Fast single layer cylindrical and helicoidal coil with voids between turns electromagnetic field calculation to be used in superconducting current limiter simulator for design purpose

This paper presents a mathematical method to quickly calculate the flux density vector B produced by the current circulating in a resistive single-phase superconducting electrical current limiter (RSCL), at any point of its whole space, using the Biot-Savart's Law. As the calculation using the exact form of the turns of each coil (single layer cylindrical coil with helicoidal form presenting voids (free space) between neighbor turns) is computationally very cumbersome to be used in a RSCL dynamic simulator, it is proposed in this paper to substitute the real coil, only for the subject of the calculation, by an imaginary coil formed by plane closed circular turns with the same number of turns, the same height and radius as the real coil. Each turn of the imaginary coil is placed exactly in the medium position between successive turns of the actual coil and will carry the same current. The coil self-inductance is also calculated to verify the accuracy of the proposed method.