Mutual Inductance and Force Calculations Between Coaxial Bitter Coils and Superconducting Coils with Rectangular Cross Section

Mutual inductance and force calculations between coaxial Bitter coils and superconducting coils with rectangular cross section in a hybrid magnet system using derived semi-analytical expressions based on two integrations were performed. The mutual inductance and force calculations are based on the assumption of the uniform current density distribution in superconducting coils. The current density distribution of a Bitter coil in radial direction, however, is inversely proportional to the radius of the Bitter coil. The influence of the current density redistribution caused by a cooling hole and an inhomogeneous temperature distribution of Bitter coil of a water-cooled magnet was not considered. The obtained expressions can be implemented by Simpson’s integration with FORTRAN programming. We confirm the validity of mutual inductance calculation by comparing it with a filament method, and give the accuracy of two methods. The mutual inductance values computed by two methods are in excellent agreement. The derived semi-analytical expressions of mutual inductance allow a low computational time compared with filament method to a specific accuracy. The force is derived by multiplying the currents of the two coils by their mutual inductance gradient.