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首页> 外文期刊>Magnetics, IEEE Transactions on >Field Distributions Around a Rectangular Crack in a Metallic Half-Space Excited by Long Current-Carrying Wires With Arbitrary Frequency
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Field Distributions Around a Rectangular Crack in a Metallic Half-Space Excited by Long Current-Carrying Wires With Arbitrary Frequency

机译：任意频率的长载电流导线激发的金属半空间中矩形裂纹周围的场分布

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摘要

In this paper, we propose a semianalytical solution for evaluation of field distributions around a short rectangular crack in a metallic half-space excited by long current-carrying wires with arbitrary frequency. The governing Helmholtz equation is solved in three dimensions by separation of variables. The solution is obtained by developing 2-D Fourier series model and using exponential functions in the third dimension. To expand all possible field components in the metal, we first hypothesize a shielded dielectric rod waveguide where the shield enclosure lies at infinity, the surrounding dielectric (i.e., the metal) is a lossy material, and the rod dielectric is the crack opening. We then introduce hybrid modes each of which consists of two components, representing the TM$_{y}$ and TE$_{y}$ modes. The mode-matching technique is finally used to numerically solve the resultant boundary value problem. The unknown eigenvalues and field coefficients are found by searching for small singular values, using the singular value decomposition (SVD) in the resultant homogeneous linear system. The validity of our modeling technique is confirmed by comparison of our results with those obtained by measurement and finite integration code.
机译：在本文中，我们提出了一种半解析解，用于评估由任意频率的长载电流导线激发的金属半空间中矩形短裂纹周围的场分布。掌控的亥姆霍兹方程通过变量分离在三个维度上求解。通过开发二维傅立叶级数模型并在三维中使用指数函数来获得解决方案。为了扩展金属中所有可能的场分量，我们首先假设一个屏蔽电介质棒状波导，其中屏蔽罩位于无限远处，周围的电介质（即金属）是有损耗的材料，而棒状电介质是裂缝。然后，我们介绍混合模式，每个混合模式都由两个组件组成，分别表示TM $ _ {y} $ 和TE $ _ {y} $ 模式。最终，将模式匹配技术用于数值求解所得的边值问题。通过在所得齐次线性系统中使用奇异值分解（SVD）搜索小的奇异值，可以找到未知的特征值和场系数。通过将我们的结果与通过测量和有限积分代码获得的结果进行比较，可以证实我们建模技术的有效性。

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