Self-Inductance of the Circular Coils of the Rectangular Cross-Section with the Radial and Azimuthal Current Densities

Slobodan Babic,Cevdet Akyel

doi:10.3390/physics2030019

Slobodan Babic, Cevdet Akyel

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https://doi.org/10.3390/physics2030019

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Journal: Physics	Publication Date: Jul 13, 2020
Citations: 5	License type: CC BY 4.0

Affiliation: InterDigital (Canada), Polytechnique Montréal

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In this paper, we give new formulas for calculating the self-inductance for circular coils of the rectangular cross-sections with the radial and the azimuthal current densities. These formulas are given by the single integration of the elementary functions which are integrable on the interval of the integration. From these new expressions, we can obtain the special cases for the self-inductance of the thin-disk pancake and the thin-wall solenoids that confirm the validity of this approach. For the asymptotic cases, the new formula for the self-inductance of the thin-wall solenoid is obtained for the first time in the literature. In this paper, we do not use special functions such as the elliptical integrals of the first, second and third kind, nor Struve and Bessel functions because that is very tedious work. The results of this work are compared with already different known methods and all results are in excellent agreement. We consider this approach novel because of its simplicity in the self-inductance calculation of the previously-mentioned configurations.

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IntroductionSeveral monographs and papers are devoted to calculating the self and the mutual inductance for the circular coils of the rectangular cross-section with the azimuthal current density [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18].The conventional coils used in many applications such as all ranges of transformers, generators, motors, current reactors, magnetic resonance applications, antennas, coil guns, medical electronic devices, superconducting magnets, tokamaks, electronic and printed circuit board design, plasma science, etc., are very well-known
The formulas are obtained in the form of a single integral whose kernel function on the interval of integration is the sum of the elementary functions
The special cases of these formulas give the self-inductance for thin-disk coil and the thin-wall solenoid in the closed and semi-analytical form

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Introduction

Several monographs and papers are devoted to calculating the self and the mutual inductance for the circular coils of the rectangular cross-section with the azimuthal current density [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18].The conventional coils used in many applications such as all ranges of transformers, generators, motors, current reactors, magnetic resonance applications, antennas, coil guns, medical electronic devices, superconducting magnets, tokamaks, electronic and printed circuit board design, plasma science, etc., are very well-known. Several monographs and papers are devoted to calculating the self and the mutual inductance for the circular coils of the rectangular cross-section with the azimuthal current density [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]. There are circular coils of the rectangular cross-section with the radial current density which are interesting from an engineering aspect. These coils are the well-known Bitter coils [19,20,21,22,23,24,25] which supply extremely high magnetic fields up to 45 T [21]

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