Mathematical model to determine the dimensions of superconducting cylindrical coils with a given central field – the case study for MgB₂ conductors with isotropic I_c(B) characteristic

Highlights: • Influence of the winding geometry on central field of cylindrical coils is studied. • Procedure to determine dimensions of coils with a given central field is developed. • The model is applied to MgB₂/Ni/Cu conductors with isotropic I_c(B) characteristic. • Influence of the thickness of stabilizing copper on coil parameters is analyzed. • Optimization with respect to coil operating current and wire length is discussed. - Abstract: In this work, we present a mathematical model which enables to design cylindrical coils with a given central field, made of the superconducting conductor with isotropic I_c(B) characteristic. The model results in a computer code that enables to find out the coil dimensions, and to calculate the coil parameters such as critical current, maximum field in the winding and field non-uniformity on the coil axis. The I_c(B) characteristic of the conductor is represented by the set of data measured in discrete points. This approach allows us to express the I_c(B) as a function linearized in parts. Then, it is possible to involve the central field of the coil, coil dimensions, and parameters of the conductor, including its I_c(B) characteristic, in one equation which can be solved using ordinary numerical non-linear methods. Since the coil dimensions and conductor parameters are mutually linked in one equation with respect to a given coil central field, it is possible to analyze an influence of one parameter on the other one. The model was applied to three commercially available MgB₂/Ni/Cu conductors produced by Columbus Superconductors. The results of simulations with the I_c(B) data at 20 K illustrate that there exists a set of winding geometries that generate a required central field, changing from a disc shape to long thin solenoid. Further, we analyze how the thickness of stabilizing copper influences the coil dimensions, overall conductor length, coil critical current, maximum field in the winding. An influence of the safety coefficient in operating current on coil dimensions and other above mentioned parameters is studied as well. Finally, we compare the coil dimensions, overall conductor length as well as coil critical current and maximum field in the winding if the value of required central field changes between 1 and 3 T.