环形轴对称锐边界等离子体的扭曲模不稳定性

本文对任意环径比、任意β值、任意截面形状的轴对称锐边界等离子体,给出了正确的边界条件,导出了无导体壳和存在导体壳两种情况下扭曲模稳定性的能量矩阵,对环向波数n为1,2,3的能量矩阵,给出了可快速、精确积分的具体形式,对不同环径比和不同拉长度b/α的椭圆形、跑道形(包括圆形)截面的等离子体进行了数值计算。计算结果表明,跑道形截面等离子体的临界β值比相应的椭圆形截面的β值高,随着b/α的增大,跑道形截面的临界β值也增加。导体壳有一定的稳定作用。从系统稳定性边缘态的本征矢量来看,存在导体壳时极向扰动的最大分量是模数1的扰动。与J.P.Freidberg和W.Grossmann的工作比较,在环径比为2时,圆截面等离子体的临界β值相差23％,临界q值相差15％。     

CT-6装置上铜壳电流的测量

在托卡马克装置中,导体壳的设置对放电时产生的等离子体起反馈平衡作用。理想导体壳产生的垂直磁场为 其中,Ⅰ为等离子体环电流;R为大半径:α为小半径;β_θ=8πP/Bθα;6为壳半径。 在非理想导体壳(如铜壳、铝壳)情况下,所产生的磁场相对减小。CT-6托卡马克(见图1)的实验中,证实了这种平衡作用的存在。放电时,一旦等离子体产生,铜壳感生电流     

椭圆截面等离子体柱的扭曲不稳定性

本文处理了锐边界椭圆截面等离子体柱的扭曲不稳定性,给出了用椭圆特征函数表示的色散关系的一般形式,对单模和两模扰动,给出了精确到椭圆率ε二级的结果。在任意椭圆率下进行了数值计算。结果表明,模数之间的耦合起解稳作用。当椭圆率增大时,稳定性所需的q_Σ值迅速增加,在无导体壳和a/b>2时,近似地有q_Σ-1∝(a/b)²。对于有限长度的系统,波长等于系统长度的扰动是最危险的。在小椭圆率情况下,对此种扰动而言,当系统的长度缩短(相应于环径比减小)时,对应的系统稳定性q_Σ值仅稍为增大一点。导体壳有一定的稳定作用。但当变形足够大时,扰动的有限波长和导体壳的存在对系统稳定性q_Σ值几乎没有多少影响。     

轴向荷载下功能梯度材料圆柱壳的动力屈曲

基于Donnell壳体理论和经典板壳理论,利用Hamilton变分原理得到轴向荷载作用下材料属性呈幂律分布的功能梯度材料圆柱壳的动力屈曲控制方程。根据圆柱壳周向连续性设出径向位移的函数表达,利用分离变量法求解得到功能梯度材料圆柱壳在轴向荷载作用下的动力屈曲临界荷载的解析表达式和屈曲解。利用MATLAB软件编程计算,讨论了径厚比、梯度指数、环向模态数、轴向模态数等对功能梯度材料圆柱壳动力屈曲临界荷载的影响。结果表明:圆柱壳的临界荷载随临界长度的增加而减小;冲击端为夹支的临界荷载比冲击端为简支的临界荷载大,说明约束条件对临界荷载有较大影响;圆柱壳的临界荷载随着模态数的增加而增大,说明临界荷载越大,高阶模态越易被激发;屈曲模态图随着模态数的增加而复杂化。     

Excel用于优化设计电容器尺寸

1 同轴柱形电容器的优化，设计两个同轴柱形导体构成了同轴柱形电容器．设电容器的内、外导体壳半径分别为r和R，长度为L(L≥R—r)，两导体壳层之间所填充电介质的介电常量为ε，其击穿场强为Emax(图1)．在外半径R一定的情况下，如何选择内圆筒导体半径r，使得设计出的电容器可以承受的电压最大?     

“电磁学”教学问题两则

1.不接地导体壳内的电荷改变位置不影响壳外电场分布的问题。 在电磁学讨论静电屏蔽时,常出现这样的问题:如图1所示,点电荷q在导体壳内移动位置时,壳外的电场分布是否改变见了这问题采用唯一性定理是易于解决的.但在普通物理范围内,如何解决呢;我们以球形导体壳为例加以说明.如图2所示,设导体壳为球形壳,在球心放置一点电荷q,此时球壳上的电势为当q从球心移到a点(离球心为r)时,设球壳上的电势为U’.由于导体是等势体以及球对称性,q在以r为半径的球面上任一处,导体壳上的电势均为U’。设 电荷Q均匀地分布在半径为r的球面上,则带电为Q 的球…     

对静电场中导体表面的电场强度的研究

在研究导体在外电场中感应产生感应电荷达到静电平衡状态时，导体表面的电荷分布与表面曲率和外电场分布情况有关，然而导体表面上的电场强度究竟由什么决定?是同导体内的电场强度即为零还是等于导体外周围附近的电场强度即为σ/ε0？还是既不等于零也不等于σ/ε0，而是由其他因素决定。     

托卡马克理想导体壁与磁流体不稳定性

为了探索等离子体磁流体力学(MHD)不稳定性的导体壁效应以及壁设计思想,研究了基于HL-2A托卡马克偏滤器位形的、自由边界和多种形式的理想导体壁条件下的等离子体MHD不稳定性与装置MHD运行β极限.在稳定性计算中,考虑的是n=1扭曲模,该模对托卡马克等离子体MHD不稳定性有决定性的影响.研究着眼于验证多种形状导体壁抑制内、外扭曲模的有效性,观察运行β极限的变化,并讨论分析相关物理.研究发现在离等离子体适当距离处放置一个理想导体壁,可有效抑制外扭曲模.在壁与等离子体表面的平均距离相同、且足够小的条件下,圆截面壁并不一定是最佳选择,设置一个经过优化的多边形导体壁能更有效地抑制MHD不稳定性,它使本装置的理想MHD运行β极限β_N提高到2.73,比自由边界条件下(即假设壁设置在无穷远处的)装置的运行β极限值(～2.56)提高了约6.5%.这暗示需要根据有拉长、有变形的等离子体的极向截面形状,优化制作一个离等离子体表面平均距离尽可能近的多边形导体壁,才能取得抑制外扭曲模、提高β极限的最佳效果.     

α-Fe中氦泡极限压强的分子动力学模拟

为了深入认识α-Fe中氦泡冲出位错环的微观机制,有必要研究α-Fe中氦泡冲出位错环时的极限压强特性.本文建立金属-氦泡的立方体型代表性体积单元模型,针对8种不同初始半径的球形氦泡,以初始氦空位比为变量,开展分子动力学模拟,得到了各模型中位错环开始形成时的氦泡极限压强和临界氦空位比.研究结果表明:对于无量纲半径介于2—10的氦泡,冲出位错环时的氦泡极限压强和临界氦空位比均随着氦泡初始半径的增大而非线性减小;基体中氦泡冲出位错环时的临界氦空位比具有明显的尺寸效应;初始时刻(0 ps),在经过立方体型模型中心的横截面上,氦泡周围Fe原子阵列的剪应力集中和最大剪应力出现在对角线与氦泡边界交点(即45°)处,并且关于横截面上平行于边的两条对折线对称分布,剪应力集中区的范围和最大剪应力均随着初始氦空位比的增大而增大;位错环冲出方向对应最大剪应力方向.本文的研究加深了对金属中氦泡物理特性的认识,为后续分析氦泡对材料宏观物理和力学性质的影响奠定了有益的基础.     

直流背场下YBCO涂层导体交流临界电流依频变化（英文）

基于对不同条件下YBCO涂层导体交流临界电流的测量结果,本文研究了YBCO涂层导体的交流临界电流、频率与外加磁场幅值和角度之间的关系,提出了一个相应的经验公式.利用该公式可计算在任意频率、任意外加直流背场下YBCO涂层导体的交流临界电流,计算结果和实验结果相一致.另外,对于YBCO涂层导体交流临界电流依频变化提出了一种可能的机理,频率的增高使得磁通穿透区域变窄,因而需要更大的电流来实现样品的完全穿透,这就使得交流临界电流随着频率增高而增大.     

Random walks on a ( 2+1)-dimensional deformable medium

A model of random walks on a deformable medium is proposed in 2+1 dimensions. The behavior of the walk is characterized by the stability parameter beta and the stiffness exponent alpha. The average square end-to-end distance l approximately equals (2nu) and the average number of visited sites approximately equals (k) are calculated. As beta increases, for each alpha there exists a critical transition point beta(c) from purely random walks ( nu = 1/2 and k approximate to 1) to compact growth ( nu = 1/3 and k = 2/3). The relationship between beta(c) and alpha can be expressed as beta(c) = e(alpha). The landscape generated by a walk is also investigated by means of the visit-number distribution N(n)(beta). There exists a scaling relationship of the form N(n)(beta)approximately n(-2)f(n/beta(z)).     

Superscaling of percolation on rectangular domains

For percolation on (RL)xL two-dimensional rectangular domains with a width L and aspect ratio R, we propose that the existence probability of the percolating cluster E(p)(L,epsilon,R) as a function of L, R, and deviation from the critical point epsilon can be expressed as F(epsilonL(y(t))R(a)), where y(t) identical with1/nu is the thermal scaling power, a is a new exponent, and F is a scaling function. We use Monte Carlo simulation of bond percolation on square lattices to test our proposal and find that it is well satisfied with a=0.14(1) for R>2. We also propose superscaling for other critical quantities.     

基于多质点模型的准球形丝阵参数优化研究

基于多质点薄壳模型对准球形丝阵负载参数进行优化,使得终态等离子体具有预期的内爆特性。通过对丝阵初始位形优化,可以获得期望的终态等离子体壳纵横比,并且终态纵横比对负载初始质量变化不敏感。对于固定电流波形(峰值1.2 MA、上升时间80ns),优化计算了初始丝长度15.4mm的丝阵线质量。结果表明,当丝阵初始线质量约为150μg/cm时,赤道半径为2mm、纵横比为1的终态等离子体壳具有最大动能1.5kJ。同时,还针对不同幅度及上升时间的电流进行优化计算,计算结果表明终态等离子体壳的优化的最高动能与电流峰值平方成正比,与最高动能相应的线质量与电流上升时间平方成正比。     

An Analytical Approach to the Turbulence-Relaxed State in Tokamak Plasmas

Starting from the continuity, temperature, and motion equations of the trapped electron fluid in generaltokamak magnetic field with positive or reversed shear and the definition of Lagrangian invariant, dL / dt = ( t u. )L =0, where u is convective velocity, the trapped electron dynamics is considered in the following two assumptions: (i) theturbulence is low frequency electrostatic, and (ii) L is a functional only of the density n, temperature T, and magneticfield B, and the effect of perturbation potential φ is included in the convective velocity u, i.e., u is a functional of n,T, B, and φ. The Lagrangian invariant hidden in the trapped electron dynamics is strictly found: L= ln[(n/B)c1(T/B2/3)c2], where c1 and c2 are dimensionless changeable parameters and c1 ∝ c2. From this Lagrangian invariant thewhich, in the limit of large aspect ratio, reduce to n(r)q(r) = const. and T3/2(r)q(r) = const., respectively. The lattertwo scaling laws are compared with existent experimental results, being in good agreement.     

Phase transition in the 2D random Potts model in the large-q limit

Phase transition in the two-dimensional q-state Potts model with random ferromagnetic couplings is studied in the large-q limit by a combinatorial optimization algorithm and by approximate mappings. We conjecture that the critical behavior of the model is controlled by the isotropic version of the infinite randomness fixed point of the random transverse-field Ising spin chain and the critical exponents are exactly given by beta=(3-sqrt[5])/4, beta(s)=1/2, and nu=1. The specific heat has a logarithmic singularity, but at the transition point there are very strong sample-to-sample fluctuations. Discretized randomness results in discontinuities in the internal energy.     

Soret效应对具有自由表面的圆柱形浅池内双组分溶液热对流影响的实验研究

为了探究Soret效应对具有自由表面的圆柱形浅液池内双组分溶液热对流过程的影响, 通过实验观察了质量分数为50%的正癸烷/正己烷混合溶液在不同深宽比的液池内流动失稳后的自由表面耗散结构及液池内的温度波动. 结果表明, 双组分溶液流动失稳的临界热毛细Reynolds数小于纯工质的值, 且其随液层深宽比的变化规律与纯工质相同. 当深宽比小于0.0848时, 流动失稳后在自由表面观察到热流体波, 监测点处温度波动主频随热毛细Reynolds数增大而增加; 当深宽比大于0.0848时, 随热毛细Reynolds数的增大, 流动失稳后自由表面依次呈现轮辐状、花苞状、分离-合并-分离交替变化的条纹状结构.     

Asymptotic scaling laws for imploding thin fluid shells

Scaling laws governing implosions of thin shells in converging flows are established by analyzing the implosion trajectories in the (A,M) parametric plane, where A is the in-flight aspect ratio, and M is the implosion Mach number. Three asymptotic branches, corresponding to three implosion phases, are identified for each trajectory in the limit of A,M >1. It is shown that there exists a critical value gamma(cr) = 1+2/nu (nu = 1,2 for, respectively, cylindrical and spherical flows) of the adiabatic index gamma, which separates two qualitatively different patterns of the density buildup in the last phase of implosion. The scaling of the stagnation density rho(s) and pressure P(s) with the peak value M(0) of the Mach number is obtained.     

Theorem on the origin of phase transitions

For physical systems described by smooth, finite-range, and confining microscopic interaction potentials V with continuously varying coordinates, we announce and outline the proof of a theorem that establishes that, unless the equipotential hypersurfaces of configuration space Sum(v)=[(q(1),...,q(N)) subset R(N)/V(q(1),...,q(N))=v], v subset R, change topology at some v(c) in a given interval [v(0),v(1)] of values v of V, the Helmoltz free energy must be at least twice differentiable in the corresponding interval of inverse temperature (beta(v(0)),beta(v(1))) also in the N--> infinity limit. Thus, the occurrence of a phase transition at some beta(c)=beta(v(c)) is necessarily the consequence of the loss of diffeomorphicity among the [Sigma(v)](vv(c)), which is the consequence of the existence of critical points of V on Sigma(v=v(c)), that is, points where inverted Delta V=0.     

论(MnF6)4-团簇光谱参量Dq的R-n律

用配位球壳势模型研究了络合分子中过渡金属离子光谱参量Dq与金属-配体间键长R的R-n律关系。结果表明指数n的变化趋势依赖于配位球壳半径R的增大或减小,在点电荷模型下n值将小于5且随R的减小而减小。在(MnF6)4-团簇键长的实验范围内(R=0.207nm←→0.214nm),理论计算值n=4.488与实验观测值n=4.45符合得很好。