| 各向异性半空间上方垂直磁偶极子电磁场的球面波展开式 |
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| 引用本文： | 江滨浩,刘永坦.各向异性半空间上方垂直磁偶极子电磁场的球面波展开式[J].地球物理学报,2005,48(5):1191-1196. |
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| 作者姓名： | 江滨浩 刘永坦 |
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| 作者单位： | 哈尔滨工业大学电气工程系,哈尔滨 150001 |
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| 基金项目： | 国家自然科学基金项目(50477009)资助. |
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| 摘 要： | 文中推导出单轴各向异性媒质半空间上方垂直磁偶极源电磁场的精确解析表达式. 应用圆柱波函数的球面波展开式和超几何函数理论，场分量中的索末菲尔德型积分被表示成快速、绝对收敛的球面波函数系展开式；展开系数是以物性参数为复宗量的勒让德多项式. 该展开式数学物理意义明显，并且不受场点和源点的位置、媒质的物性参数和频率等条件的限制. 利用本文的结果可十分方便地计算和分析任意场点处的电磁场分布.
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| 关 键 词： | 电磁理论 索末菲尔德积分 单轴各向异性媒质 球面波展开式 |
| 文章编号： | 0001-5733（2005）05-1191-06 |
| 收稿时间： | 2005-03-02 |
| 修稿时间： | 2005-03-022005-06-10 |
Expansion of spherical wave functions for electromagnetic fields of a vertical magnetic dipole over an anisotropic half-space |
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| JIANG Bin-Hao,LIU Yong-tan.Expansion of spherical wave functions for electromagnetic fields of a vertical magnetic dipole over an anisotropic half-space[J].Chinese Journal of Geophysics,2005,48(5):1191-1196. |
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| Authors: | JIANG Bin-Hao LIU Yong-tan |
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| Institution: | Department of Electric Engineering, Harbin Institute of Technology, Harbin 150001,China |
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| Abstract: | We derive an accurate and analytical expression for electromagnetic fields of a vertical magnetic dipole over an anisotropic uniaxial medium half-space. By using the expansion of spherical wave functions for a cylindrical wave function and with the help of the theory of hypergeometric functions, the Sommerfeld type integral contained in the electromagnetic fields is expressed as a rapidly and absolutely convergent series of spherical wave functions; and the coefficients of the series are the Legender Polynomials with the complex argument for the constitutive parameter. The results have explicit mathematical and physical implications and no restriction on the locations of dipole sources and observational points, medium parameters, and frequency. The expression can be used conveniently to calculate and analyze electromagnetic fields at any points. |
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| Keywords: | Electromagnetic theory Sommerfeld type integral Uniaxial anisotropic medium Expansion of spherical wave function |
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