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。     

流动等离子体对托卡马克中撕裂模的影响

本文分析了托卡马克中的等离子体具有一个整体流动速度时,撕裂模的活动情况。分析与数值计算指出,等离子体的整体流动(等价于具有一个旋转频率)不影响撕裂模的活动,只是使撕裂模具有一个和等离子体相同的旋转频率。外加螺旋场在撕裂层能有效地抑制住等离子体的旋转。螺旋场对撕裂模的稳定作用不受等离子体旋转的影响。 关键词：     

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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.     

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。     

自由边界载流等离子体柱的电阻螺旋模不稳定性的数值计算

本文采用两步隐式差分格式研究了自由边界载流等离子体柱的电阻螺旋模不稳定性。发现等离子体温度剖面越宽和越高,m=2的撕裂模的线性稳定就越好。计算结果与实验相符合。     

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。     

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.     

托卡马克中撕裂模的抑制

本文分析与计算了共振螺旋场对自发撕裂模的抑制作用。通过解电阻MHD方程证实了螺旋场能使m=2的撕裂模增长速度减慢一倍左右。同时也讨论和计算了边界控制场对撕裂模的抑制作用。 关键词：     

用电子迴旋共振加热抑制托卡马克中的撕裂模

利用电子迴旋共振加热的定域性,改善等离子体电流分布,从而改善撕裂模的稳定条件,只要电子迴旋共振加热的吸收区能覆盖住撕裂模的共振层,就有很好的稳定效应;而不一定要求电子迴旋共振面与撕裂模的共振面重合,在迴旋加热期间,撕裂模被有效地抑制住。 关键词：     

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.     

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From the point of view of resistive MHD theory, the linear resistive tearing mode model in the low β plasma with macroscopic axial motion of plasma was deduced in a cylindrical geometry. Numerical study shows that the axial velocity of the plasma itself has a stable effect on tearing mode and the axial velocity shear role is not obvious. Analyses indicate that the axial motion reduces the tearing mode growth rate by changing the phase difference between the plasma potential perturbation and magnetic flux perturbation (deviating from π/2), and results in a lower tearing mode frequency.     

托卡马克中共振螺旋场对撕裂模的影响

本文在共振螺旋场(RHF)条件下,对撕裂模的时间演化过程进行了数值计算。在等离子体内部磁扰动与外加RHF的相位差不同时,分析了撕裂模的不同发展过程和结果。认为RHF可以最终改变托卡马克中的饱和磁岛宽度。     

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.     

Effect of Hyper-Resistivity on Nonlinear Tearing Modes

We analytically investigate nonlinear tearing modes with the anomalous electron viscosity or,as it is normally called,hyper-resistivity.In contrast to the flux average method used by previous work,we employ the standard singular perturbation technique and a quasilinear method to obtain the time evolution equation of tearing modes.The result that the magnetic flux grows with time in a scaling as t~(2/3)demonstrates that nonlinear tearing modes with the hyper-resistivity effect alone have a weaker dependence on time than that of the corresponding resistive case.     

Toroidal plasma rotation induced by the dynamic ergodic divertor in the TEXTOR tokamak

The first results of the Dynamic Ergodic Divertor in TEXTOR, when operating in the m/n=3/1 mode configuration, are presented. The deeply penetrating external magnetic field perturbation of this configuration increases the toroidal plasma rotation. Staying below the excitation threshold for the m/n=2/1 tearing mode, this toroidal rotation is always in the direction of the plasma current, even if the toroidal projection of the rotating magnetic field perturbation is in the opposite direction. The observed toroidal rotation direction is consistent with a radial electric field, generated by an enhanced electron transport in the ergodic layers near the resonances of the perturbation. This is an effect different from theoretical predictions, which assume a direct coupling between rotating perturbation and plasma to be the dominant effect of momentum transfer.     

Resonant field amplification near the RWM stability boundary in a tokamak

Evolution of a resistive wall mode (RWM)—a magnetic field perturbation produced by a plasma and partially stabilized by a conducting wall—is considered. It is assumed that there is a small resonant harmonic in the spectrum of the static error field. It is shown that the effect of this harmonic on the dynamics of stable RWMs increases as the plasma approaches the RWM stability boundary. The error field is “amplified” during the transition through this boundary. The smaller the rotation velocity of the perturbation and the longer the time during which the plasma stays near the stability boundary, the stronger this amplification is.     

Excitation of the Potential Relaxation Instability in a Weakly Magnetized Discharge Plasma by a Voltage Step

An instability is triggered in a weakly magnetized discharge plasma by the application of a positive voltage step to a planar collector immersed into the plasma column with its surface perpendicular to the magnetic field lines. Time developement of the plasma density after the application of the pulse is measured by a Langmuir probe. Radial and axial velocity of the plasma density perturbation are measured. Radial velocity is consistent with the increase of the plasma potential in the current channel. Axial velocity is very high. It is interpreted as phase velocity of radial quasiperiodic motion of the plasma in and out of the current channel. Response time of the collector current to the applied voltage step is measured versus different parameters. Experimental results are in agreement with a qualitative model presented in previous work [1] where the observed instability is modeled as a two dimensional potential relaxation instability (PRI). Minor improvements of the previous model are proposed. A rarefaction pulse that moves towards the collector is found as the initial stage of the instability.     

The influence of mode coupling on the non-linear evolution of tearing modes

On the basis of tearing mode theory a simple but physically explicit model of the evolution of toroidally coupled rotating magnetic islands has been developed. The basic mechanism identified by the model in the island evolution is the locking in phase of rotating islands that leads to rapid destabilisation of an initially stable mode. Destabilisation of marginally stable (2, 1) and (3, 1) modes is analysed in several scenarios. It is shown that mode coupling is an effective way of destabilising a m=3 island in a low- plasma. The numerical examples presented show the individual roles of coupling, inertia and a resistive wall. The model was applied for the analysis of MHD observations of an ASDEX discharge. Received 4 May 1999 and Received in final form 23 July 1999