Calculation of mutual inductance and magnetic force between two thick coaxial Bitter coils of rectangular cross section

摘要

The mutual inductance and magnetic force between coaxial Bitter coils with rectangular cross section were recently calculated by some authors using semi-analytical expressions based on two integrations (Ren et al.) and by using the Bessel function approach (Conway). In this study, these important electrical quantities are calculated using the analytical and semi-analytical expressions based on elliptical integrals of the first and second kinds, Heuman's Lambda function, and two simple integrals with their kernel functions continuous on the whole integration interval. Simple Gaussian numerical integration is used. This method can be applied to calculate the mutual inductance and magnetic force between two thin Bitter disk coils (pancakes) as well as between two Bitter coils, where one has a rectangular cross section and the other is a thin disk (pancake). The calculations of the mutual inductances and magnetic forces are validated by comparison with values already published in the literature. The presented approach has advantages of high accuracy and low computational time.