绕于芯棒上的电流环在多层环状媒质中的电磁响应

Electromagnetic Response of a Current Loop Rounding on a Mandrel in Multicircularly Layered Medium

本文严格导出了绕于任意多层同轴芯棒上的电流环在多层同轴媒质中所产生电磁场的解析解．芯棒和各层媒质中的介电常数、磁导率和电导率均同时考虑在内，所得公式具有普遍意义，场解为含复宗量贝塞尔函数的广义积分．计算中取芯棒的电导率为零时，可得到绕于绝缘芯棒上电流环所产生的电磁场，其结果与磁偶极子点源场对比，场值差别一般在1％以内，证实了公式与计算方法的正确性．最后，通过计算考察了金属芯棒的影响．

When a current loop rounding on a multicylindrically layered mandrel is located in multicicular media, the expressions of eletromagnetic fields are derived analytically. The dielectric constants, conductivities and permeabilities of the mandrel and the media are taken into account simultaneously so the formulae are of universal significance. Solutions of the fields are expressed as some generalized integrals whose integrands contain Bessel functions with complex arguments. When the conductivity of the mandrel is replaced by zero in the programme, the electromagnetic fields of a loop rounding on an insulated mandrel can be calculated whose differences contrasted with that of a point magneitc dipole are generally less than 1%.In such way, the reliability of the expressions and the algorithm has been examined. Finally, the influence of a metallic mandrel has been discussed.