论文标题
迈向通过磁力计测量的磁通量的分析计算
Towards analytical calculation of the magnetic flux measured by magnetometers
论文作者
论文摘要
本文在准静态近似下使用矢量球形谐波扩展来回顾磁通信号的计算，并提出了通过每个扩展程度通过任意的可参数式拾取环评估通量的近分析方法。这是通过将表面通量积分（2D）简化为积分（1D）的。对于切向圆形传感器的特殊情况，我们提出了一个完全分析的递归计算。然后，我们将常用的立方体近似值与我们的（近）分析形式进行了比较，并表明立方体近似值较高的空间频率成分的误差增加。这表明需要对正在开发的日益敏感的传感器进行更准确的评估，而我们的（近）分析形式本身就是解决此问题的解决方案。
This paper reviews magnetic flux signal calculations through pick-up loops using vector spherical harmonic expansion under the quasi-static approximation, and presents a near-analytical method of evaluating the flux through arbitrary parametrizable pick-up loops for each expansion degree. This is done by simplifying the surface flux integral (2D) into a line integral (1D). For the special case of tangential circular sensors, we present a fully analytical recursion calculation. We then compare commonly-used cubature approximations to our (near-)analytical forms, and show that cubature approximations suffer from increasing errors for higher spatial frequency components. This suggests the need for more accurate evaluations for increasingly sensitive sensors that are being developed, and our (near-)analytical forms themselves are a solution to this problem.
