关于电磁场解析方法的一些认识  

Reviews of Analytical Methods for Electromagnetic Fields

作　　者：雷银照[1] 

机构地区：[1]北京航空航天大学自动化科学与电气工程学院,北京100191

出　　处：《电工技术学报》2016年第19期11-25,共15页Transactions of China Electrotechnical Society

摘　　要：对电磁场解析方法进行了综述。指出了解析解的重要性:能够直观揭示电磁场的变化规律,不存在数值不稳定问题,表达式能被他人重复导出,表达形式具有科学美,是数值解的基础,并作为计算公式被广泛用于解决工程问题。介绍了几种常用解析方法:分离变量法、复变函数法、格林函数法、积分变换法以及近似解析法。重点回顾了历史上的若干经典解析解:兰帕-汤普森定理、范德堡公式、螺线管中心的均匀磁场表达式、放置式线圈的阻抗增量、Halbach永磁体的磁场计算法、脑磁测量基准计算公式、浅表面缺陷涡流场的三维渐近解析解、金属管道涡流场的三维解析解。给出了有助于解析求解的几本参考书。最后提出了今后需要进一步研究的一些问题:用保角变换方法求解稳恒磁场、现有解析方法的综合使用、借鉴最新数学物理方法、瞬态涡流场的解析求解、微扰法中高阶导数项的求解、逆问题的解析求解。This paper reviews the analytical methods for electromagnetic fields. Firstly, the importance of analytical solutions is pointed out, i.e. analytica/ solutions reveal the variation law of electromagnetic fields visually; there is no numerical instability; expressions can be derived repeatedly by others and their form is full of scientific beauty; they are the foundation of numerical solutions and widely used as calculation formulas to solve engineering problems. Secondly, several frequently-used analytical methods are introduced, such as the method of separation of variables, the complex variable function method, the Green function method, the integral transform method, and the approximate analytical method. Furthermore, some classical analytical solutions are reviewed, including the Lampard-Thompson theorem, the van der Pauw formula, the expression of the uniform magnetic field in the central zone of a solenoid coil, the analytical solution to the impedance variation of a probe coil above a conductive plate, calculation method for the magnetic field of the Halbach permanent- magnet, the standard calculation formula of the brain magnetic measurement, the three-dimensional asymptotic analytical solution to the eddy current field of a conductive plate with shallow surface defect, and the three- dimensional analytical solution to the eddy current field of a metal pipe. What~ more, several reference books are selectively introduced to find analytical solutions. Finally, a number of problems are proposed for further study, containing applying conformal mapping method in solving problems of static magnetic field, integrating existing analytical methods, introducing latest methods of mathematical physics, analytically solving the transient eddy current field, deducing higher order derivative terms of the field quantity in the perturbation method, and analytically solving inverse problems.

关 键 词：电磁场理论 解析方法 解析解 综述 

分 类 号：TM15[电气工程—电工理论与新技术]