Inductance calculations for non‐coaxial Bitter coils with rectangular cross‐section using inverse Mellin transform

Abstract

Recently, the mutual inductance between Bitter coils with rectangular cross-section has been calculated through Bessel function approach or figured out with analytical and semi-analytical formulas. In this study, using the inverse Mellin transform, relevant Bessel integrals will be continued analytically to the complex plane, and then by virtue of contour deformation and residue theorem, they can be expanded to the series containing the hypergeometric functions. In addition, the results obtained by this method are compared with those by finite element method software. Also, the presented approach shows great advantages of high accuracy and very short computational time.

Analytical and Semi-Analytical Formulas for the Self and Mutual Inductances of Concentric Coplanar Ordinary and Bitter Disk Coils

“…The self-and the mutual inductance of the concentric coplanar disk coils are verified by the methods given in Refs. [17][18][19]. With obtained amazingly easy analytical and semi-analytical expressions, we solved many examples which show excellent agreement with already given results for the real coils of the rectangular cross-section under some valuable conditions.…”

“…The Bitter coils of the rectangular cross-section are coils, where the azimuthal current densities in the coils conductor are inversely proportional to their radii. The mutual inductance between two concentric Bitter circular coils of the rectangular cross-section is given by [17][18][19]: and , are the current densities, which are not constant [13]. The total current through one Bitter coil [13] is:…”

“…where, C is the constant which depends on the thickness function ℎ( ). If the thicknesses of the first and second Bitter coil of the rectangular cross-section are constants from [17][18][19], we obtain the current densities in them: 4) becomes the mutual inductance between two coplanar Bitter disks [22]. In Figure 3, the non-uniform azimuthal current is shown for one thin disk coil.…”

“…Additionally, there are circular coils with a not uniform current density (massive coils of the rectangular cross-section, disk coils) which are interesting from an engineering aspect. These coils are the well-known Bitter coils [14][15][16][17][18][19][20][21][22][23][24], which supply extremely high magnetic fields of up to 45 T. Bitter magnets are constructed of circular conducting metal plates and insulating spacers stacked in a helical configuration rather than coils of wire. The current flows in an azimuthal path through the plates and is not uniform.…”

The Analytical Formula for Calculating the Self-Inductance for the Circular Coil of the Rectangular Cross-Section With a Non-Uniform Current Density

“…These calculations are used in many electromagnetic applications (tubular linear motors, magnetically controllable devices and sensors, current reactors, cochlear implants, defibrillators, instrumented orthopedic implants, in magnetic resonance imaging (MRI) systems, superconducting coils, and tokamaks, etc.). Also, there are nonconventional circular coils with nonuniform density current which are used in many technical applications such as superconducting coils and the homopolar motors [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Coils with rectangular cross-section and the nonuniform current density, which changes inversely with the cylindrical coordinate r known as Bitter coils, can produce extremely high magnetic fields up to 45 T. In this paper, we give a new formula for calculating the self-inductance of the circular thick coil of the rectangular cross section with nonuniform current density.…”