, the nonlinear beating of the fastest growing small-scale interchange modes drives a magnetic island with an enhanced growth rate to a saturated size that is proportional to the turbulence generated anomalous diffusion. For a linearly unstable tearing mode the island saturation size scales inversely as one-fourth power of the linear tearing growth rate in accordance with weak turbulence theory predictions. Turbulence is also seen to introduce significant modifications in the flow patterns surrounding the magnetic island.     

Structure-driven nonlinear instability of double tearing modes and the abrupt growth after long-time-scale evolution

The new nonlinear destabilization process is found in the nonlinear phase of the double tearing mode (DTM). This process causes the abrupt growth of DTM and subsequent collapse after long-time-scale evolution in the Rutherford-type regime. The nonlinear growth of the DTM is triggered when the triangular deformation of magnetic islands with sharp current point at the X point exceeds a certain value. Hence, the mode can be called the structure-driven one. Decreasing the resistivity increases the sharpness of the triangularity and the spontaneous growth rate in the abrupt-growth phase is almost independent of the resistivity.     

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.     

Nonlinear evolution of q=1 triple tearing modes in a tokamak plasma

In magnetic configurations with two or three q=1 (with q being the safety factor) resonant surfaces in a tokamak plasma, resistive magnetohydrodynamic modes with poloidal mode numbers m much larger than 1 are found to be linearly unstable. It is found that these high-m double or triple tearing modes significantly enhance through nonlinear interactions the growth of the m=1 mode. This may account for the sudden onset of the internal resistive kink, i.e., the fast sawtooth trigger. Based on the subsequent reconnection dynamics that can proceed without formation of the m=1 islands, it is proposed that high-m triple tearing modes are a possible mechanism for precursor-free partial collapses during sawtooth oscillations.     

Tearing mode suppression by using resonant magnetic perturbation coils on J-TEXT tokamak

A series of experiments on the interactions between external resonant magnetic perturbations (RMP) and plasmas has recently been conducted, using static resonant magnetic perturbation (SRMP) coils on the Joint Texas Experimental Tokamak (J-TEXT). The tearing mode can be completely suppressed by applying SRMP. However, the locked mode is likely to be stimulated under a larger SRMP field even though the tearing mode has been first suppressed. A numerical simulation shows three typical regimes of RMP?s effects on the tearing mode, which are consistent with experimental results.     

Experiment and simulation of tearing mode evolution with electron cyclotron current drive in KSTAR

The tearing mode (TM) plasma instability was observed in low confinement (L-mode) plasmas when non-axisymmetric magnetic perturbation (MP) was applied using external coils during 2011 campaign of KSTAR. Based on the collected information of the magnetic island location in a plasma, a discharge was designed for suppression of a (2,1) TM mode by adjusting electron cyclotron (EC) launcher angles to the estimated island position. Here, the (m,n) notation describes the poloidal mode number and the toroidal mode number of the TM, respectively. The discharge is analysed with experimental observations and numerical simulations. Mirnov coil (MC) arrays and electron cyclotron emission (ECE) are used for analysis of the island width and the location as well as the mode number. The EC deposition and its alignment with the island are estimated by X-ray imaging crystal spectroscopy (XICS) and ECE measurements. An integrated numerical system is employed for modelling of this discharge to analyse a temporal evolution of the mode activity by integrating plasma equilibrium, transport, heating and current drive, and the magnetic island evolution, in a self-consistent way. The effect of EC current drive is discussed by comparing with another TM discharge but without ECCD. Some possibilities for classifying this mode to neoclassical tearing mode (NTM) and stabilisation effect of ECCD are suggested based on the experimental observation and the simulation results.