Calculation of some electromagnetic quantities for circular thick coil of rectangular cross-section and pancake with inverse radial currents

Here, the new expressions for the mutual inductance and the magnetic force between two Bitter coils (thick coil and pancake) with the inverse radial current densities are presented. These types of coils are used for producing the high magnetic fields. For producing strong magnetic fields, the coils are extremely heated, so that they could be cooled to avoid this problem. During a water-cooled magnet trip, the induced current in coil changes as a function of decay time constant which is determined by the self-inductance and the resistance of the water-cooled magnet. Moreover, such high fields develop the strong magnetic forces which can cause the mechanical stress upon the supporting structure. This way the precise evaluation of these electrical quantities between coils must be calculated to optimise the support structure of Bitter coils. With the newly presented approach, these quantities are obtained in an analytical and semi-analytical form expressed over elliptical integrals and simple integrals. For validating this method, the comparative improved filament method is used.