Single layer cylindrical and helicoidal coil with voids between successive turns electromagnetic field calculation to be used in superconductor current limiter simulator for design purpose

A very accurate mathematical method, named helicoidal method, to calculate the flux density vector B produced by the current circulating in the resistive single-phase superconductor electrical current limiter (RSCL) coils, at any point of the its whole space, using the Biot-Savart´s Law is presented in this paper. It is very important to remember that these coils are single layer concentric cylindrical coils with voids (free space) between its neighbor turns which turns present helicoidal form. The calculation of the vector B, at any point of the space of the coils, is used in the dynamic simulation of the RSCL for design and operation purposes, but it is also used to calculate the self-inductance of each electrical current limiter coil and the mutual inductance between each pair of coils, which are necessary to determine the equivalent impedance of the RSCL. To verify the proposed method accuracy the self-inductance of three different coils, made with copper wire, are calculated, measured and the results are compared.