Understanding the Magnetic Polarizability Tensor
Understanding the Magnetic Polarizability Tensor
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DOI：
10.1109/tmag.2015.2507169
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发表时间：
2015-10
影响因子：
2.1
通讯作者：
P. Ledger;W. Lionheart
中科院分区：
文献类型：
--
作者：
P. Ledger;W. Lionheart
本文的目的是提供新的见解秩2极化率张量M的性质提出的莱杰和Lionheart描述的扰动在磁场中所造成的存在下，一个导电的物体在涡流制度。特别是，我们探索它与磁极化张量和Polya-Szego张量的联系，以及如何通过引入M的新分裂，形成一个2秩张量家族，用于描述不同类别的传导（可渗透）对象的响应。我们包括新的边界上的不变量的Pólya-Szego张量和表达式的低频和高电导率限制系数的M。我们表明，对于高电导率的情况下（和频率的准静态近似的限制），重要的是要考虑对象是简单的或多连接，但对于低频的情况下，系数是独立的对象的连通性。此外，我们探讨了一系列简单和多连通对象的系数的频率响应。
The aim of this paper is to provide new insights into the properties of the rank 2 polarizability tensor M̆ proposed by Ledger and Lionheart for describing the perturbation in the magnetic field caused by the presence of a conducting object in the eddy-current regime. In particular, we explore its connection with the magnetic polarizability tensor and the Pólya-Szegö tensor and how, by introducing new splittings of M̆, they form a family of rank 2 tensors for describing the response from different categories of conducting (permeable) objects. We include new bounds on the invariants of the Pólya-Szegö tensor and expressions for the low-frequency and high-conductivity limiting coefficients of M̆. We show, for the high-conductivity case (and for frequencies at the limit of the quasi-static approximation), that it is important to consider whether the object is simply or multiply connected but, for the low-frequency case, the coefficients are independent of the connectedness of the object. Furthermore, we explore the frequency response of the coefficients of M̆ for a range of simply and multiply connected objects.