基于矢量椭球面波函数展开的椭球体电磁感应研究
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摘要
由于椭球体模型存在于许多实际工程和科学研究中,对其电磁感应特性的研究一直以来都受到人们的广泛关注.基于此,本文对具有导电和渗透性能的椭球体的电磁感应特性进行了研究.具体做法是首先得到椭球体内部满足矢量波动方程的磁场和可以表示为拉普拉斯解的梯度的外部磁场,然后在椭球面坐标系中采用分离变量法,对磁场按照矢量椭球面波函数进行展开,得到任意初始激励下的磁解;最后对轴向和横向激励情况下的归一化感应磁偶极矩在宽频段范围进行了数值仿真,得到了依赖于感应数的电磁感应特性.
Due to spheroidal models existing in many paractical engineerings and scientific researchs,the electromagnetic induction characteristic research for them draw peoples close attention to all the time. In view of this,the electromagnetic induction characteristic research for conducting and permeable spheroids is studied. The concrete implement is that the magnetic field inside the spheroid satisfying the vector wave equation and the magnetic field outside can expressed as the gradient of the Laplace solution is first obtained,and then the magnetic field solution is derived under arbitrary primary field excitation using the separation of variables method in spheroidal coordinates system by expanding the magnetic field in terms of vector spheroidal wavefunctions. The electromagnetic induction characteristic depended on the induction number is shown by the simulation of the normalized induced magnetic dipole moment under the axial excitation and transverse excitation in the broadband limit finally.
Due to spheroidal models existing in many paractical engineerings and scientific researchs,the electromagnetic induction characteristic research for them draw peoples close attention to all the time. In view of this,the electromagnetic induction characteristic research for conducting and permeable spheroids is studied. The concrete implement is that the magnetic field inside the spheroid satisfying the vector wave equation and the magnetic field outside can expressed as the gradient of the Laplace solution is first obtained,and then the magnetic field solution is derived under arbitrary primary field excitation using the separation of variables method in spheroidal coordinates system by expanding the magnetic field in terms of vector spheroidal wavefunctions. The electromagnetic induction characteristic depended on the induction number is shown by the simulation of the normalized induced magnetic dipole moment under the axial excitation and transverse excitation in the broadband limit finally.
引文
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[2]刘磊,李浩,高太长.雨滴的近似椭球模型及其近红外散射特性研究[J].气象科学,2008,28(3):271-275.
[3]BELL T,BARROW B,MILLER J,et al.Time and frequency domain electromagnetic induction signatures of unexploded ordnance[J].Subsurface Sensing Technologies&Applications,2001,2(3):153-175.
[4]BRAUNISCH H,AO C O,ONEILL K,et al.Magnetoquasistatic response of conducting and permeable prolate spheroid under axial excitation[J].IEEE Transactions on Geoscience&Remotes Sensing,2001,39(12):2689-2701.
[5]FAZLI R,NAKHKASH M.An analytical approach to estimate the number of small scatterers in 2D inverse scattering problems[J].Inverse Problems,2012,28(7):75012-75033.
[6]ZHAO Q,HAO J,CHEN G,et al.Application of the method of auxiliary source to the sensitivity analysis of high frequency magnetic induction tomography system[C].Instrumentation&Measurement Technology Conference,2012,80(11):539-544.
[7]MCFADDEN M,JR W R S.Computing simple models for scatterers in eddy current problems using a modal decomposition[J].J Appl Geophys,2013,95(5):104-114.
[8]童创明,袁乃昌,付云起,等.电磁响应的时、频域同时外推法[J].电波科学学报,2002,17(4):337-340.
[9]KAHNERT M.Electromagnetic scattering by nonspherical particles:Recent advances[J].J Quant Spectrosc&Ra,2010,111(11):1788-1790.
[10]VOSHCHINNIKOV N V,FARAFONOV V G.Light scattering by a multilayered spheroidal particle[J].Appl Optics,2012,51(10):1586-1597.
[11]COORAY M F R,CIRIC I R.Scattering by systems of spheroids in arbitrary configurations[J].Comput Phys Commun,1991,68(1):279-305.
[12]PAZOS-PEREZ N,GARCIA F J,FERY A,et al.From nano to micro:synthesis and optical properties of homogeneous spheroidal gold particles and their superlattices[J].Langmuir,2012,28(24):8909-8914.
[13]韩一平,吴振森.平面波用椭球波函数的展开[J].西安电子科技大学学报,1999,26(2):227-231.
[14]胡传水.用分离变量法求解长旋转椭球坐标下的Maxwell方程[J].电子学报,1982,(4):25-30.
[15]孙向阳,聂在平,李爱勇,等.用于电磁感应建模的一种快速有效计算方法[J].电波科学学报,2008,23(5):932-936.