Structure-driven nonlinear instability as the origin of the explosive reconnection dynamics in resistive double tearing modes

The onset of abrupt magnetic reconnection events, observed in the nonlinear evolution of double tearing modes (DTM), is investigated via reduced resistive magnetohydrodynamic simulations. We have identified the critical threshold for the parameters characterizing the linear DTM stability leading to the bifurcation to the explosive dynamics. A new type of secondary instability is discovered that is excited once the magnetic islands on each rational surface reach a critical structure characterized here by the width and the angle rating their triangularization. This new instability is an island structure-driven nonlinear instability, identified as the trigger of the subsequent nonlinear dynamics which couples flow and flux perturbations. This instability only weakly depends on resistivity.     

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.     

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 ($m=2n$, $n\ge 2$) 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.     

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.     

X-point collapse and saturation in the nonlinear tearing mode reconnection

We study the nonlinear evolution of the resistive tearing mode in slab geometry in two dimensions. We show that, in the strongly driven regime (large delta'), a collapse of the X point occurs once the island width exceeds a certain critical value approximately 1/delta'. A current sheet is formed and the reconnection is exponential in time with a growth rate proportional eta(1/2), where eta is the resistivity. If the aspect ratio of the current sheet is sufficiently large, the sheet can itself become tearing-mode unstable, giving rise to secondary islands, which then coalesce with the original island. The saturated state depends on the value of delta'. For small delta', the saturation amplitude is proportional delta' and quantitatively agrees with the theoretical prediction. If delta' is large enough for the X-point collapse to have occurred, the saturation amplitude increases noticeably and becomes independent of delta'.     

Resistivity of ferromagnetic metal near the reorientation phase transition point

Anomalies of the resistivity near the reorientation phase transition point are studied theoretically. The resistivity is shown to have an asymmetrical peak at the point of the transition. The derivatives of the resistivity with respect to temperature as well as magnetic field diverge at this point.     

Tokamak resistive magnetohydrodynamic ballooning instability in the negative shear regime

Improved confinement of tokamak plasma with central negative shear is checked against the resistive ballooning mode. In the negative shear regime, the plasma is always unstable for purely growing resistive ballooning mode. For a simplest tokamak equilibrium model, the s--α model, characteristics of this kind of instability are fully clarified by numerically solving the high n resistive magnetohydrodynamic ballooning eigen-equation. Dependences of the growth rate on the resistivity, the absolute shear value, the pressure gradient are scanned in detail. It is found that the growth rate is a monotonically increasing function of α while it is not sensitive to the changes of the shear s, the initial phase \ta₀ and the resistivity parameter \va_R.     

On Solving the Lorenz System by Differential Transformation Method

The differential transformation method （DTM） is employed to solve a nonlinear differential equation, namely the Lorenz system. Numerical results are compared to those obtained by the Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. In particular, we examine the accuracy of the （DTM） as the Lorenz system changes from a non-chaotic system to a chaotic one. It is shown that the （DTM） is robust, accurate and easy to apply.     

Propagation dynamics of finite-energy Airy beams in nonlocal nonlinear media

We investigate periodic inversion and phase transition of normal and displaced finite-energy Airy beams propagating in nonlocal nonlinear media with the split-step Fourier method. Numerical simulation results show that parameters such as the degree of nonlocality and amplitude have profound effects on the intensity distribution of the period of an Airy beam. Nonlocal nonlinear media will reduce into a harmonic potential if the nonlocality is strong enough, which results in the beam fluctuating in an approximately cosine mode. The beam profile changes from an Airy profile to a Gaussian one at a critical point, and during propagation the process repeats to form an unusual oscillation. We also briefly discus the two-dimensional case, being equivalent to a product of two one-dimensional cases.     

Experimental verification of the mechanisms for nonlinear harmonic growth and suppression by harmonic injection in a traveling wave tube

Understanding the generation and growth of nonlinear harmonic (and intermodulation) distortion in microwave amplifiers such as traveling wave tubes (TWTs), free electron lasers (FELs), and klystrons is of current research interest. Similar to FELs, the nonlinear harmonic growth rate scales with the harmonic number in TWTs. In klystrons, the wave number scaling applies to the nonlinear harmonic bunching and associated nonlinear space-charge waves. Using a custom-modified TWT that has sensors along the helix, we provide the first experimental confirmation of the scaling of nonlinear harmonic growth rate and wave number in TWTs. These scalings of a nonlinearly generated harmonic mode versus an injected linear harmonic mode imply that suppression by harmonic injection occurs at a single axial position that can be located as desired by changing the injected amplitude and phase.     

Abnormal resistivity behavior of Cu–Ni and Cu–Co alloys in undercooled liquid state

The resistivity behavior of undercooled liquid Cu–Ni and Cu–Co alloys had been studied in the contactless method, to probe the structure transition in undercooled melts during the cooling process. Over the entire concentration range, linear behavior of resistivity with temperature was obtained in liquid and undercooled liquid Cu–Ni system. It implied that the formation of icosahedral order might not influence the electron scattering in undercooled liquid Cu–Ni alloys. Similar results were obtained in Cu–Co system in the vicinity of liquidus temperature. A turning point was obvious in temperature coefficient of resistivity for undercooled liquid Cu–Co alloys around the bimodal line, which was interpreted to be responsible for metastable liquid–liquid phase separation. During liquid phase separation process, resistivity decreased and the temperature coefficient of resistivity was larger than that of homogeneous melts. In combination with transmission electron microscopy and scanning electron microscope studies on the as-solidified microstructure, this was interpreted as the formation of egg-type structure and concentration change in Cu-rich and Co-rich phases. The mechanism controlling the separation and droplets motion was also discussed in undercooled liquid Cu–Co system.     

高功率微波土壤击穿的数值验证研究

高功率微波在土壤中传播时, 会引起土壤击穿电离而导致土壤电阻率的非线性变化, 土壤电阻率的变化又将反作用于传播过程, 加剧高功率微波衰减, 影响其能量传输效率. 通过对土壤动态电离过程的分析, 结合Maxwell方程组构建了高功率微波土壤传播模型, 采用时域有限差分法对该模型进行数值验证. 数值结果显示了高功率微波在土壤中传播、衰减等物理图像, 以及土壤电阻率的非线性变化过程. 理论分析验证了这些数值结果.     

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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.     

Temperature dependence of the electrical resistivity in amorphous metals

In amorphous metals the electrical resistivity increases linearly in the temperature range from 2 to 40 K. This result differs fundamentally from the nonlinear behaviour known for crystalline metals and it suggests the conduction electrons not to be scattered by the vibrations of the amorphous point lattice. The temperature dependent part of the resistivity in amorphous metals is explained with scattering of conduction electrons by fluctuations ofp-electrons.     

Phase Effect on Mode Coupling in Kelvin-Helmholtz Instability forTwo-Dimensional Incompressible Fluid

This paper studies the phase effect in mode coupling of Kelvin-Helmholtzinstability in two-dimensional incompressible fluid. It is found that thereis an important growth phenomenon of every mode in the mode couplingprocess. The growth changes periodically with phase difference and in thecondition of our simulation the period is about 0.7π. The periodcharacteristic is apparent in all stage of the mode coupling process,especially in the relatively later stage.     

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。     

二维不可压流体Kelvin-Helmholtz不稳定性的弱非线性研究

通过将扰动速度势展至三阶,提出了Kelvin-Helmholtz（KH）不稳定性的弱非线性理论.在模耦合过程中观察到一个重要的共振现象,共振使得模耦合过程变得相当复杂,单模扰动很快进入非线性区,产生大量高次谐波,共振加强了非线性作用.分析了单模扰动中二次和三次谐波产生效应,以及对基模指数增长的非线性校正.模拟结果支持了解析理论.利用该理论,分析了KH不稳定的非线性阈值问题. 关键词： Kelvin-Helmholtz不稳定性 弱非线性理论 非线性阈值     

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。     

直接利用磁场和温度精确确定磁性材料La0.67Ca0.33MnO3和Pr0.7Sr0.3MnO3的电阻率

电阻率是研究钙钛矿结构锰氧化物磁性材料的重要参数之一,它与温度和外加磁场有密切关系.本文的工作之一是寻找合适的方法,确定在金属-绝缘体转换过程中,不同磁场情况下,材料La0.67Ca0.33MnO3和Pr0.7Sr0.3MnO3的电阻率随温度变化的数学解析关系.通过非线性数值拟合,找到了满足这一关系的函数为双曲正切修正的高斯函数.同时,获得金属-绝缘体转换时居里温度Tc满足的微分方程以及与该温度对应的最大电阻率ρmax.本文的另一个工作是寻求最大电阻率ρmax和磁场之间的函数关系,发现采用玻尔兹曼函数可以精确反映两者之间的数学联系.两项工作得到的数学拟合结果与实验数据之间的最小相关系数为0.998,最大平均相对误差4.35％,说明数据拟合的结果与实验结果十分符合.     

Suppression of superconductivity in disordered interacting wires

We study superconductivity suppression due to thermal fluctuations in disordered wires using the replica nonlinear sigma-model (NLsigmaM). We show that in addition to the thermal phase slips there is another type of fluctuations that result in a finite resistivity. These fluctuations are described by saddle points in NLsigmaM and cannot be treated within the Ginzburg-Landau approach. The contribution of such fluctuations to the wire resistivity is evaluated with exponential accuracy. The magnetoresistance associated with this contribution is negative.