有限长厚壁载流螺线管的磁场分布

对于通以恒定电流的有限长厚壁螺线管,用柱函数展开法推导出矢势的表达式,再根据磁感应强度与矢势的关系式得出磁场的积分形式表达式．用直接积分的方法,计算出厚壁螺线管内部和外部的磁场分布的级数表达式．另外还用本文得出的公式求得中轴线上的磁场．     

载流有限长密绕螺线管的磁场分布

对于通以恒定电流的有限长螺线管,首先用柱函数展开法推导出矢势的表达式,再利用磁感应强度与矢势的关系式,得出积分形式的磁场表达式.然后用直接积分的方法计算出磁场分布的级数表达式.最后讨论了某些特殊位置处的磁场.     

用级数拟合求圆电流磁场解析解

采用将圆电流磁矢势表达式中一部分展成分数，使被积函数变成可积分的函数，用解析函数拟合积分的级数，代替无穷级数求和运算，得到可以计算圆电流在空间任保一点磁场的解析解，解决了计算非近轴区圆电流磁场问题。     

Comparison of different techniques for the FLUENT$^{\copyright}$-based treatment of the electromagnetic field in inductively coupled plasma torches

A new technique for using the CFD commercial code FLUENT ^©^{\copyright} to simulate inductively coupled plasma torches by means of two-dimensional axisymmetric models is presented. The method is based on an external user-defined function (UDF) which fully solves the electromagnetic field equations, letting the FLUENT ^©^{\copyright} built-in module calculate only the plasma temperature and velocity fields inside the torch region. In this framework, computations have been carried out for LTE, optica lly thin argon plasmas at atmospheric pressure, using extended grid models with either magnetic dipole or vanishing vector potential boundary conditions for the electromagnetic field. It is shown that our newly developed technique is up to 60% faster on each iteration than that using user-defined scalars (UDS) previously proposed in the literature, as the need of solving flow field equations also outside the plasma zone is eliminated. Calculations are also performed using exact integral boundary conditions for the vector potential, as given by the standard electromagnetic field approach, taking into account the effects of both exciting and induced currents. The corresponding results are compared with the approximate ones obtained by employing extended grid models, showing that for small radial dimensions of the electromagnetic field domain, the magnetic dipole boundary conditions give more realistic solutions than those assuming a vanish ing vector potential.     

轴对称的静磁场的两种简便解法

对于轴对称的静磁场,推导出了矢势的柱函数展开式,得出了用对称轴上的磁场表示轴外任意点磁场分布的级数展开式.最后,给出了用这两种方法求解轴对称静磁场的例子.     

Formal Similarity Between Mathematical Structures of Electrodynamics and Quantum Mechanics

Electromagnetic phenomena can be described by Maxwell equations written for the vectors of electric and magnetic field. Equivalently, electrodynamics can be reformulated in terms of an electromagnetic vector potential. We demonstrate that the Schrödinger equation admits an analogous treatment. We present a Lagrangian theory of a real scalar field φ whose equation of motion turns out to be equivalent to the Schrödinger equation with time independent potential. After introduction the field into the formalism, its mathematical structure becomes analogous to those of electrodynamics. The field φ is in the same relation to the real and imaginary part of a wave function as the vector potential is in respect to electric and magnetic fields. Preservation of quantum-mechanics probability is just an energy conservation law of the field φ.     

对一类静电问题的进一步计算分析

用Bessel函数积分对圆环电流磁矢势及均匀带电圆环电势作进一步的计算分析,引申出磁感应强度及电场强度新的级数表达式,分析讨论了所得结果.     

基于二阶矢量位的矩形截面回折线圈阻抗和脉冲磁场的解析建模与计算

本文基于二阶矢量位建立了回折线圈的阻抗和磁场计算的解析模型,并提出了计算磁场脉冲响应的方法.根据回折线圈用于涡流检测和电磁超声检测时的通用模型,将回折线圈的阻抗和磁场计算问题转化为多个单匝矩形线圈阻抗和磁场的叠加问题.基于二阶矢量位和时谐电磁场方程,推导了回折线圈的频域标势表达式;利用标势与矢量磁位和磁通密度间的关系,推导了计算区域的磁通密度和式样表面涡流的频域解析计算公式;通过计算线圈的感应电势和阻抗变化表达式,得到了线圈阻抗的频域解析表达式;采用FFT-IFFT方法计算了脉冲磁场的时域响应.以一双层双 关键词： 无损检测 回折线圈 二阶矢量位 解析建模     

CALCULATION OF THE 3-DIMENSIONAL MAGNETIC FIELD BY USE OF THE MODIFIED SCALAR POTENTIAL

A new method for calculating the 3-dimensional magnetic field is described. The modified scalar potential is used to reduce the order of the coupled equations in the comparison with the vector potential under the same node number.     

Numerical modelings of superconducting wires for AC loss calculations

Superconducting properties of superconducting wires as well as the influence of their composite structure and twisting should be taken into account for their numerical modeling for AC loss calculations. Furthermore, complicated electromagnetic conditions in electrical apparatuses under which superconducting wires are used influence their AC loss properties; superconducting wires carry their transport current and are exposed to the external magnetic field whose direction and magnitude vary spatially. A series of numerical models of superconducting tapes based on the finite element method has been developed. In each model, some of the above-mentioned factors that could influence the AC loss properties are taken into account. The models are formulated with the current vector potential and the scalar magnetic potential (T–Ω method). Superconducting property is given by the E–J characteristic represented by a power law. The current distributions in non-twisted and twisted superconducting tapes carrying their transport current and/or exposed to the external magnetic field are calculated with these models to estimate their AC loss. The current distribution in a short piece of superconducting tape exposed to AC magnetic field is also calculated.     

铝电解槽内电-磁-流场的耦合仿真方法及应用

基于电磁流体力学的基本理论,应用等效电阻网络法与有限元相结合计算铝电解槽电流场,标量电位法和双标量磁位法计算铝电解槽磁场,k-ε双方程模型计算电磁力驱动下的铝液流动,并与工业测试结果进行比较.对200 kA侧部四点进电的铝电解槽进行计算与测试,其结果吻合良好;水平磁场形成一个顺时针的漩涡,垂直磁场沿长轴和短轴呈反对分布;铝液流动呈现出沿长轴方向排列的4个漩涡.仿真磁场误差小于10.0%,流场误差不超过5.0%.     

Dirac bound states of anharmonic oscillator in external fields

We explore the effect of the external magnetic and Aharonov–Bohm (AB) flux fields on the energy levels of Dirac particle subjects to mixed scalar and vector anharmonic oscillator field in the two-dimensional (2D) space. We calculate the exact energy eigenvalues and the corresponding un-normalized two-spinor-components wave functions in terms of the chemical potential parameter, magnetic field strength, AB flux field and magnetic quantum number by using the Nikiforov–Uvarov (NU) method.     

The two-body multipole problem of electrodynamics

A 2-body system composed of two objects having arbitrary distributions of charge and current is discussed. An expression for the velocity dependent potential between these two objects has been obtained in the non-relativistic approximation. This potential consists of two parts viz. a velocity independent scalar potential Φ_eff and another part which is linearly dependent on the relative velocity between the objects. The second part naturally suggests a vector potential A_eff. The potentials have been expanded into multipole terms. It has been found that Φ_eff is a sum of two components viz. Φ_EE and Φ_MM such that each multipole term in Φ_EE represents an interaction between the electric multipoles of the two systems, each term in Φ_MM represents an interaction between their magnetic multipoles whereas each term in A_eff represents an interaction between an electric multipole of one and a magnetic multipole of the other. The results have been applied to the interaction between an electric dipole and a magnetic dipole. The symmetry among the multipole terms in A_eff suggests vanishing vector potential between two identical objects. A corollary of this appears to be absence of spin orbit interaction between two identical particles in the same spin state.     

一般情况下两共轴圆线圈间互感系数的简便计算

采用级数展开的方法,得到了一般情况下两共轴圆线圈间互感系数的严格无穷级数表达式,所得结果在除两线圈重合之外的所有情况下均是收敛的.并且在计算过程中利用磁矢势而非磁感应强度求出磁通量,使得该方法较为简便.     

Heisenberg Model in a Rotating Magnetic Field

We study the Heisenberg model under the influence of a rotating magnetic field. By using a time-dependent unitary transformation, the time evolution operator for the Schrödinger equation is obtained, which involves no chronological product. The spin vectors (mean values of the spin operators) are obtained as explicit functions of time in the most general case. A series of cyclic solutions are presented. The nonadiabatic geometric phases of these cyclic solutions are calculated, and are expressed in terms of the solid angle subtended by the closed trace of the total spin vector, as well as in terms of those of the individual spins.     

Modeling of the electromagnetic wavefront sharpening in a nonlinear dielectric

The results of physical and numerical modeling of electromagnetic wavefront sharpening in a nonlinear dielectric are given. A technique of mathematical modeling of wave propagation is described in terms of a modified vector magnetic potential. It is shown how the level of the applied field strength and the degree of nonlinearity of the dielectric affect the electromagnetic wavefront sharpening.     

Numerical calculation of current density distributions in high temperature superconducting tapes with finite thickness in self field and external field

The current density distribution of high temperature superconducting (HTS) tapes is modeled for the combined case of an alternating self and applied magnetic field. This numerical analysis is based on the two-dimensional Poisson equation for the vector potential. A one-dimensional current (z-direction) and a one-dimensional applied field (y-direction) are assumed. The vector potential is rewritten into an equation of motion for the current density J(x,y,t). The model covers the finite thickness of the conductor and an n-power E–J relation. The magnetic field dependence of J_c is also included in this E–J relation. A time-dependent two-dimensional current distribution that is influenced by the aspect ratio of the conductor and the material properties in E=f(J,B) is calculated numerically. The numerical results are compared with the experimental results for the AC loss of a tape driven by a transport current. Finally, a total AC loss factor is given for two cases in magnetic field direction, perpendicular and parallel to the conductor broad side.     

圆形载流导线的磁场

给出了圆形载流导线产生的矢势，并利用磁感应强度与矢势的关系导出了此导线在空间任意点的磁场．     

Electron spin polarization in field emission: Calculation of the effects due to external fields

In field emission experiments with spin polarized electrons a magnetic field is superposed on the electric emission field to define the preferred spin direction. The motion of the polarization vector in these fields was calculated for rays emanating from individual points of the emitter by integrating the equation of motion and taking into account relativistic terms. There is a slight shift of the polarization vector from its initial direction. If the initial polarization is aligned with the magnetic field and the emission tip is sufficiently well centred in the magnetic field, the tilting of the polarization vector for a beam of electrons starting not too far from the tip apex is less than 10°.