Fast and Precise Method for Inductance Calculation of Coaxial Circular Coils With Rectangular Cross Section Using the One-Dimensional Integration of Elementary Functions Applicable to Superconducting Magnets

A new and extremely fast and precise method for calculating mutual inductance between coaxial circular coils in air with rectangular cross section and uniform current densities is presented. It is thoroughly compared with all recently published methods in the same computing environment, and the results confirm the aforementioned. Along with the high accuracy and low computational time, the emphasis is put on the easiness of implementing the method, using only the elementary functions. The method can be used in all combinations of the coils' radii and heights, from narrow coils to coils with extremely large radii, such as the coils used in superconducting magnets. Excellent numerical stability and agreement with professional software was found in all testing cases.