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Bitter coils are electromagnets used for the generation of extremely strong magnetic fields superior to 30 T. In this paper we calculate the mutual inductance and the magnetic force between Bitter disk (pancake) coil with the nonlinear radial current and the circular filamentary coil with the azimuthal current. The close form expressed over complete elliptic integrals of the first and second kind as well as Heuman’s Lambda function is obtained for this configuration either for the mutual inductance or for the magnetic force. The results of this method are compared with those obtained by the improved modified filament method for the presented configuration. All results are in an excellent agreement.

In the literature and scientific papers the calculation of the mutual inductance and the magnetic force between ordinary circular coils with the uniform current densities have been given by different methods either analytical or numerical [

The mutual inductance and magnetic force between a disk coil (pancake) with the uniform azimuthal current density

The thin Bitter disk coil (pancake) and the filamentary circular coil.

In [

Let us suppose the disk coil be the Bitter coil in which the current density is not uniform [

Integrating in (

This case is the regular case covered by (

This case is the singular case (

In [

Configuration of mesh matrix: Filamentary coil-thin disk coil (pancake).

Applying some modification in the mutual inductance calculation given in [

To verify the validity of the new formulas, we apply them to the following set of examples.

Calculate the mutual inductance and the magnetic force between the Bitter disk coil and a filamentary circular coil with the following dimensions and the number of turns. Currents in coils are unit.

Applying (

By using the modified filament, (

Calculate the mutual inductance between a disk and a filamentary circular coil with the following dimensions and the number of turns.

Applying (

By using the modified filament, (

Calculate the mutual inductance between a disk and a filamentary circular coil with the following dimensions and the number of turns.

This case is the singular case because

Applying (

By using the modified filament, (

Calculate the mutual inductance between a disk and a filamentary circular coil with the following dimensions and the number of turns.

This case is also the singular case for which

Applying (

By using the modified filament, (

In comparative calculations the significant figures which agree are bolded.

Thus, with these examples we confirmed the validity of the present analytical method for calculating the mutual inductance and the magnetic force between the Bitter disk with the nonlinear radial current distribution and an ordinary filamentary circular coil. All calculations were executed in Matlab programming.

The new accurate mutual inductance and magnetic force formulas for the system of the Bitter disk with the nonlinear radial current and the filamentary circular with the azimuthal in air are derived and presented in this paper. All expressions for either the mutual inductance or the magnetic force are obtained in the close form expressed over complete elliptic integrals of the first and second kind and Heuman’s Lambda function. Also we gave in this paper the improved formulas for the mutual inductance and the magnetic force between treated coils by using the filament method. All singular cases are obtained in a closed form. The presented method can be used to calculate these important electrical quantities such as the mutual inductance and the magnetic force for coils combinations comprising Bitter coils of rectangular cross section and the circular coils with uniform current densities.

The first integral in (

The first integral in (

The authors declare that there is no conflict of interests regarding the publication of this paper.