Improvement in calculation of the self- and mutual inductance of thin-wall solenoids and disk coils
Improvement in calculation of the self- and mutual inductance of thin-wall solenoids and disk coils
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DOI：
10.1109/tmag.2000.875240
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发表时间：
2000-07
影响因子：
2.1
通讯作者：
S. Babic;C. Akyel
中科院分区：
文献类型：
--
作者：
S. Babic;C. Akyel
Yu和Han（1987）给出的矩形截面空心圆形线圈、薄线圈和圆盘线圈的自感表达式只能用数值积分法求解。我们建议作为一种替代方案相结合的分析和数值方法。该方法在计算超导储能（SMES）问题中可能遇到的薄壁线圈和圆盘线圈的自感方面带来了一定的改进。文中还给出了计算圆盘线圈和薄壁线圈互感的方法。结果得到的第一和第二类完全椭圆积分和Heuman的Lambda函数的解析形式。值得注意的是，这些积分的核总是积分区间上的连续函数，因此避免了奇异性。计算结果使人们能够准确、快速地计算任意细空心线圈的自感和互感。在实际应用中，所得结果易于使用，避免了奇异情况的求解问题。
The self-inductance expressions given by Yu and Han (1987) for air-core circular coils with rectangular cross sections, thin solenoids, and disk coils can be solved only by the numerical integration methods. We propose as an alternative a combined analytic and numeric approach. The approach brings some improvement in the calculations of self-inductance of thin-wall solenoids and disk coils that can be encountered in superconducting magnetic energy storage (SMES) problems. We also give a method for the calculation of mutual inductance of disk coils and of thin-wall solenoids. The results are obtained in an analytical form over the complete elliptic integrals of the first and second kind and Heuman's Lambda function. It is important to mention that the kernels of these integrals are always continuous functions on intervals of integration, so singularities are avoided. The results enable one to calculate the self-inductance and the mutual inductance of any thin air-core coil precisely and fast. For practical applications, the results are so simple to use that we recommend them to avoid the problems of solving the singular cases.